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1. 1 1 14LINE 1 1 END14LINE 15 STRT 15POS1 1 15POS1 2 END15POS1 3 16 LMTS 16MXNI END16MERR 17 NONE 18 NONE Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Example of Program Use TEST RUN NUMBER 20 FLOATING BOX 40M DRAUGHT 48 FACETS ALBOX21 Q w WwW Ww m 9500E6 0000E0 0000E0 7700E7 3200E3 0000 0 0000 4 3900 4 0000E6 w O w O o 2 4000E6 2 4000E6 2 2500E7 2 2500E7 1 0700E3 1 0700E3 1 9400 4 1 9400 4 1 4715E6 1 4715E6 1 4715E6 1 4715E6 0000E0 9500E6 7700E7 0000E0 0000E0 3200E3 3900 4 0000 4 Figure 8 4 Input for Data Run on Box Structure Page 95 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 14 Information Supplied by Data Run The DATA run produces the following form of output and is shown in Figures 8 5 to 8 13 Figure 8 5 AQWA LIBRIUM Header Page Used for Identification Figure 8 6 Card Echo mandatory for Decks 9 to 20 This is used to check data input Figure 8 7 Added mass and damping at drift frequency Figure 8 8 Current and wind information Figure 8 9 Wind Current Forces and Thruster Forces Tabulation of the data input in Deck 10 Figure 8 10 Constraints This table shows all the freedoms that are active Articulations are not yet implemented Figure 8 11 Formulated Spectra The wave spectrum and current and wind conditions input in Deck 1
2. D DIRECTION ECTION OF PROFILED CURRENT CURRENT PROFILES Z ORDINATE CURRENT CURRENT W R T SEA LEVEL VELOCITY DIRECTION Figure 7 16 Wind and Current Conditions Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 67 of 122 AQWA LIBRIUM User Manual Description of Output From the consideration of the influence of sea state on the system equilibrium the environmental parameters are specified either as those corresponding to formulated spectra i e Pierson Moskowitz or Jonswap or user defined spectra In the case of formulated spectra the environmental parameters are output as shown in Figure 7 17 Included in the parameter list is the spectral type and the spectral resolution limits i e the number of lines and rasters and the upper and lower frequency cut offs The spectral parameters depend on the spectrum type and are defined in the following table Table 7 2 Spectral Parameters for Formulated Spectra Parameter Number Pierson Moskowitz Jonswap 1 Significant wave height Gamma constant 2 Zero cross over period Alpha constant 3 Peak spectral frequency The wave direction is also defined for each spectrum along with the associated wind and current speeds and directions Note this data will replace the uniform current and wind data output discussed in Section 7 5 1 KO C SOS MU Tp WAVE A
3. 01 0402 04 4728 04 3 8293 08 Figure 8 22 Structure Hydrostatic Stiffness and Mooring Stiffness Matrices Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Example of Program Use Page 114 of 122 AQWA LIBRIUM User Manual Example of Program Use SPECTRUM NUMBER 1 MOORING COMBINATION 1 NUMBER OF LINES 4 NOTE STRUCTURE 0 IS FIXED TYPE LENGTH LENGTH NODE TENSION FORCE X POSN X AT NODE TENSION FORCE X POSN X STIFFNESS RANGE VERT ANGLE Y Y STRUC VERT ANGLE Y 501 1 38E 06 38E 06 511 1 38E 06 1 38 06 47E 06 2 94E 03 17E 02 2 78E 03 2 78E 03 94E 03 37 04 35E 01 1 11E 02 3 1 11 02 s 17E 02 2 35E 01 37 04 502 1 17 06 7 16E 02 0 512 1 17 06 7 16 02 0 16 04 91 02 1 01 01 1 17 06 45 1 17 06 146 91 02 47 06 1 65E 02 1 32E 02 0 1 32 02 0 01E 01 65 02 1 16E 04 503 1 56E 06 1 56E 06 44 513 1 56 06 56E 06 146 47E 06 91 03 1 17 02 3 12 03 0 12 03 0 91 03 55 04 2 34 01 1 26 02 0 1 26 02 0 1 17 02 34E 01 1 55 04 504 1 77 06 1 10E 03 3 514 1 77 06 10E 03 0 75 04 05 02 1 01E 01 1 77 06 77 06 146 05 02 47E 06 1 63E 02 1 98E 02 2 98 02 0 01 01 1 63E 02 1 75E 04 Figure 8 23 Mooring Force and Stiffness Table Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 115 of
4. AQWA LIBRIUM User Manual Running the Program 9 1 2 AQWA File Organisation Every run of an AQWA program involves the use of a number of specially named input output and backing files The following files are used by AQWA LIBRIUM res file restart file backing file The restart file is used to store all information relating to the structures being analysed This information can easily be retrieved on the next run of the analysis sequence so the input data for the next run can be considerably simplified This file is an unformatted binary file hyd file hydrodynamics database file backing file This file is used by AQWA LIBRIUM and contains a subset of the restart file It is read only if the ALDB option is used or restart from stages 1 to 5 plt file graphics file backing file This file is created and contains positions velocities accelerations and all force acting on the structure at every iterative step of the simulation It is used by AGS to produce iterative history plots dat file input data file The input data file contains all the AQWA format data decks needed for the current stage of analysis Information from previous stages of analysis may be supplied from the restart file The input data file is the readable input file used in the AQWA suite It is a normal ASCII text file 16 file output data file listing file The output data file receives the main results from a program run It is a norm
5. Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 36 of 122 AQWA LIBRIUM User Manual Modelling Techniques The program evaluates the line tension and stiffness The program allows the line to lift off the sea bed i e the tangent to the line at the anchor has non zero slope up to the point where the line tension exceeds a user specified default maximum AQWA admits catenary mooring lines between a body and the sloped sea bed for cable dynamic mooring line the seabed is assumed to be horizontal and a catenary mooring line joining two bodies 4 15 5 Fender There are three types of fender non directional fixed directional fixed and floating The fender is characterised by its stiffness size similar to unstretched length for a mooring line friction and damping coefficients It acts between a node on one body and a contact plane on another body The stiffness is defined by a polynomial of up to 5th order see 4 15 1 although it is compressive instead of tensile It is the only way to simulate contact between two bodies in AQWA 4 16 ITERATION PARAMETERS FOR SOLUTION OF EQUILIBRIUM 4 16 1 Iteration Limits A well conditioned system coupled with a good initial guess should require a small number of iteration steps As a safeguard against modelling errors the user may limit the number of iteration steps in the first run Examination of the output should indicate whether the proce
6. and the structure numbers and node numbers of the two attachment points For a line joining a structure to a fixed point the structure number corresponding to the fixed point should be set to zero The node numbers and their positions to which the mooring lines are attached must be input in coordinate Deck 1 Each mooring line of 100 metres unstretched length has a stiffness of 1 471E6 Newtons per metre Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 91 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 11 Initial Position for Analysis The initial position used to position the structure for each equilibrium analysis may be either the value used in the AQWA LINE analysis or estimated manually The initial positions for this analysis were selected to produce a few iterations to demonstrate the iteration and convergence information given in the program output The positions were as shown below Spectrum No Surge X Sway Y Heave Z Roll RX Pitch RY Yaw RZ 1 0 0 0 0 11 00 0 0 0 0 0 0 2 0 0 0 0 11 00 0 0 0 0 0 0 3 0 0 0 0 11 00 0 0 0 0 0 0 8 1 12 Iteration Limits for Analysis The iteration limits used for the equilibrium search in this analysis were 20 0 01 metres 0 01 degrees Maximum number of iterations Displacement tolerances Rotation tolerances Default values will be used if no data is supplied see AQWA Refere
7. buoyancy when CG is at Z Mg K sea water density 2 A Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 20 of 122 AQWA LIBRIUM User Manual Theoretical Formulation The analysis of a multi body system is essentially the same as that of the simple example above except that 1 the system requires NDOF coordinates to describe its position NDOF 6 x Number of bodies the system is fully coupled through the actions of the moorings 3 dz is replaced by a NDOF order vector dX containing the three translations and three rotations of each of the bodies 4 F is replaced by a NDOF order vector containing the sum of the residual forces moments in each of the coordinates 5 K K is now the GLOBAL STIFFNESS MATRIX of the system in the sense that K measures the change in the force moment in the i th coordinate due to a change in displacement in the j th coordinate only The Residual Force Moment Vector Before equilibrium is reached a set of unbalanced forces and moments will act on the bodies The residual forces and moments include hydrostatic pressures weights of the structures mooring tensions wind drag current drag thruster forces and steady wave drift forces as described in Sections 3 1 and 3 10 The Stiffness Matrix AQWA LIBRIUM computes all the stiffness contributions directly from analytical expressions for the load displacement derivatives or through the use of nu
8. 122 AQWA LIBRIUM User Manual Running the Program CHAPTER 9 RUNNING THE PROGRAM To run a program in the AQWA suite it is necessary to have details of the computer system on which the program is loaded 9 1 Running AQWA LIBRIUM on the PC This chapter is written for the following systems and is NOT applicable to any others MS Windows PC 9 1 1 File Naming Convention for AQWA Files The user is recommended to adopt the following convention of naming the files to be used by the AQWA programs Every file name consists of three parts the file prefix a two character string used to identify a particular AQWA program The file prefixes are as follows Program Prefix AQWA LINE al AQWA LIBRIUM ab AQWA FER af AQWA DRIFT ad AQWA NAUT an AQWA WAVE aw the run identifer a name up to 26 characters to identify a particular run the filenames associated with the run will contain the same run identifier in their names the file extension a three character string to identify the type of the AQWA file restart file hydrodynamics file etc The file extension is separated from the rest of the filename by a character Example The filename alvlcc dat consists of the prefix al short for AQWA LINE the run identifier vlcc e g name of vessel the extension dat input data file Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 116 of 122
9. 494 10 484 10 933 08 Figure 7 27 Small Displacement Static Stability Table Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 80 of 122 AQWA LIBRIUM User Manual Description of Output 7 8 DYNAMIC STABILITY REPORT If the user has requested a dynamic stability analysis the program will output a dynamic stability report giving the transient stability characteristics of each moored structure for small perturbations from equilibrium This information allows the user to assess the dynamic stability of each vessel e g due to a random seaway wind gusting etc and identify any problem modes of motion which may require a redesign of the mooring configuration Note that the drift frequency added mass and hydrodynamic damping matrices are used in the AQWA LIBRIUM dynamic stability analysis More precise estimation of dynamic stability can be carried out interactively using the AGS in which the added mass and hydrodynamic damping matrices near each natural frequency of the system are used 7 8 1 Stability Characteristics of Moored Vessel The dynamic stability characteristics are output as shown in Figure 7 26 Eigenvalues are determined for each mode of motion from the real and imaginary parts of which the critical damping fishtailing period and stability of that mode of motion can be assessed The stability regions are defined as follows 1 STABLE The str
10. 6 1 STAGE 1 DECKS 1 TO 5 GEOMETRIC DEFINITION AND STATIC ENVIRONMENT Input for Stage 1 of the analysis is only necessary if the restart stage at which the analysis begins is 1 see Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 44 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation Chapter 5 for details If the restart stage is greater than 1 there should be no data input for Stage 1 of the analysis 6 1 1 Description Summary of Physical Parameters Input The data input in these decks relates to the description of each structure and the environment which normally remains unchanged throughout the analysis This includes any point referenced on or surrounding the structure the mass inertia hydrostatic and hydrodynamic model and the constant water depth i e the coordinates of any point on the structure or its surroundings referenced by any other deck element description of the structure mass and geometry using plate point mass point buoyancy and tube elements see Appendix A of the AQWA Reference Manual for details a table of material values associated with each element a table of geometric values associated with each element the depth and density of the water and acceleration due to gravity The data requirement for each program in the AQWA suite is not the same and may also be dependent on the type of analysis to be performed These require
11. 845 07 103 07 521 07 131 10 287 11 775 08 483 06 030 07 729 06 760 08 814 08 655 411 STRUCTURE STRUCTURE 409 06 464 06 638 04 575 07 226 07 577 06 464E 06 762E 07 178 04 338 08 658 07 968 07 638 04 178 04 416 04 681 06 054 06 379 05 166 07 227 08 805 05 941 09 111 09 133 08 109 07 344 07 120 06 067 09 008 08 610 08 396 07 510 08 782E 06 396 09 949 09 637 11 Figure 7 26 Components of Global Stiffness Matrix Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 79 of 122 AQWA LIBRIUM User Manual Description of Output 7 7 5 System Small Displacement Static Stability An eigenvalue analysis of the global stiffness matrix is carried out from which the system stability can be assessed This information is output in the system small displacement static stability report as shown in Figure 7 27 The system stability is assessed from an eigenvalue analysis of the global stiffness matrix all eigenvalues of which must either be defined as stable or neutral for the system to be free from static instabilities We ce e SMA F DISPLACEMENT STATIC S LA BST diy TY Ra Ree SPECTRUM NO HAWSER COMBINATION NO OF HAWSERS 4 PRINCIPAL COORD LOAD PER UNIT DISPLACEMENT STABILITY IN THE PRINCIPAL COORD 932 06 928 06 147 07
12. AQWA suite The stages are as follows Stage 1 Geometric Definition and Static Environment Stage 2 Input of the Diffraction Radiation Analysis Parameters Stage 3 The Diffraction Radiation Analysis Stage 4 Input of the Analysis Environment Stage 5 Motion Analysis As Stage 3 has no direct calculations in programs other than AQWA LINE the programs will correct a request to finish at Stage 2 to one to finish at Stage 3 This remains transparent and requires no action by the user 5 3 STAGES OF ANALYSIS A typical analysis using AQWA LIBRIUM requires the following stages Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 41 of 122 AQWA LIBRIUM User Manual Analysis Procedure Select a consistent set of units Assemble geometric and material data for all the structures Specify one or more point masses to represent the mass and mass inertia of each of the structures In the case of tubes structural mass may be input through the geometric properties Calculate the coordinates of the node points for each of the mooring attachments and the elements used in the modelling of the body Specify the water depth and the density of the water Specify frequencies and directions and the corresponding drift force coefficients for each structure if equilibrium is required in a sea state For dynamic stability analysis specify the drift added mass and damping matrices for
13. CURRENT SPEED DIRECTION DEGREES WAVE 5 Ge LOWER UPPER SIGNFCNT MAX PEAK SPECTRAL OF FREQUENCY FREQUENCY WAVE SPECTRAL FREQUENCY DIRECTION RASTERS RAD SEC RAD SEC HEIGHT VALUE RAD SEC DEGREES 1 8850 14 95 31 83 0 6414 WIND SPEED DIRECTION DEGREES BE DOS 0 6 M R D WAVE SPECTRA FREQUENCY FREQUENCY ORDINATE NUMBER Q N PPP P P o QN FO RAD SEC e re PP PP PP O O O O Figure 7 18 User Defined Spectra and Wind and Current Conditions Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 69 of 122 AQWA LIBRIUM User Manual Description of Output 7 6 ITERATION PARAMETERS 7 6 1 Initial Equilibrium Positions The initial equilibrium position of the centre of gravity specified by the user for each structure spectrum and hawser combination will be output in the format shown in Figure 7 19 If the user does not specify a structure s initial position for a given combination that structure s initial position will correspond to that of the previous combination If no position has been specified at all in Deck 15 the structure s centre of gravity will be output at the original location in the FRA system RE koe Te ONS OP T OA X EQUILIBRIUM HAWS COMB STRUCTURE SPECTRUM TRANSLATIONAL POSITION FRA ROTATION ABOUT AXES NUMBER NUMBER NUMB
14. Stage 4 and finishes at the end of Stage 4 is equivalent to running with the DATA option Deck 9 This deck has no input and so has a NONE deck header Deck 10 Wind and current force coefficients and thruster forces for the structure Deck 11 This deck has no input and so has a NONE deck header Deck 12 This deck has no input and so has a NONE deck header Deck 13 Description of the wave spectra Wind speed and direction for the spectra Current speed and direction for the spectra Deck 14 Description of each mooring line property and combination Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 93 of 122 AQWA LIBRIUM User Manual Example of Program Use Deck 15 Initial estimates of the equilibrium positions for the spectra and the mooring line combination required to be analysed Deck 16 Iteration limits Deck 17 This deck has no input and so has a NONE deck header Deck 18 This deck has no input and so has a NONE deck header Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 94 of 122 AQWA LIBRIUM User Manual JOB T001 LIBR STAT TITLE OPTIONS REST END RESTART 4 4 09 10 HLD1 10CUFX 10CUFY 10CURX 10CURY 1OWIFX l10WIFY 10WIRX 10WIRY END10THRS 11 NONE 12 NONE 13 SPEC 13CURR 13WIND 13SPDN 13PSMZ 13SPDN 13PSMZ 13SPDN END13PSMZ 14 MOOR 14LINE 14LINE PPP
15. USED 13SPDN 0 0 90 000 0 000 0 000 13PSMZ 0 300 000 000 13SPDN 45 000 000 000 13PSMZ 0 300 000 000 13SPDN 0 000 000 END13PSMZ 0 300 000 DECK 14 14LINE 1 472E 06 1 000E 02 0 000E 00 0 000E 00 0 000E 00 14LINE 1 472E 06 1 000E 02 0 000E 00 0 000E 00 0 000E 00 14LINE 1 472E 06 1 000E 02 0 000E 00 0 000E 00 0 000E 00 END14LINE 1 472E 06 1 000E 02 0 000E 00 0 000E 00 0 000E 00 DECK 15 15POS1 15POS1 END15POS1 DECK 16 END16MERR DECK 17 Figure 8 6 Card Echo of Decks 9 to 18 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 98 of 122 AQWA LIBRIUM User Manual Example of Program Use HYDRODYNAMIC PARAMETERS 0092 08 0000 00 0000 00 0000 00 7459 08 0000 00 0000 00 0092 08 0000 00 7459 08 0000 00 0000 00 0000 00 0000 00 3199 08 0000 00 0000 00 0000 00 0000 00 7036 08 0000 00 5698 10 0000 00 0000 00 7036 08 0000 00 0000 00 0000 00 5698 10 0000 00 0000 00 0000 00 0000 00 0000 00 0000 00 2209 11 DAMPING AT DRIFT FREQUENCY 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 0000E 00 00
16. adt0001 RUNDIR C AQWA Projects Tests MODEL2 echo Change directory to path C AQWA Projects Tests MODEL RUN alt0002 END ALL RUNS COMPLETE Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 119 of 122 AQWA LIBRIUM User Manual Appendix A APPENDIX A AQWA LIBRIUM PROGRAM OPTIONS The options listed below may be used when running the program AQWA LIBRIUM They should appear on the options card which follows the job identification card in Administration Deck 0 see Section 6 0 REST RESTART Option This option is used when the program is being restarted at any stage greater than the first see Section 5 2 A restart card must follow the options list when the restart option is used This card indicates the stage at which the program is to continue and the stage at which the program is to stop see AQWA Reference Manual DATA DATA Option This option is used to check the data input to the program and is equivalent to performing the first two stages of the program analysis see Sections 6 1 and 6 2 If the data is correct then the program would be restarted at Stage 3 of the AQWA LIBRIUM analysis by using the RESTART option PRST PRINT GLOBAL STIFFNESS MATRIX This option causes the global stiffness matrix which is computed in the equilibrium analysis Stage 5 to be output PPEL PRINT PROPERTIES of Each Element on Each Structure This option allows
17. are used in each program is required The only general rule is that the value of the spectral ordinate at the beginning and end of the frequency range should be small If the values are not small only part of the spectra has effectively been specified this may be the intention of the user however 4 15 MOORING LINES 4 15 1 Linear Non Linear Elastic Hawsers The line properties are specified by their unstretched lengths ends nodes on respective bodies and their load extension characteristics For linear hawsers the line stiffness load per unit extension is required For non linear hawsers the program permits up to a fifth order polynomial approximation of the elastic property of the following form see Section 3 10 1 P e aje ase 4 15 1 where line tension extension o The use of a higher order polynomial than necessary could lead to erroneous negative stiffness while a lower order fit could be perfectly adequate see Figure 4 3 It is always useful to check the polynomial fit prior to its use as input data Note for small extensions the term a is usually a good approximation to the linear stiffness Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 35 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 15 2 Constant Tension Winch Line The winch line is characterised by its constant tension attachment points and
18. forces are output to allow the user to assess the contributions from the system components 7 7 1 Hydrostatic Reports of Freely Floating Structures Two reports are generated for the structure hydrostatics The first is common to other programs within the AQWA SUITE and creates hydrostatic fluid loading details output by AQWA LIBRIUM for each body in the EQUILIBRIUM position This hydrostatic output is grouped into the following four categories and as shown in Figure 7 22 1 Hydrostatic Stiffness Matrix at the Centre of Gravity The coordinates of the centre of gravity are output with respect to the FRA with the body in the prescribed analysis position The heave roll and pitch components of the hydrostatic stiffness matrix are given with respect to the body s centre of gravity Hydrostatic Displacement Properties The actual and equivalent volumetric displacements are given together with the coordinates of the centre of buoyancy These coordinates are measured with the body in the equilibrium position and with respect to the FRA system The accuracy of the structure equilibrium is checked by considering the normalised force moment components output Cut Water Plane Area Properties The properties of the body s cut water plane are output and these include the total area centre of area and principal second moments of area The angle PHI output is the angle between the body s principal cut waterplane axes and the FRA N B the X and Y axe
19. of freedom This is achieved by assigning the relevant d o f to zero displacement The program will automatically uncouple the singular degrees of freedom from the rest AQWA also allows structures to be connected by articulated joints These joints do not permit relative translation of the two structures but allow relative rotational movement in a number of ways that can be defined by the user The reactions at the articulations can be output in global structure or local articulation axes 3 8 WIND AND CURRENT LOADING The wind and current drag forces are calculated from a set of user prepared empirical environmental load coefficients covering a range of heading angles The drag coefficients for any heading are obtained by linear interpolation The input load coefficients are defined as 2 drag force or moment wind or current velocity According to the above definition the coefficients are dimensional and the user must conform to a consistent set of units For details see Appendix A of Reference Manual 3 9 THRUSTER FORCES Up to 10 thruster forces may be applied to a body The magnitude of the thrust vector is constant and the Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 15 of 122 AQWA LIBRIUM User Manual Theoretical Formulation direction of the vector is fixed to and moves with the body The program will calculate the thruster moments from the cross product
20. of the latest position vector of the point of application and the thrust vector 3 10 MOORING LINES The effect of mooring lines is to contribute to the external forces and stiffness matrix of a structure This in turn will affect the static equilibrium position and its stability in this position AQWA LIBRIUM allows the user to specify the following forces of constant magnitude and direction constant tension winch lines connecting two bodies or a body and a fixed point linear non linear elastic weightless hawsers connecting two bodies or a body and a fixed point composite elastic catenary chains between a body and a sea anchor or connecting two bodies fenders between two bodies or body and a fixed point N B Current drag on all mooring lines is ignored if without cable dynamics option Within the program the tension vector and stiffness matrix of each mooring line are initially evaluated with respect to a set of axes local to the vertical plane containing the line The detailed method by which the GLOBAL force vector and system stiffness matrix are transformed to the FRA is given in Section 3 10 3 Force of Constant Magnitude and Direction A constant FORCE line is always assumed to act at the specified point of the body in question The force magnitude and direction are assumed fixed and DO NOT CHANGE with movement of the body Constant Tension Winch Line A WINCH line maintains a constant tension provided the distan
21. of wind current headings velocity profiles and directions The drag coefficients at any heading are obtained by linear interpolation 4 11 THRUSTER FORCES Up to ten thruster forces may be specified The point of application of the force vector is defined by a NODE The magnitude of the vector remains constant and the direction of the vector is fixed in relation to the body fixed axes LSA Note that thruster forces affect the frequency domain solution through the change in equilibrium position which in turn may change the stiffness of any non linear mechanism present 4 12 CURRENT AND WIND VELOCITIES AND DIRECTIONS The wind and current velocities and associated directions can be included along with the spectral information as discussed in Section 4 13 In applications where the user is not interested in wave conditions the data can be input independently However this data will be overwritten if current and wind conditions are specified along with the spectral information Two types of current velocity can be specified the first is a uniform velocity and the second is a profiled current velocity varying with both direction and depth between the sea bed and water surface 4 13 CONSTRAINTS OF STRUCTURE MOTIONS It is quite common in the analysis of floating systems to have one or more singular degrees of freedom causing failure in the solution of the equations For the majority of floating systems the program checks and removes these degr
22. subsidiaries and affiliates Page 19 of 122 AQWA LIBRIUM User Manual Theoretical Formulation section the 12x12 stiffness matrix K is given by I 0 0 0 0 t T 0 0 0 K _r T 1 1 a a 38 3 10 9 t t 0 0 0 P T where 0 z y 0 P T z 0 x P P 0 P y x AP 0 X Coordinates of the attachment point on the second structure relative to its centre of gravity Px Py Pz X Y and Z components of the tension in the mooring line at the attachment point on the second structure 3 11 WAVE SPECTRA The method of wave modelling for irregular seas is achieved within the AQWA suite by the specification of wave spectra For further details the user is referred to Appendix E of the AQWA Reference Manual 3 12 EQUILIBRIUM AND STABILITY ANALYSIS 3 12 1 Solution of the Equilibrium Position The FRA system is used for the equilibrium and stability analysis of the floating system Where force moment vectors and stiffness matrices are initially evaluated at the LSA see Section 4 3 the program will transform the vectors matrices to the FRA prior to the calculation of equilibrium and stability Multi Degree of Freedom Systems Consider the simple case of a wall sided ship with mass M and cut waterplane area A If Zo is an initial guess of the vertical position of the centre of gravity then dz the displacement required to move the ship to the equilibrium position is given by dz F K 3 12 1 where F
23. terms of second order or higher the linearised equations of motion of the system can be expressed as These equations of motion can be put into the Hamiltonian form Pale eal ans Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 22 of 122 AQWA LIBRIUM User Manual Theoretical Formulation B X _ B 0 ar By letting Xo k i n the eigenvalues of equation 3 12 6 can be solved by MR MEME num Eigenvectors of the system given by equation 3 12 7 will give the modes of motion of the system as follows 1 f 0 STABLE 2 f gt Oand 0 UNSTABLE 3 f 0 and 0 FISHTAILING Also the period and damping are given by Period zd On Critical damping T _ 100 3 12 8 f vo For a single degree of freedom system the percentage of critical damping can be simplified as Critical damping 100 3 12 9 24 MK 3 13 LIMITATIONS THEORETICAL APPLICATIONS At present AQWA LIBRIUM only provides stability information which is valid for small displacements about the equilibrium position The user should be aware of the limitations of extrapolating such data to large displacements from equilibrium However a stability report for a single structure with hydrostatic forces only can be generated see AQW A Reference 4 16B 5 The report written in LIS file gives a list of positions of the structure and the corresponding f
24. the change in forces and moments acting on that structure at the centre of gravity is therefore given by K M T 3 10 7 EL xls 10 E IT 4 JO P T where 0 tex 0 P Tex 0 x 0 P y ww P P 0 X y z Coordinates of the attachment point on the structure relative to the centre of gravity Px Py Pz The x y and z components of the tension in the mooring line at the attachment point on the structure t The term P T is not symmetric In general only a structure in static equilibrium will have a symmetric t stiffness matrix where T is the transpose matrix of T However this also means that if the mooring forces are in equilibrium with all other conservative forces then the total stiffness matrix will be symmetric The force at the centre of gravity F in terms of the forces at the attachment point F is given by 3 10 8 3 10 4 Stiffness Matrix for a Mooring Line Joining Two Structures When two structures are attached by a mooring line this results in a fully coupled stiffness matrix where the displacement of one structure results in a force on the other This stiffness matrix may be obtained simply by considering that the displacement of the attachment point on one structure is equivalent to a negative displacement of the attachment point on the other structure Using the definitions in the previous Contains proprietary and confidential information of ANSYS Inc and its
25. to restrictions stated in the ANSYS Inc software license agreement and FAR 12 212 for non DOD licenses Third Party Software The products described in this document contain the following licensed software that requires reproduction of the following notices Copyright 1984 1989 1994 Adobe Systems Incorporated Copyright 1988 1994 Digital Equipment Corporation Permission to use copy modify distribute and sell this software and its documentation for any purpose and without fee is hereby granted provided that the above copyright notices appear in all copies and that both those copyright notices and this permission notice appear in supporting documentation and that the names of Adobe Systems and Digital Equipment Corporation not be used in advertising or publicity pertaining to distribution of the software without specific written prior permission Adobe Systems amp Digital Equipment Corporation make no representations about the suitability of this software for any purpose It is provided as is without express or implied warranty Microsoft Windows Windows 2000 and Windows XP are registered trademarks of Microsoft Corporation The ANSYS third party software information is also available via download from the Customer Portal on the ANSYS web page If you are unable to access the third party legal notices please contact ANSYS Inc Published in the United Kingdom AQWA LIBRIUM User Manual Contents CONTENTS CHAP PERT AaNTRODU
26. 0 O PW K 0 0 p 0 0 vi 3 10 5 If a constant tension device e g a winch is used at an attachment point then the elastic stiffness 5 becomes zero Note also that the P L terms in the equation tend to zero as the mooring line increases in length This means that if a mechanism is used at the attachment point to give a constant direction of the force P this has the effect of an infinitely long mooring line i e P L is zero The stiffness matrix K for each mooring line is defined at the attachment point on the structure and must be translated to a common reference point i e the centre of gravity in the AQWA suite This as formulated in Section 3 10 3 as the transformation procedure is applied to any local stiffness matrix and force applied at a point on a structure 3 10 2 Tension and Stiffness for Catenaries Catenaries in AQWA are considered to be uniform As the solution of the catenary equations is well documented e g Berteaux 1976 Barltrop 1998 the summary of the solution used in AQWA is presented The equations can be expressed in an axis system whose local X axis is the projection of the vector joining the attachment points on the sea bed and whose Z axis is vertical For catenaries which have zero slope at the contact attachment point on the sea bed these equations can be written as H AE w H AE V 1 2 2 T VH V 3 10 6 where L unstretched su
27. 00E 00 0000E 00 0000E 00 0000E 00 Figure 8 7 Added Mass and Damping at Drift Frequency Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 99 of 122 AQWA LIBRIUM User Manual Example of Program Use WIND CURRENT LOADS THRUSTER NODE POSITION OF THRUSTER FRA LOCAL THRUSTER FORCES IN SURGE X SWAY Y HEAVE Z 45 000 0 000 20 000 2 000 06 0 000 00 0 000 00 FORCES FREQUENCY DEGREES SURGE X 32 03 1 07 03 0 00 00 SWAY Y 00 00 1 07 03 1 32E 03 HEAVE 2 00 00 0 00 00 0 00E 00 ROLL RX 00 00 1 94 04 2 39E404 PITCH RY 39E 04 1 94 04 0 00 00 YAW RZ 00E 00 00E 00 00E 00 SURGE X 95 06 2 40E 06 0 00E 00 SWAY Y 00E 00 40 06 2 95E 06 HEAVE Z 00E 00 00E 00 00E 00 ROLL RX 00E 00 2 25E 07 2 77E 07 PITCH RY 77E 07 2 25E 07 0 00E 00 YAW RZ 00 00 00 00 00 00 Figure 8 8 Wind Current Loads and Thruster Forces Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 100 of 122 AQWA LIBRIUM User Manual Example of Program Use UNIFORM CURRENT VELOCITY UNIFORM CURRENT DIRECTION UNIFORM WIND VELOCITY NO PROFILED CURRENT Figure 8 9 Current and Wind Information CONSTRAINTS STRUCTURE Figure 8 10 Constraints Contains proprietary and confidential information of ANSYS Inc and its subsi
28. 2000 Windows XP and Excel are registered trademarks of Microsoft Corporation NASTRAN is a registered trademark of the National Aeronautics and Space Administration PATRAN is a registered trademark of MSC Software Corporation SentinelSuperPro is a trademark of Rainbow Technologies Inc SESAM is a registered trademark of DNV Software Softlok is a trademark of Softlok International Ltd other trademarks or registered trademarks are the property of their respective owners Disclaimer Notice THIS ANSYS SOFTWARE PRODUCT AND PROGRAM DOCUMENTATION INCLUDE TRADE SECRETS AND ARE CONFIDENTIAL AND PROPRIETARY PRODUCTS OF ANSYS INC ITS SUBSIDIARIES OR LICENSORS The software products and documentation are furnished by ANSYS Inc its subsidiaries or affiliates under a software license agreement that contains provisions concerning non disclosure copying length and nature of use compliance with exporting laws warranties disclaimers limitations of liability and remedies and other provisions The software products and documentation may be used disclosed transferred or copied only in accordance with the terms and conditions of that software license agreement ANSYS Inc and ANSYS Europe Ltd are UL registered ISO 9001 2000 Companies U S Government Rights For U S Government users except as specifically granted by the ANSYS Inc software license agreement the use duplication or disclosure by the United States Government is subject
29. 3 is tabulated showing also the number of spectral lines by default Figure 8 12 Cable Mooring Line Configurations Tabulation of the mooring lines input in Deck 14 Figure 8 13 Initial Equilibrium Positions of the Centre of Gravity Tabulation of the initial position input in Deck 15 Figure 8 14 Equilibrium Iteration Limits Tabulation of the iteration limits input in Deck 16 Figure 8 15 Morison Element Parameters Tabulation of the default Morison element parameters Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 96 of 122 AQWA LIBRIUM User Manual Example of Program Use DATE 28 11 08 TIME 14 56 37 JOB T001 LIBR STAT TITLE TEST RUN NUMBER 20 FLOATING BOX 40M DRAUGHT 48 FACETS OPTIONS REST END RESTART AQWA LIBRIUM VERSION 12 0 00 AAAAAA Qooooo 000000 QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ QQ 00 000000 09000 QQ szzzzzzz IIIIII BBBBBBB IIIIII IIIIII BBBBBBBB IIIIII II BB BB II II BB BB II II BBBBBBB RRRRRRRR II II BBBBBBB RRRRRRR II II BB BB RRRRR II II BB BB RR RRR II LLLLLL BBBBBBBB RR RRR IIIIII LLLLLL BBBBBBB RR RRR RR RR 888888388 88888388 k k He e He He He k He He k He He k k k k k He k k k He k k He k He k k k k He k AQWA 12 0 LEGAL NOTICES k k KK k k k k k k k He k k k k k k k k k k k k k k k k k k k k
30. 372 01 9450 02 11 0000 3 2875 09 0000 00 0000 00 0000 00 2161 04 0000 00 0961 07 2566 09 10 6200 2566 09 2566 09 0000 00 0000 00 0000 00 1074 01 6041 02 0441 02 10 6200 3 2566 09 0000 00 0000 00 0000 00 1074 01 6041 02 0441 02 2566 09 Figure 8 17 Iteration Report Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates 0000 00 0562 01 0000 00 0000 00 0000 00 0000 00 0000 00 0562 01 0 0145 0000 00 1595 06 8694 02 7040 01 0000 00 440 06 0280 02 8435 05 0 0145 0000 00 1595 06 8694 02 7040 01 0000 00 440 06 0280 02 8435 05 0000 00 2494 03 7728 07 3775 06 0000 00 0000 00 8760 07 4108 06 0 0103 0000 00 3965 06 7728 07 3775 06 0000 00 9998 06 8760 07 3126 04 0 0103 0000 00 3965 06 7728 07 3775 06 0000 00 9998 06 8760 07 3126 04 Example of Program Use 0000E 00 2500E 02 0000E 00 0000E 00 4709E 00 0 0000E 00 0000E 00 4084E 00 0 0009 0000E 00 2800E 02 0000E 00 0000E 00 5069E 00 8368 03 7350 03 2322 03 0 0009 0000 00 2800 02 0000 00 0000 00 5069 00 8368 03 7350 03 2322 03 Page 109 of 122 AQWA LIBRIUM User M
31. 8 51 6 5 STAGE 5 NO INPUT EQUILIBRIUM ANALYSIS nennen 51 CHAPTER 7 DESCRIPTION OF etes troie denota Sr rag da 22 7 1 STRUCTURAL DESCRIPTION OF BODY CHARACTERISTICS eere 53 7 1 1 Properties of All Body Elements ee demde 53 T2 DESCRIPTION OE ENVIR NMENT iu aaa aaa 57 43 DESCRIPTION OF FEUID LOADING u a aa aaa eA ER ER 59 uma u Da D aD 59 Drift MORES RO 60 7 3 3 Drift Added Mass Wave Damping 61 7 4 DESCRIPTION OF STRUCTURE LOADING eerte eene r a 62 7 4 1 Thruster Forces and Wind and Current Coefficient esee 62 7 5 Constraints oues btts natant tuta 63 7 4 3 Cable Line Mooring Configurations eee 65 7 5 DESCRIPTION OF ENVIRONMENTAL CONDITIONS eese nnne nennen 67 7 5 1 Wind and Current Conditions no waves enne enne eerte nnn 67 7 6 ITERATION PARAMETERS rRNA AREA ERAN EN ER RU eee Ea T RUE 70 7 6 1 Initial Equilibrium POoSIUODS eere ete teen teen t PR nen eae aaa 70 7 0 2 Iter tion Limits eR ORE RENTRER DRAN NR RM MARMOR
32. 9 4 Running the PEOBEATES A4 ER RT cases oe NER oa Aaa aad dA A 118 APPENDIX A AQWA LIBRIUM PROGRAM nnne renes 120 APPENDIX B REPERENCGCES diana a ia a ERREUR ERR RR RENE eR ae adda UNE RUE 122 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 7 of 122 AQWATMLIBRIUM User Manual Introduction CHAPTER 1 INTRODUCTION 1 1 PROGRAM INTRODUCTION AQW A LIBRIUM is a computer program which finds the static equilibrium configuration of a floating system calculates the mooring loads and examines the static and or dynamic stability about this position The program has the following three modes of operation 1 Find STATIC equilibrium position report mooring loads and investigate the static stability characteristics 2 Given static equilibrium position investigate the slow DYNAMIC stability characteristics 3 Find static equilibrium position report mooring loads and investigate both STATIC and drift frequency DYNAMIC stability characteristics The static equilibrium configuration will form the basis of dynamic analyses of floating systems 1 2 MANUAL INTRODUCTION The AQWA LIBRIUM Manual describes the various uses of the program together with the method of operation The theory and bounds of application are outlined for the analytical procedures employed within the various parts of AQWA LIBRIUM When using AQWA LIBRIUM the u
33. A WAR M SM NEAR MR REMANERE 71 7 6 3 Report S 72 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 6 of 122 AQWA LIBRIUM User Manual Contents 727 STATIC EQUILIBRIUM REPORT Susanna en AA 73 7 7 1 Hydrostatic Reports of Freely Floating Structures a 73 7 7 2 Structure Hydrostatic Stiffness Matrix 77 7 7 3 Mooring Forces and Stiffness 78 7 7 4 Global System Stiffness Matrix EE REP a UR NEUES 79 7 1 5 System Small Displacement Static 80 7 8 DYNAMIC STABILIEY REPOR T esee eee 81 7 8 1 Stability Characteristics of Moored 81 CHAPTER 8 EXAMPLE OF PROGRAM dr v e etaed vae VE 82 S T BOX STRUCTURE oed in MM MR M ERR M RM MX RU REX RM WR A DE 83 8 1 1 Problem PSEUD RR 83 BOX but bari 86 8 1 3 The Body Surfaces so euh ee ehh ed eee a er d e 86 SII d The Body Mass and Ierfl deo ee Me UNE 88 8 15 AOWX LEINBE Analysts e ee e GS eni es EE ERR
34. AQWA LIBRIUM MANUAL Release 12 0 April 2009 Revision Information The information in this guide applies to all ANSYS Inc products released on or after this date until superseded by a newer version of this guide This guide replaces individual product installation guides from previous releases Copyright and Trademark Information 2009 Ansys Inc All rights reserved Unauthorized use distribution or duplication is prohibited ANSYS ANSYS Workbench CFX AUTODYN ASAS AQWA and any and all ANSYS Inc product and service names are registered trademarks or trademarks of ANSYS Inc or its subsidiaries located in the United States or other countries ICEM is a trademark licensed by ANSYS Inc ABAQUS is a registered trademark of ABAQUS Inc Adobe and Acrobat are registered trademarks of Adobe Systems Incorporated Compaq is a registered trademark of Compaq Computer Corporation Delphi is a registered trademark of Borland Software orporation DXF is a trademark of Autodesk Inc FEMGV FEMGEN and FEMVIEW are trademarks of Femsys Limited FLEXIm FLEXnet are registered trademarks of Macrovision Corporation Formula One is a trademark of Visual Components Inc GINO is a registered trademark of Bradly Associates Ltd IGES is a trademark of IGES Data Analysis Inc Intel is a registered trademark of Intel Corporation Mathcad is a registered trademark of Mathsoft Engineering amp Education Inc Microsoft Windows Windows
35. Acceleration due to Gravity Used to calculate all gravity forces and various dimensionless variables throughout the program suite Density of Water Used to calculate fluid forces and various dimensionless variables throughout the program suite Water Depth Used to calculate the clearance from the sea bed used in the other programs of the suite to calculate wave properties 4 7 LINEAR STIFFNESS This section is only applicable if the user specifies that the stiffness is to be considered linear i e the stiffness remains linear even for large angle displacement This is an optional specification see Appendix A and means that a linear hydrostatic stiffness matrix is used in the analysis instead of assembling the stiffness from the hydrostatic element description 4 7 1 Hydrostatic Stiffness There are some cases where a finite element mesh of a body is neither possible through lack of detailed geometrical data nor necessary e g only horizontal planar motion is required or the movement of the body is likely to be small In these cases the user can model the hydrostatic stiffness of that particular body via the LSTF option Linear Stiffness The LSTF option requires only user input of buoyancy and hydrostatic stiffness matrix at equilibrium The program will assume constant buoyancy and stiffness throughout 4 7 2 Additional Linear Stiffness The additional linear stiffness is so called to distinguish between the linear hydrostatic stiff
36. C TION tert cetero tette retento oi tette ute ie pete eie eo tet obere bere IL TPROGRAMINTROBUCGTION tat titi nisl nil E e e Rt Red DH 3 BIBL OX TION pen CHAPTER 2 PROGRAM aqaqaqaqananasa s 2 PROGRAMKCAPABIELDIES 2 1 11 rtr tro treten ette iie orte ben te beso beku kuq 2 2 THE COMPUTERPROGRAM PUT CHAPTER 3 THEORETICAL ST AYDROSTATIC LOADING DIVO ISON FORCES C 3 3 DIFFRACTION RADIATION WAVE 8 0042 24 4 1 01 000 00 3 4 MEAN WAVE DRIFT FORCES SEE M REM REM ARP ERE ERR 3 5 VARIABLE WAVE DRIFT FORCES Pape apre 3 6 INTERACTIVE FLUID LOADING RR 3 7 STRUCTURAL ARTICULATIONS AND 8 8 3 8 WIND AND CURRENT LOADING rasa 39 THRUSTER FORCES ise ta ee ve LE eat rtt E ra ea e a E Y ERR EE Mt Rt RUE 3 10 MOORING LI ES s SA RA RE RN REM ERAS RN RA a EAR ERR pa RUE 3 10 1 Tension and Stiffness for Mooring Lines with No Mass eene 3 10 2 Tens
37. E ER EE dead ER ERE 88 8 1 6 Meam Wave Drift Forces ere ie eb E pe pupa aiu eie M M nagual AE 88 8 1 7 Drift Frequency Added Mass ue e te E tA e e Ree oun 89 8 1 8 Current and Wind Force Coefficients 89 71 9 Sca Spectra Current and Wand ect et tte tert e e e e e Une Ov tu et ee eie a repose 9 8 1 10 Specification of the Mooring Lines uasa e e RE RR RR RR A RR REA MA ARM MAR ARAM 91 81 11 Enstal Position Tor RN aee 92 8 1 12 Iteration Limits for Analysis st attese sk ep E E MEAE 92 8 1 13 Input Preparation for Data Run Stage 4 sss 92 8 1 14 Information Supplied by Data R m cu td betae te hee Lees 96 8 1 15 The Equilibrium Analysis Run e e ete hee sees 107 8 1 16 Output from Equilibrium Processing Run eee terne peus 108 CHAPTER 9 RUNNING THE PROGRAM eden ni 116 9 1 Running AQWA LIBRIUM on the PC nene 116 9 1 1 File Naming Convention for AQWA a 116 9 1 2 AQWA File urat ust ed vade ud 117 9 1 3 Program Size Requirements 117
38. ER Figure 7 19 Initial Equilibrium Positions Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 70 of 122 AQWA LIBRIUM User Manual Description of Output 7 6 2 Iteration Limits The iteration limits used in the equilibrium search are output as shown in Figure 7 20 These correspond to maximum movement in each mode per iteration and the maximum allowable convergence error for each degree of freedom of each structure In addition the maximum number of iterations is also stated If these values are not input in Deck 16 the values in the output will correspond to the program default values see AQWA Reference Manual Xe GS Re TP BOR AST T O N Lor M ICGTCUS e MAXIMUM NUMBER OF ITERATIONS STRUCTURE TRANSLATION ROTATION DEGREES NUMBER MAXIMUM MOVEMENT FOR ONE ITERATION MAXIMUM ERROR IN FINAL 0 0100 0 0100 0 0100 0 0100 0 0100 0 0100 EQUILIBRIUM POSITION Figure 7 20 Iteration Limits Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 71 of 122 AQWA LIBRIUM User Manual Description of Output 7 6 3 Iteration Report An iteration report for each structure is made at the conclusion of each iteration step specifying each structure s centre of gravity position and the residual forces and moments at that structure s CG in an axis system parallel to the Fixed Reference Axis system Thes
39. Figure 8 19 Figure 8 20 Figure 8 21 Figure 8 22 Figure 8 23 Iteration Report Structure Hydrostatic Properties in the Free Floating Position Global System Stiffness Matrix Small Displacement Static Stability Structure Hydrostatics at Equilibrium Structure Hydrostatic Stiffness and Mooring Stiffness Matrices Mooring Force and Stiffness Table Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 108 of 122 AQWA LIBRIUM User Manual JOB TITLE TEST RUN NUMBER 21 FLOATING BOX 40M DRAUGHT 48 FACETS STRUCTURE POSITION FORCES NUMBER AND MOMENTS AT ITER NO CENTRE OF GRAVITY POSITION GRAVITY 0000 00 HYDROSTATIC 7787E 01 CURRENT DRAG 8880 06 WIND 9700 05 DRIFT 4233E 03 MOORING 0000 00 THRUSTER 0000E 06 TOTAL FORCE 8495E 05 POSITION 0 0603 GRAVITY 0000E 00 HYDROSTATIC 6000E 01 CURRENT DRAG 8880 06 WIND 9700 05 DRIFT 6711 00 MOORING 8506 05 THRUSTER 0000E 06 TOTAL FORCE 7375 01 POSITION 0 0603 GRAVITY 0000E 00 HYDROSTATIC 6000E 01 CURRENT DRAG 8880E 06 WIND 9700E 05 DRIFT 6711E 00 MOORING 8506E 05 THRUSTER 0000E 06 TOTAL FORCE 7375 01 0 0000 0000E 00 6213E 01 0000E 00 0000E 00 0208E 05 0000E 00 0000E 00 0206E 05 0 2052 0000E 00 5475E 02 0559E 01 8072E 00 0207E 05 0191E 05 2372E 01 9450 02 0 2052 0000 00 5475 02 0559 01 8072 00 0207 05 0191 05 2
40. IUM parameters are read from backing file automatically or may be input manually In the latter case the ranges of frequencies and directions specified are those at which the parameters are to be input within these decks Note Although not directly applicable to AQWA LIBRIUM if all the diffraction radiation parameters are either read from an AQWA LINE backing file or input within Deck 7 a natural frequency analysis can be carried out using the same card image file with the appropriate JOB card The user is referred to the AQWA FER Manual for further details 6 2 3 Total Data Input Summary for Decks 6 to 8 Deck 6 A range of frequencies A range of directions Details relating to alterations of the results of a previous run Deck 7 all the data in deck 7 are optional if the relevant values are imported from other sources Linear hydrostatic stiffness matrix Additional stiffness matrix usually not required The buoyancy force at equilibrium Added mass matrix Additional mass matrix usually not required Radiation damping matrix Additional linear damping matrix usually not required Diffraction forces Froude Krylov forces Response motions or RAOs for checking only Deck 8 all the data in deck 8 are optional if the relevant values are imported from other sources Second Order Drift Forces It is unusual for all the data above to be required for any particular analysis in which case the user simply omits the
41. Inc and its subsidiaries and affiliates Page 62 of 122 AQWA LIBRIUM User Manual Description of Output In addition the wind and current forces and moments which are functions of direction are output for each structure as shown in Figure 7 12 The wind and current forces which are both a function of the square of velocity are given for unit velocity FORCES DUE TO SURGE X SWAY Y HEAVE 2 ROLL PITC YAW SURG SWAY RX H RY RZ X Y HEAVE 2 ROLL RX PITCH YAW RZ FREQUENCY DIRECTION DEGREES RADIANS SEC Figure 7 12 Wind and Current Force Coefficients 7 4 2 Structure Constraints Structure to structure or structure to a fixed point can be connected by articulated joints using DCON card in Deck12 Four joint types are available in AQWA Suite see AQWA Reference 4 12 3 These joints do not permit relative translation of the two structures but allow relative rotational movement in a number of ways that can be defined by the user One or more specified degrees of freedom of each structure can be deactivated by using DACF card in DECK12 The information of joint s and the degrees of freedom active for each structure during the analysis is signified by the character X in the constraint table as shown in Figure 7 13 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliate
42. ON FORCE OR STRUCT ELEM STRUCTURE LENGTH TENSION WIND IN PAY OUT ELASTIC 1 1 472 06 LINEAR LINEAR LINEAR Figure 7 14 Mooring Configuration Table CABLE MOORING LINE CONFIGURATIONS s GROUP GROUP 2 D L EXT PARAMETER PARAMETER PARAMETER PARAMETER PARAMETER NUMBER TYPE DATABASE POLYNOMIAL 4715E 06 0000 05 0000 04 0000 00 0000 00 5 4000 02 6000 02 0000 00 0000 00 0000 00 ELASTIC 5000 02 0000 02 0000 08 5000 06 0000 02 ELASTIC CAT 2000 02 0000E 02 0000E 08 5000F 06 0000F 02 FLASTIC CAT 7000 02 0000E 02 0000E 08 5000F 06 0000F 02 Figure 7 15 Non Linear Mooring Properties Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 66 of 122 AQWA LIBRIUM User Manual Description of Output 7 5 DESCRIPTION OF ENVIRONMENTAL CONDITIONS This section outputs the details of the environmental conditions at which equilibrium is required i e wind wave and current 7 5 1 Wind and Current Conditions no waves The wind and current conditions not associated with wave spectra are output as shown in Figure 7 16 i e the data input in Deck 11 This output consists of uniform wind and current fields with a superimposed profiled current condition characterised by a variation of current speed and direction with water depth RENT VELOCITY RENT DIRECTION D VELOCITY
43. Properties in the Free Floating Position Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 110 of 122 AQWA LIBRIUM User Manual Example of Program Use ee GLOBAL SYSTEM STIFFNESS MATRIX SPECTRUM NO MOORING COMBINATION NO OF CABLES 4 STRUCTURE STRUCTURE 972 06 447 01 339 02 351 02 156 07 271 05 447 01 972 06 277 02 156 07 049 02 268 06 339 02 277 02 147 07 779 05 255 04 020 01 351 02 156 07 779 05 493 10 219 03 303 06 156 07 049 02 255 04 321 03 484 10 238 06 975 03 692E 03 020 01 684 07 428 06 929 08 Figure 8 19 Global System Stiffness Matrix Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 111 of 122 AQWA LIBRIUM User Manual Example of Program Use SMALL DISPLACEMENT STATIC S TA B ILT TY SPECTRUM NO HAWSER COMBINATION NO OF HAWSERS 4 PRINCIPAL COORD LOAD PER UNIT DISPLACEMENT STABILITY IN THE PRINCIPAL COORD 932 06 928 06 147 07 493 10 484 10 929 08 Figure 8 20 Small Displacement Static Stability Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 112 of 122 AQWA LIBRIUM User Manual HY DROSTATICS OF STRUCTURE AT EQUILIBRIUM CEN
44. S SPECTRUM WAVE NUMBER NUMBER LOWER UPPER COMBINATION SPECTRUM OF OF FREQUENCY FREQUENCY NUMBER LINES RASTERS RAD SEC RAD SEC PIERSON M 3 4 0000 11 0000 JONSWAP 1 5000 4 4290 0 0074 JONSWAP gt 0 5869 15 0000 0 0022 output line continued below SPECTRAL CURRENT CURRENT MEAN DIRECTION SPEED DIRECTION WIND DIRECTION DEGREES DEGREES SPEED DEGREES Figure 7 17 Formulated Spectra and Wind and Current Conditions Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 68 of 122 AQWA LIBRIUM User Manual In the case of user defined spectra the environmental parameters are output as shown in Figure 7 18 Included in the parameter list is the spectral resolution limits i e the number of lines and rasters and the upper and lower frequency cut offs The spectral parameters are computed from the user defined spectral ordinates and frequencies input in Deck 13 and are output as shown in Figure 7 18 These include the significant wave height the maximum spectral value and the associated peak frequency The wave spectrum direction is also defined for each spectrum along with the associated wind and current speeds and Description of Output directions This data will replace the uniform current and wind data output discussed in Section 7 5 1 UOS Dy Br N p D SPECTRUM NUMBER NUMBFR COMBINATION OF NUMBER LINES CURRENT
45. S 0 203 PRINCIPAL SECOND MOMENTS OF AREA IXX 5 468E 06 IYY 5 468E 06 ANGLE THE PRINCIPAL AXES MAKE WITH PHI 11 344 THE FIXED REFERENCE AXIS SYSTEM SMALL ANGLE STABILITY PARAMETERS DISTANCE BETWEEN C O G AND C O B 380 METACENTRIC HEIGHTS WITH RESPECT TO 495 THE PRINCIPAL AXES OF THE CUT AREA 495 DISTANCE BETWEEN THE C O B AND THE 16 875 METACENTRE BMX GMX BG BMY GMY BG 16 875 RESTORING MOMENT ABOUT THE PRINCIPAL 4 260 08 AXES PER DEGREE ROTATION 4 260 08 Figure 7 22 Structure Hydrostatic Properties in the Free Floating Position Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 74 of 122 AQWA LIBRIUM User Manual Description of Output The second hydrostatic report as shown in Figure 7 23 which is specific to AQWA LIBRIUM generates similar data to the first However the output coordinate data is referred to the structure centre of gravity in an axis system parallel to the FRA system rather than the FRA system as in the previous report This report is grouped into the following three sections 1 The Equilibrium Position This is the structure CG position and orientation at equilibrium in the Fixed Reference Axis system In addition the structure FRA direction cosines are provided 2 Hydrostatic Forces and Moments The hydrostatic forces and moments acting on the structure are output along with the centre of buoyancy with resp
46. TRE OF GRAVITY 1 000 0 000 0 010 0 000 1 000 RZ 0 001 0 000 0 000 HYDROSTATIC FORCES AND MOMENTS AXES AT CG PARA BUOYANCY 3 257E 09 CENTRE OF BUOYANCY 4 397E 06 0 002 6 158E 06 9 380 3 055E 10 WATERPLANE AREA PROPERTIES AXES AT CG PARA 1 550E 01 2 172E 01 5 468E 06 5 468 06 Figure 8 21 Structure Hydrostatics at Equilibrium Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Example of Program Use Page 113 of 122 AQWA LIBRIUM User Manual HYDR 000 00 000 00 000 00 000 00 000 00 000 00 9721 06 4465E 01 3395 02 3511E 02 1564 07 7 9748 03 is 000 00 000 00 000 00 000 00 000 00 000 00 4466 01 9722 06 2769 02 1564 07 0492 02 6918 03 mS 000 00 000 00 141 07 183 05 558 05 000 00 3395 02 2769E 02 8271 04 5960 05 3202 04 0197 01 000 00 000 00 183 05 441 10 248 03 0 000E 00 3511E 02 1564 07 5960 05 2664 08 8761 04 9394 06 000 00 000 00 558 05 248 03 441 10 000 00 1564 07 0492 02 3202 04 0924 04 2668 08 6 4287 06 000 00 000 00 000 00 397 06 158 06 000 00 9748 03 6918 03 0197
47. TURE 0 IS FIXED POSN X 47 06 02 03 63E 02 17 04 87E 03 03 00 47E 06 82 03 45 02 76 04 93 03 03 00 Figure 7 25 Mooring Force and Stiffness Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates STIFFNESS 02E 03 62E 03 57 00 87 03 47E 06 69 02 82 03 4 04 1 45 00 93E 03 47 06 68E 02 Page 78 of 122 63E 02 57 00 62E 03 03 00 69 02 17 04 45E 02 45 00 34 04 03 00 68 02 75 04 AQWA LIBRIUM User Manual Description of Output 7 7 4 Global System Stiffness Matrix The system stiffnesses are output in the global stiffness matrix part of which is shown in Figure 7 26 This comprises the individual structure hydrostatic components and also the contributions from other structures passed via the moorings Figure 7 26 shows the stiffness experienced by one structure and other structure moored to it The global stiffness matrix is output only when the PRST option is used see Appendix A X OG no OB Ae E SYSTEM STIFFNESS SPECTRUM NO MOORING COMBINATION NO OF CABLES STRUCTURE STRUCTURE 530 06 545E 06 232 03 627 07 845 07 360 06 545 06 777 07 315 04 350 08 103 07 369 07 540 03 288 04 645E 07 803 05 521 07 368E 06 627 07 350 08 803 05 540E 09 119 10 797 08
48. YS Inc and its subsidiaries and affiliates Page 40 of 122 AQWA LIBRIUM User Manual Analysis Procedure 5 1 TYPES OF ANALYSIS Classification of the types of problem listed below based on the function of the analysis is the same whether the program is used independently or as a post processor to AQWA LINE and is as follows Calculation of the static equilibrium positions for a floating system of one or more bodies Determination of the hydrostatic loads and the small angle static stability characteristics of the structures and the mooring loads within the system when in equilibrium Calculation of the drift frequency dynamic stability characteristics of the system about a given static equilibrium position All the above are controlled by the job card and may be requested in any combination The dynamic stability analysis within both drift frequency range and wave frequency range may be carried out interactively using the AQWA Graphical Supervisor AGS 5 2 RESTART STAGES All programs in the AQWA suite have the facility of running one or more stages of the analysis separately These stages are referred to in the documentation as RESTART STAGES See AQWA Reference Manual Chapter 2 Use of the restart process implies that information is available on a backing file from a previous program run and not via the normal card image file This process is also used to transfer information from one program to another program in the
49. a Drag coefficient cos relative heading In this example the drag coefficient at heading 0 or 90 degree is 1 6 whilst at 45 degree it is 1 3 Thus the forces in the X and Y directions due to currents at 0 45 and 90 degree headings are respectively 233 520 F 0 90 0 5 1025 0 40 0 90 0 1 6 cos 0 2 95 6 Ns m 2 2 90 0 5 1025 0 40 0 90 0 1 6 sin 0 0 00E0Ns m 25272 F 45 45 0 5 1025 0 40 0 127 0 1 3 cos 45 2 40 6 m The moments at the centre of gravity 10 62 metres below the waterline centre of area at Z 20 0 are At a heading of 0 0 0 00 0 M 0 F 0 10 62 20 0 2 77E7 At a heading of 45 M 45 F 45 10 62420 0 2 25E7 M 45 F 45 10 62 20 0 225E7 At a heading of 90 M 90 F 90 C10 62420 0 2 77E7 M 90 0 0080 2 The units for the moment coefficients are Ns m Similarly the forces on the superstructure due to the wind at 0 45 and 90 degree headings in the X and Y directions respectively for unit velocity are 22 22 1 32E3 Ns m 0 F 90 0 F 90 F 45 F 45 0 5 1 22 15 0 90 0 1 6 cos 0 o gt oog 0 00E0 Ns m END 1 07E3 Ns m 0 5 1 22 15 0 90 0 1 6 0 0 5 1 22 15 0 127 0 1 3 cos 45 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 89 o
50. al ASCII text file mes file message file This file contains warning and error messages if any from the program run This is a normal ASCII text file 9 1 3 Program Size Requirements Not applicable for the PC Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 117 of 122 AQWA LIBRIUM User Manual Running the Program 9 1 4 Running the Programs Running from the Windows Start Menu After installation the AQWA programs appear on the Start Menu under ANSYS 12 0 AQWA runs the batch programs and AQWAGS starts the AQWA Graphical Supervisor AGS They can be run from here or the user can create icons on the desktop E ANSYS 11 0 2 fm ANSYS 12 0 gt Ej ANSYS FLEXIm License Manager gt 7 Utilities gt 9 asas gt AQWA RSM gt AQWAGS T ANSYS Client Licensing gt mag AQWAWAVE A ansys AQWAWB A ANSYS Product Launcher ANSYS Workbench Clicking on AQW AGS starts the AGS directly Clicking on AQWA brings up a dialog box that allows you to browse to an input file OPEN DAT FILE 2 xl Look in 9 Desktop Fe My Documents e 4 Computer My Recent My Network Places Documents Desktop Res lt My Documents BL My Computer c j My Network File name F DAT Places Files of type DAT Cancel EZ If a desktop icon is created for AQWA analyses can b
51. ams in the AQWA suite must consult the literature of the source used to obtain this data Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 24 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 1 INTRODUCTION The model of a floating structure requires different modelling depending on the type of problem that the user wishes to solve An approximate model may be acceptable in one analysis or even omitted altogether in another In general there are only two differences in the models required for each program The first is in the description of the structure geometry the mass distribution model is common which is achieved by describing one or more tubes and pressure plates In total the elements describe the whole structure and thus the hydrostatic and hydrodynamic model The second is in the description of the environment i e mooring lines wind current irregular and regular waves These parameters are not common to all programs AQWA DRIFT and AQWA FER do not necessarily require a hydrostatic or hydrodynamic model but only the hydrostatic stiffness matrix and hydrodynamic loading coefficients which are the RESULTS of calculations on these models Thus when AQWA LINE has been run all these parameters may be transferred automatically from backing files If AQWA LINE has not been run previously the hydrostatic stiffness matrix and wave loading coefficients are required as i
52. anual Example of Program Use HYDROSTATIC PROPERTIES FLOATING POSITION 0 060 0 205 2 2 8 141 07 2 183E 05 558 05 ROLL RX 2 183E 05 2 441E 10 248 03 1 558 05 7 248 03 441 10 2 HYDROSTATIC DISPLACEMENT PROPERTIES MESH BASED DISPLACEMENT 3 24000E 05 MASS BASED DISPLACEMENT 24000 05 POSITION OF THE CENTRE OF BUOYANCY 0 062 0 203 20 000 AN INCOMPLETE ELEMENT DESCRIPTION OF 0 000 THE HULL GIVES OUT OF BALANCE FORCES 0 000 AND MOMENTS IF THE C O B IS NOT 0 000 BELOW THE C O G THIS GIVES OUT OF 0 002 BALANCE MOMENTS FORCES ARE DIVIDED 0 001 BY THE WEIGHT AND ARE W R T AXES 0 000 PARALLEL TO THE FIXED REFERENCE AXES 3 CUT WATER PLANE AREA PROPERTIES CUT WATER PLANE AREA 8 100E 03 CENTRE OF FLOATATION I E CENTROID 0 062 POSITION IN THE FIXED REFERENCE AXES 0 203 PRINCIPAL SECOND MOMENTS OF AREA IXX 5 468 06 IYY 5 468 06 ANGLE THE PRINCIPAL AXES MAKE WITH PHI 34 901 THE FIXED REFERENCE AXIS SYSTEM SMALL ANGLE STABILITY PARAMETERS DISTANCE BETWEEN C O G AND C O B 9 380 METACENTRIC HEIGHTS WITH RESPECT TO 7 495 THE PRINCIPAL AXES OF THE CUT AREA 7 495 DISTANCE BETWEEN THE C O B AND THE 16 875 METACENTRE 16 875 RESTORING MOMENT ABOUT THE PRINCIPAL MX 4 260E 08 AXES PER DEGREE ROTATION MY 4 260E 08 Figure 8 18 Structure Hydrostatic
53. bsidiaries and affiliates Page 29 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 4 STRUCTURE GEOMETRY AND MASS DISTRIBUTION When AQWA LIBRIUM is used following an AQWA LINE run the structure geometry and mass distribution can be transferred automatically from the backing files produced by AQWA LINE This section therefore describes the modelling of the structure geometry and mass distribution when AQWA LIBRIUM is used independently See the AQWA LINE manual when this is not the case 4 4 1 Coordinates Any point on the structure in the modelling process is achieved by referring to the X Y and Z coordinates of a point in the FRA which is termed a NODE The model of structure geometry and mass distribution consists of a specification of one or more elements see also Sections 4 1 4 4 2 each of whose position is given by one or more nodes Each node has a node number which is chosen by the user to be associated with each coordinate point Nodes in themselves do not contribute to the model but may be thought of as a table of numbers and associated coordinate points to which other parts of the model refer Although several coordinates must be defined if several elements are used to define the geometry mass distribution normally a single point mass is used which means that only a single node is defined at the centre of gravity of the structure Note that nodes are also used to define the position of other points not necessarily
54. ce Manual It also uses the concept of the card image deck which is a section of two or more records between which the card image input is divided It assumes that the user is familiar with this concept details of which may also be found in the AQWA Reference Manual A summary of the possible data that may be input is listed together with a summary for various forms of analysis In the latter case a typical input data summary is given where the more unusual facilities have been omitted Most data requirements listed are optional unless specified otherwise and if not input the program defaults are used These defaults may be found together with the detailed format description in the AQWA Reference Manual Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 43 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation 6 0 ADMINISTRATION CONTROL DECK 0 PRELIMINARY DECK This deck is always required when performing AQWA program analysis runs The information input relates directly to the administration of the job being done and the control of the AQWA program being used Program Control has the following functions identification of the program to be used within the AQWA suite the type of program analysis to be performed if a choice exists the analysis stages to be performed i e restart stages Administration of the analysis being performed is as follows us
55. ce between the ends of the line is GREATER THAN a user specified unstretched length The direction of the tension depends the movement of the end points Weightless Elastic Hawser The elastic hawser tensions are simply given by the extension over the unstretched length and the load extension characteristics The load extension characteristics can either be linear like a spring or take the following polynomial form P e aye ase 3 10 1 where P line tension extension For details of the elastic mooring equations see Section 3 10 1 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 16 of 122 AQWA LIBRIUM User Manual Theoretical Formulation Elastic Catenary Chain The submerged weight length and attachment points of a catenary determine its profile tension and stiffness The standard catenary equations are solved for tension by the Newton Raphson technique Fender A fender can have a non linear stiffness defined by a polynomial as above friction and damping It acts in compression only between a point on one structure and a contact plane on another 3 10 1 Tension and Stiffness for Mooring Lines with No Mass The tension in a mooring line whose mass is considered negligible and thus has no deflection may be expressed in terms of a series of coefficients and its extension e from an unstretched length The force exe
56. d and this is done by way of the different categories of loading 7 3 1 Hydrostatic Stiffness The hydrostatic stiffness matrix output by AQWA LIBRIUM as shown in Figure 7 8 when printing from backing file is in the analysis position used in AQWA LINE for the diffraction radiation analysis If used independently the stiffness matrix output is the sum of the hydrostatic stiffness and the additional stiffness input by the user RR DR OODYNAMITC PARAMETERS BUOYANCY 53 550 0 rA 3 2566 09 Z POSITION OF THE CENTRE OF GRAVITY 1 0620 01 STIFFNESS MATRIX 0000 0000 7484 2 4408 0 0000 Figure 7 8 Hydrostatic Stiffness Matrix Output Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 59 of 122 AQWA LIBRIUM User Manual Description of Output 7 3 2 Wave Drift Forces The wave drift forces and moments as functions of wave period and direction are output as shown in Figure 7 9 They are given for each body and for the range of user specified frequencies The mean wave drift forces are functions of the wave amplitude squared and are given for unit wave amplitude WAVE A M P b I TU DELS 2 FORCES FREQUENCY DIRECTION DUE TO RADIANS SEC Figure 7 9 Wave Drift Forces Moment for far field solution Contains proprietary and confidential information of ANSYS Inc and its subsidiar
57. data which is not applicable The following sections show the required data input for the available modes of analysis Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 47 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation 6 2 4 Input for AQWA LIBRIUM using the Results of a Previous AQWA LINE Run If there are no changes to the results from a previous AQWA LINE run all the data is read automatically from the backing file and this stage is completely omitted Thus these decks are not required at all and must be removed from the card image data deck as the analysis is restarted at the beginning of Stage 4 Deck 6to8 No Input Required 6 2 5 Input for AQWA LIBRIUM with Results from Source other than AQWA LINE Although the parameters calculated by AQWA LINE can be transferred automatically to other programs in the AQWA suite this is NOT mandatory This means that if the backing file produced by an AQWA LINE run is NOT available e g AQWA LINE has not been run previously or the user wishes to input data from a source other than AQWA LINE then data may be input in these decks All data appropriate to the analysis summarised in Section 6 2 3 may then be input in card image format The exact input will depend on the type of analysis and the particular structure analysed The input data required is Case Deck 6 Deck 7 Deck 8 No drift None None None Hydrostatic mo
58. del No drift None Linear hydrostatic None No hydrostatic model stiffness matrix Drift Range of frequencies None Second order drift Hydrostatic model and directions forces Drift Range of frequencies Linear hydrostatic Second order drift No hydrostatic model and directions stiffness matrix forces Note that a hydrostatic model may consist of TUBE TPPL or QPPL elements 6 2 6 Input for AQWA LIBRIUM with Results from a Previous AQWA LINE Run and a Source other than AQWA LINE The new user is advised to ignore this facility If the user wishes to APPEND to or CHANGE the parameters calculated by a previous AQWA LINE run for the current analysis this can be achieved by using the card image input as described in the previous section in addition to reading the results from a previous AQWA LINE run As the program does not expect a database HYD file from AQWA LINE to exist at Stage 2 of the analysis the ALDB option must be used in the options list see Section 6 0 to indicate that it exists and must be read Using this option means that the Stage 2 data is input twice once from the backing file and once from the card image deck Alternatively use FILE CSTR CPDB cards in deck 6 to copy the hydrodynamic data from a backing file Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 48 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation HYD fr
59. dent program These coefficients which are required as input data further details may be found in the following sections are dependent on frequency and or direction A range of frequencies and directions is therefore required as input data which are those at which the coefficients are defined There are only two criteria for the choice of values of frequency and direction which may be summarised as follows 1 The extreme values must be chosen to adequately define the coefficients at those frequencies where wave energy in the spectra chosen see Section 4 15 is significant and at all possible directions of the subsequent response analysis If geometric symmetry has been specified see Section 4 3 3 only those directions for the defined quadrants are required 2 Sufficient values are required to adequately describe the variation of these coefficients Clearly if either of these criteria is violated erroneous results will be obtained Where possible the program will indicate this accordingly However this should not be relied on as anticipation of the intentions of the user is not usually possible 4 9 WAVE LOADING COEFFICIENTS The mean wave drift force is calculated from a set of drift coefficients for a range of headings either determined from AQWA LINE or another source and a wave energy spectrum If wave drift coefficients are calculated by AQWA LINE they can be transferred automatically from backing file See Section 4 9 o
60. diaries and affiliates Page 101 of 122 AQWA LIBRIUM User Manual Example of Program Use FORMULATED WAVE SPECTRA SPECTRUM WAVE LOWER UPPER PARAMETERS SPECTRAL CURRENT CURRENT MEAN COMBINATION SPECTRUM FREQUENCY FREQUENCY DIRECTION SPEED DIRECTION WIND DIRECTION TYPE LINES RASTERS RAD SEC RAD SEC DEGREES DEGREES SPEED DEGREES PIERSON M 4 0000 11 0000 0 0000 90 0 PIERSON M 6 0000 11 0000 0 0000 45 0 PIERSON M 8 0000 11 0000 ASSOCIATED WIND SPECTRA IF DEFINED Freq range rad sec 0 0063 6 2832 Freq range Hertz 0 0010 1 0000 Period Range 1000 0000 1 0000 SPECTRUM WIND NUMBER REFERENCE FREQUENCY SPECTRUM VELOCITIES AT 10M REF HT TURBULENCE COMBINATION SPECTRUM OF ELEVATION COEFF COEFF INTENSITY TYPE STAN DEV Figure 8 11 Formulated Spectra Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 102 of 122 AQWA LIBRIUM User Manual Example of Program Use CABLE MOORING LINE CONFIGURATIONS CABLE ATTACHMENTS STRUCTURE 0 IS GROUND COMBINATION CABLE ATTACHED TO NODE LINKED TO NODE UNSTRETCHED STIFFNESS WINCH FRICTION FORCE OR STRUCT ELEM NO STRUCTURE NO LENGTH TENSION WIND IN PAY OUT ELASTIC 100 000 1 472E 06 ELASTIC 100 000 1 472E 06 ELASTIC 100 000 1 472E 06 ELASTIC 100 000 1 472E 06 Figure 8 12 Cable Mooring Line Configurations Contains proprietary and confid
61. dures are converging to a solution or otherwise The default is a maximum of 100 steps Note that the more accurate the initial estimation of the equilibrium position the fewer iterations will be required to find equilibrium Users should exercise caution in placing the structures in the fluid since the iteration step is determined using the hydrostatic stiffness which may be not be defined if the structure is either submerged or emerged 4 16 2 Iteration Step Size Due to the non linearities in the system it is quite possible to overshoot and miss the intended equilibrium configuration Hence the program will restrict the movement of each body according to a user specified or default iteration step size The step size for each body is characterised by three translations and three rotations The program will scale the movement of all the bodies by a constant factor such that none of the displacements total of 6 x number of bodies exceeds its corresponding step size In other words equation 3 12 3 is modified such that xD xe 4 16 1 where II Min C C d dS dS is the allowed iteration step size Min 1 0 dS ax Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 37 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 16 3 Convergence Limits The equilibrium configuration is assumed to be found if the movements o
62. e and direction to the specified structure Degrees of freedom to be deactivated and constraints Degrees of freedom can be deactivated by specifying the structure and freedom This sets the relevant d o f to zero displacement Structures can be connected by articulated joints These joints do not permit relative translation of the two structures but allow relative rotational movement in a number of ways that can be defined by the user Wave spectra wind and current The sea state is defined by a wave spectrum together with its wind and current see Section 4 14 Wind spectra and profiled current can be input as well Mooring lines The physical characteristics and attachment points of mooring lines hawsers and tethers may be input if required see Section 4 15 Initial estimate of equilibrium positions The initial estimate of the equilibrium position of each structure can be specified for each mooring line and spectrum combination required to be analysed Limits of the iterations to be used in the equilibrium analysis The maximum number of iterations iteration step and error considered acceptable can be specified by the user Otherwise the default values will be used Morison element parameters These are either the Local Reynolds Number or the drag scale factor as applied to the drag coefficients of Morison elements already specified in Deck 4 within that structure Additional output items Requests
63. e of and parallel to the FRA In this example the DEFINITION position and ANALYSIS position of the body are the same as ZLWL value defined in Deck 2 is zero 8 1 3 The Body Surface The body has the property of 4 fold symmetry and this may be utilised when modelling the surface of the body We need only describe therefore one quarter of the box s surface and this is shown in Figure 8 2 Type of Plate Element Since each of the box surfaces is rectangular and planar we may best utilise QPPL elements Sizing of QPPL Elements The model beneath the free surface 15 the same as that used in AQWA LINE and satisfies the AQWA LINE modelling criteria see AQWA LINE Manual Section 8 1 1 The superstructure is composed of non diffracting quadrilateral plates whose only limitation is that the superstructure geometry should be properly modelled Additional nodes were placed on the structure and the fixed locations to represent the mooring attachment points see Figure 8 1 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 86 of 122 AQWA LIBRIUM User Manual Example of Program Use View from above View from beneath Y A View A View B Z Z X 8 Y Figure 8 2 Modelling of Body s Wetted Surface Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 87 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 4 T
64. e 06 hun beg Ef 36 4 15 4 Composite catenary Line 36 4 16 ITERATION PARAMETERS FOR SOLUTION OF EQUILIBRIUM 37 6 Limits s u 37 416 2 Iteration Step SIZE RT 37 4 16 3 C onyerpence ue error errre ok narra ee a EET O Er RET ee ET 38 4 17 TIME HISTORY INTEGRATION IN IRREGULAR WAVES AQWA DRIFT NAUT 39 4 18 TIME HISTORY INTEGRATION IN REGULAR WAVES AQWA NAUT ONLY 39 4 19 SPECIFICATION OF OUTPUT REQUIREMBNTIS rettet rhe XR HR XA PENA EUR RARE 39 CHAPTER 5 ANALYSIS PROCEDURE 40 5 1 TYPESOF ANALYSIS e MEME RH MER RR NNMERO RARE MUR RUN MUR M RR MER EE nasa 41 5 2 RESTART STAGES u eet eie ER VR EX RE Od ue dU Ud NE 41 5 3 STAGES OF ANALYSIS nan n nn aetna 41 CHAPTER 6 DATA REQUIREMENT AND PREPARATION eere nennen nennen 43 6 0 ADMINISTRATION CONTROL DECK 0 PRELIMINARY DECK 44 6 1 STAGE 1 DECKS 1 TO 5 GEOMETRIC DEFINITION AND STATIC ENVIRONMENT 44 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 5 o
65. e of buoyancy with respect to the centre of gravity Note that K46 and K56 will be zero and the stiffness matrix symmetric if the centre of buoyancy and the centre of gravity are located on the same vertical line For a freely floating body in EQUILIBRIUM this is automatically the case however before equilibrium is reached the matrix will not be symmetric In general if the body is in EQUILIBRIUM under the influence of mooring lines the centre of buoyancy and the centre of gravity will not be located on the same vertical line Hence the hydrostatic stiffness matrix can be asymmetric while the global system stiffness matrix will still be symmetric There are instances where the detailed geometry of the bodies is not available or not required The user may input directly a buoyancy force and a stiffness matrix which will be assumed constant throughout the analysis 3 2 MORISON FORCES These forces are only determined for tubular members of a structure The full Morison equation for the fluid forces acting on a unit length of such a structural member is 1 PDE uf Uf Us pACquy p A Cq D s 3 2 1 Drag Force Wave force Inertia Force where drag coefficient a characteristic drag diameter fluid velocity in the transverse direction of tube DA structure velocity in the transverse direction of tube a inertia coefficient area of cross section fluid density gt AaS Note tha
66. e run by dropping a DAT file from Windows Explorer onto the icon Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 118 of 122 AQWA LIBRIUM User Manual Running the Program Running from a Command Prompt It is also possible to run AQWA by issuing a command at a command prompt If the file is installed in the default location the command will be C Program Files ANSYS Inc v120 aqwa bin win32 aqwa exe option FileName where option is an optional command line option and FileName is the name of the dat file Possible command line options are STD tells AQWA to accept commands from an AQWA command file In this case FileName will be the name of the command file NOWIND will automatically close all progress and message windows allowing AQWA to be run from a conventional DOS batch file without user intervention The AQWA command file The commands available in the command file are listed below They are very similar to standard DOS commands comment line REM ECHO END RUNDIR RUN COPY RENAME MOVE DELETE Below is an example of running AQWA using a command file The run command could be C Program Files ANSYS Inc v120 aqwa bin win32 aqwa exe STD test com The file test com could be REM Example of a command file for multiple AQWA analyses RUN alt0001 echo 00011 AQWA LINE test complete copy alt0001 res abt0001 res RUN abt0001 RUN
67. e will be continuously reported as shown in Figure 7 21 until either equilibrium is achieved or the maximum number of iterations is exceeded whereby an error message will be output If the user requires further data expansion a PBIS option in the options list will generate the component force contributions in the output e g gravity stiffness mooring forces etc For further details see Appendix A ITERATION TOWARDS THE EQUILIBRIUM POSITION SPECTRUM NO MOORING COMBINATION l NO OF CABLES 4 LOCATIONS OF CG ORIENTATIONS DEGREES STEP STRUCTURE output line continued below RESIDUAL FORCES AND MOMENTS AXES PARA TO FRA 83 06 8 39E 06 3 10E 07 41 07 07 06 26 02 18 06 5 37E 06 1 98 07 02 07 83 06 07 05 24 05 2 37E 06 8 73 06 64 07 55 06 84 05 08E 02 4 43E 03 2 71E 02 11 05 73 04 08 05 08 02 25 02 5 30E 02 08 02 80 03 14 04 08 02 25 02 30 02 08 02 80 03 14 04 Figure 7 21 Iteration Report Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 72 of 122 AQWA LIBRIUM User Manual Description of Output 7 7 STATIC EQUILIBRIUM REPORT At the conclusion of the equilibrium analysis a stiffness report is generated for the global system along with a general static stability assessment In addition hydrostatic particulars of the structures and mooring
68. each structure The following preparation is required for AQWA LIBRIUM whether used independently or as a post processor to AQWA LINE 8 9 10 11 12 13 14 Prepare thruster forces and coefficients for wind and current drag for each structure Specify the wave spectra and the current and wind velocities Determine mooring line combinations and properties Specify an initial estimate of the equilibrium position of each structure for each spectrum and mooring line combination Code up the above information in a suitable manner acceptable to AQWA LIBRIUM See AQWA Reference Manual and Chapter 6 of this manual Perform a DATA run i e with the DATA option switched on which will provide preliminary checks on the card image data file After a successful DATA run select mode of analysis on the first card of the card image input data static dynamic both and re run with the restart option Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 42 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation CHAPTER 6 DATA REQUIREMENT AND PREPARATION This chapter describes the form in which data is expected by the program and is not intended as a detailed list of the data requirements Rather it describes the general format for each type of analysis that may be performed when running AQWA LIBRIUM The detailed format may be found in the AQWA Referen
69. ect to the centre of gravity 3 Water Plane Properties The water plane properties are also referred to the structure CG parallel to the Fixed Reference Axes and include the centre of floatation and the first second and product moments of area This retains the water surface properties used in the calculation of the angle between the principal and FRA as shown in Figure 7 22 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 75 of 122 AQWA LIBRIUM User Manual Description of Output HYDROSTATICS OF STRUCTURE SPECTRUM NO MOORING COMBINATION NO OF CABLES 4 EQUILIBRIUM POSITION WITH RESPECT TO FRA CENTRE OF GRAVITY 0 001 0 000 1 000 HYDROSTATIC FORCES AND MOMENTS AXES AT BUOYANCY 3 257 09 CENTRE OF BUOYANCY 2 834 07 6 353 06 3 055 10 WATERPLANE AREA PROPERTIES AXES PARA CENTRE EA XBAR 9 988E 01 EA YBAR 2 237 01 SECOND MOMENTS AREA RODUCTS OF AREA 5 468 06 XY AXIS 1 913E 00 5 468E 06 Figure 7 23 Structure Hydrostatics at Equilibrium Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 76 of 122 AQWA LIBRIUM User Manual Description of Output 7 7 2 Structure Hydrostatic Stiffness Matrix The free floating hydrostatic stiffness matrix is output for each structure as shown in Figure 7 24 This is the stiffness matrix at
70. ees of freedom such that the global stiffness matrix K becomes non singular and the displacements in the singular coordinates are zero However for more complicated systems the user can constrain directly specific degrees of freedom This is achieved by assigning the relevant d o f to a zero displacement Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 34 of 122 AQWA LIBRIUM User Manual Modelling Techniques AQWA also allows structures to be connected by articulated joints These constraints do not permit relative translation of the two structures but allow relative rotational movement in a number of ways that can be defined by the user There are four different types of articulation available These are as follows 0 Ball and Socket Free to rotate in all freedoms 1 Universal Free to rotate in two freedoms transmitting a moment in the third freedom at right angles to the first two 2 Hinged Transmitting a moment in two freedoms and free to rotate in the third freedom at right angles to the first two 3 Locked Transmitting a moment in all three freedoms and not free to rotate at all 4 14 WAVE SPECTRA WIND AND CURRENT SPECIFICATION The user may specify one or more spectra wind and current speeds with associated directions which may be different for all three For the majority of applications specification is straightforward and no knowledge of the way in which the spectra
71. ential information of ANSYS Inc and its subsidiaries and affiliates Page 103 of 122 AQWA LIBRIUM User Manual Example of Program Use EQUILIBRIUM POSITIONS STRUCTURE SPECTRUM 11 000 11 000 11 000 Figure 8 13 Initial Equilibrium Positions of the Centre of Gravity Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 104 of 122 AQWA LIBRIUM User Manual Example of Program Use eee ITERATION LIMITS MAXIMUM NUMBER OF ITERATIONS STRUCTURE TRANSLATION ROTATION DEGREES MAXIMUM MOVEMENT FOR ONE ITERATION MAXIMUM ERROR IN FINAL 0 0100 0 0100 0 0100 EQUILIBRIUM POSITION Figure 8 14 Equilibrium Iteration Limits Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 105 of 122 AQWA LIBRIUM User Manual Example of Program Use PARAMETERS AFFECTING HYDRODYNAMI MORISON ELEMENT 5 5 STRUCTURE DRAG ADDED MASS SLAM SIGNIFICANT FROUDE NUMBER SQUARED 0 040 VELOCITY PROFILE RATIO 100 VELOCITY ALIGNMENT ANGLE 730 REYNOLDS NUMBER RELATED PARAMETERS SCALE FACTOR 000 KINEMATIC VISCOSITY 569E 06 UNIT REYNOLDS NUMBER 375 05 Figure 8 15 Morison Element Parameters Contains proprietary and confidential information of ANSYS Inc and its subsidiaries a
72. ents are normally considered constant as is often the case at full scale i e large Reynolds numbers However experimental evidence shows that Reynolds number is not just a simple function of the velocity and diameter for cylinders with arbitrary orientation to the direction of the fluid flow Considerable improvement in agreement with model tests can be obtained by using a Scale Factor to obtain a local Reynolds Number and interpolating from classical experimental results UD 1 4 Scale factor Local Reynolds Number where U Local velocity transverse to the axis of the tube D Tube diameter u Kinematic viscosity of water from which drag coefficients can be interpolated from the Wieselberg graph of drag coefficient versus Reynolds number for a smooth cylinder see AQWA Reference Appendix Alternatively a general multiplying factor for drag can be used It is the interpolated value multiplied by this factor which is used as the drag coefficient Note that for steady state conditions as in AQWA LIBRIUM there are no added mass or slam effects Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 31 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 6 STATIC ENVIRONMENT 4 6 1 Global Environmental Parameters The global or static environmental parameters are those which often remain constant or static throughout an analysis and comprise the following
73. er title identification given to the analysis choice of output required from program run i e program options The above information is input to the program through the following cards contained in Deck 0 JOB Card This contains information stating the program to be used the type of program analysis to be undertaken and the user identifier for the run in question TITLE Card This lets the user prescribe a title for the run OPTIONS Card Various program options are available within the AQWA suite which are common to all programs while others are for use with specific programs The options within AQWA LIBRIUM control the type of output required from the program and the restart stages of analysis to be performed see Appendix A RESTART Card If the restart option is used then the start and finish stages of the analysis must be prescribed via the restart card For complete details of the above card formats see the AQWA Reference Manual For a list of options for use within AQWA LIBRIUM see Appendix A One option commonly used is the DATA option and it is worth noting its purpose The DATA option performs Stages 1 to 4 of an AQWA LIBRIUM analysis This means that all information relating to the analysis is read allowing all data checking to be performed After the user is satisfied with the acceptance of data then the equilibrium analysis can be undertaken by restarting the program at Stage 5 to perform the analysis itself
74. ether with the locations of the centre of buoyancy and the centre of gravity of the body determine the hydrostatic stiffness matrix As each body is moved towards equilibrium the hydrostatics are recalculated at each iteration based on the new submerged volume In AQWA LIBRIUM the hydrostatic forces and stiffnesses acting on each body are specified with respect to a set of axes whose origin is located at and move with the centre of gravity of the body while the axes remain parallel to the fixed reference axes see Section 4 3 at all times The hydrostatic stiffness matrix 15 as follows 0 0 0 O 0 0 0 K33 K34 K35 0 K43 K44 45 46 K53 K54 55 K56 0 0 0 08 cO occ cO cc cocco 3 1 1 where the various terms the hydrostatic stiffness matrix hys K33 A K34 ydA A K35 K53 xdA K44 y dA z vol A K45 K54 xydA A K46 x vol K55 x dA z vol A K56 y vol The integrals are with respect to the body s cut water plane and the total area of the cut water plane is A The displaced volume of fluid is given by vol The following coordinates are also used z are the coordinates defined in the body fixed axes Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 12 of 122 AQWA LIBRIUM User Manual Theoretical Formulation x y and give the centr
75. f 122 AQWA LIBRIUM User Manual Contents 6 1 1 Description Summary of Physical Parameters Input eese nennen 45 6 1 2 Description of General 45 6 1 3 Data Input Summary for Decks 1 to 5 45 6 2 STAGE 2 DECKS 6 TO 8 THE DIFFRACTION RADIATION ANALYSIS PARAMETERS 46 6 2 1 Description Summary of Physical Parameters Input eese nenne 46 6 2 2 Description of General Format RR UR ERN ERR ER MARE MAU UE REA RANA A 47 6 2 3 Total Data Input Summary for Decks 47 6 2 4 Input for AQWA LIBRIUM using the Results of a Previous AQWA LINE Run 48 6 2 5 Input for AQWA LIBRIUM with Results from Source other than AQWA LINE 48 6 2 6 Input for AQWA LIBRIUM with Results from a Previous AQWA LINE Run and a Source other than AQWA LINE a 48 6 3 STAGE 3 NO CARD IMAGE INPUT DIFFRACTION RADIATION ANALYSIS 49 6 3 1 Stage 3 in tenete 49 6 4 STAGE 4 DECKS 9 TO 18 INPUT OF THE ANALYSIS 49 6 4 1 Description of Physical Parameters 49 6 4 2 AQWA LIBRIUM Data Input Summary for Decks 9 to 1
76. f 122 AQWA LIBRIUM User Manual Example of Program Use The moments at the centre of gravity 10 62 metres below the waterline and centre of area at Z 7 5 are At a heading of 0 M 0 0 00 0 M 0 2 39E4 At a heading of 45 M 45 1 94 4 M 45 1 94 4 At a heading of 90 90 2 39 4 M 90 0 00E0 The units for the moment coefficients are Ns m In addition a thruster force of 2E6 N was applied to the box as shown in Figure 8 3 i e a thruster force vector of 2E6 0 0 newtons ELEVATION Thruster loree 20 Thruster Torce Figure 8 3 Thruster Force Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 90 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 9 Sea Spectra Current and Wind The following three wave spectra and their associated directions were used in this example Spectrum Type Frequency Range Significant Zero Crossing radians sec Wave Height Period 0 30 1 00 0 30 1 00 0 30 1 00 For each spectrum the wind and current speeds and directions used were as follows Wind speed E 15 0 m s Wind direction 0 0 degrees Current speed 0 8 m s Current direction 0 0 degrees 8 1 10 Specification of the Mooring Lines The mooring lines are simple linear elastic hawsers and therefore require one line of input data for each mooring line Each line contains the stiffness unstretched length
77. f each body as a result of the action of residual forces and moments are smaller than the default or user specified limits The limits are specified in terms of the translations and the finite angular rotations of each body Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 38 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 17 TIME HISTORY INTEGRATION IN IRREGULAR WAVES AQWA DRIFT NAUT Not applicable to AQWA LIBRIUM see AQWA DRIFT Manual 4 18 TIME HISTORY INTEGRATION IN REGULAR WAVES AQWA NAUT ONLY Not applicable to AQWA LIBRIUM see AQWA NAUT Manual 4 19 SPECIFICATION OF OUTPUT REQUIREMENTS See options list Appendix A Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 39 of 122 AQWA LIBRIUM User Manual Analysis Procedure CHAPTER 5 ANALYSIS PROCEDURE This chapter assumes that the user is familiar with the analysis procedure and how to model the structure in its environment It deals with the methodology of analysis associated with running the program and links the modelling information in the previous chapter with the stages of analysis necessary to solve a given type of problem This involves classification of the types of problem details of the program runs and stages within each program run together with their associated options Contains proprietary and confidential information of ANS
78. f mean drift coefficients D w and a wave energy spectrum S o The coefficients are specified over a range of frequencies and directions The mean wave drift force is given by F 2 7 S D d 4 2 y S D do 3 4 1 The coefficients for any specific heading angle are obtained through linear interpolation If required these Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 14 of 122 AQWA LIBRIUM User Manual Theoretical Formulation coefficients may be supplied by AQWA LINE Only the steady components of the drift forces and moments are computed in the program see Section 3 4 of AQWA LINE User Manual for derivation of the wave drift coefficients 3 5 VARIABLE WAVE DRIFT FORCES Not applicable to AQWA LIBRIUM see AQWA DRIFT Manual 3 6 INTERACTIVE FLUID LOADING The hydrodynamic interaction effects on the mean drift forces near field solution and added mass matrix are included 3 7 STRUCTURAL ARTICULATIONS AND CONSTRAINTS It is quite common in the analysis of floating systems to have one or more singular degrees of freedom causing failure in the solution of the equations For the majority of floating systems the program checks and removes these degrees of freedom such that the global stiffness matrix becomes non singular and the displacements in the singular coordinates are zero However for more complicated systems the user can constrain directly specific degrees
79. f the AQWA LINE Manual for modelling of the wave drift forces If the coefficients are determined from another source the coefficients have to be specified for a range of frequencies and directions as described in the previous Section The mean drift force at any frequency within the range is obtained by linear interpolation Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 33 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 10 WIND AND CURRENT LOADING COEFFICIENTS AND THRUSTERS The wind and current loading coefficients are required to model the forces and moments on the structure due to these environmental effects These forces are proportional to the square of the velocity and produce terms for steady forces stiffness and damping In the calculation of the equilibrium position and static stability analysis the effect of the steady forces is to change the equilibrium position and thus the stiffness of any non linear mechanism present e g catenaries hydrostatic stiffness The effect of wind or current stiffness per deg 1 rate of change of wind or current force with yaw will directly affect both the equilibrium position and the stability The wind or current damping has no effect on the static stability calculations The wind and current drag loads can be modelled simply as a force or in more detail by specifying the wind and current drag coefficients over a range
80. for additional listing file output where specific information is required to define its extent and format It is supplementary to the output obtained from the general printing requests of the Options List in the Preliminary Deck as the requests in this deck are necessarily more detailed Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 50 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation 6 4 2 AQWA LIBRIUM Data Input Summary for Decks 9 to 18 Deck 9 Deck 10 Deck 11 Deck 12 Deck 13 Deck 14 Deck 15 Deck 16 Deck 17 Deck 18 Low frequency added mass Low frequency damping Wind loading coefficients for the superstructure Current loading coefficients for the hull Wind and current speed and direction when no sea state is specified Profiled current data Degrees of freedom of structures which are to be deactivated Constraints between structures Wind speed and direction for each spectrum Current speed and direction for each spectrum Description of the wave spectra and or wind spectra Description of each mooring line property Description of mooring layout for each combination Initial estimates of the equilibrium positions for each spectrum and mooring line combination to be analysed Iteration and convergence limits Morison element parameters Additional printing options 6 5 STAGE 5 NO INPUT EQUILIBRIUM ANALYSIS This stage
81. he Body Mass and Inertia The mass and inertia characteristics are modelled by using a single point mass element PMAS placed at the centre of gravity This is positioned at X 0 0 Y 0 0 Z 10 62 metres with respect to the FRA This PMAS element will have the required mass and inertia properties described by the relevant material and geometric group properties as follows Mass input via material group 1 with associated value of 3 321E8 kg Inertia input via geometry group 1 with associated values of 2 3 6253E11 kgm 2 3 4199E11 kgm 2 3 599 E11 kgm I I 00 8 1 5 AQWA LINE Analysis The equilibrium position used to position the structure for each analysis is normally obtained from an AQW A LIBRIUM analysis where each drift force has been estimated manually In simple cases the equilibrium positions may be calculated manually as in this case The equilibrium positions calculated for the chosen spectra are as shown below Spectrum No Surge X Sway Y Heave Z Roll RX Pitch RY Yaw RZ 1 0 0 0 0 10 62 0 0 0 0 0 0 2 0 0 0 0 10 62 0 0 0 0 0 0 3 0 0 0 0 10 62 0 0 0 0 0 0 The model as described in the previous sections was run using AQWA LINE for Stages 1 to 3 in order to generate the hydrodynamic data required by the AQWA LIBRIUM analysis 8 1 6 Mean Wave Drift Forces The mean wave drift loads for unit wave amplitude necessary to determine the equilibrium position of
82. his chapter can be easily followed by the user and if so desired the user can repeat the whole procedure using the same data as used here to obtain the same results In this manner the new user can quickly obtain confidence in using the program Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 82 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 BOX STRUCTURE 8 1 1 Problem Definition The first example is a rectangular box structure for which the analysis has been run using AQWA LINE for Stages 1 to 3 This is the simplest and most common form of analysis i e an AQWA LINE run of Stages 1 to 3 followed by an AQWA LIBRIUM run It is assumed that the user is familiar with the box structure example in AQWA LINE The characteristics of the body are as follows Length 90 0 metres Breadth 90 0 metres Depth 55 0 metres Draught 40 0 metres Mass ofthe body 3 321 8 kg 3 321E5 tonnes 2 Mass inertia I 3 6253E11 kgm 2 E 3 4199E11 kgm 2 I 3 5991E11 kgm The centre of gravity position vector is 0 0 0 0 10 62 measured with respect to the FRA The environmental parameters may be defined as 250 0 metres 3 1025 0 kg metre 12 to 18 seconds 0 0 45 0 and 90 0 degrees Water depth Water density Wave periods Wave directions The box structure is moored by horizontal soft moorings attached to the mid sides of the box at the water line as s
83. hown in Figure 8 1 Unstretched length of each mooring line 100 0 metres Stiffness of each mooring line 1 471E6 N m Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 83 of 122 AQWA LIBRIUM User Manual Example of Program Use In addition a thruster force acts on the vessel side in the X direction as shown in Figure 8 1 Structure thruster force F r 2 0E6 Newtons It is required to obtain the equilibrium position of the box in irregular waves for three given sea states Note that the analysis is performed using SI units Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 84 of 122 AQWA LIBRIUM User Manual Example of Program Use ELEVATION gt 52 I Eg Mooring Dana 3 Monne Lane 1 101 m 101 m O0 m Figure 8 1 Box Structure Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 85 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 2 Idealisation of Box The following requires modelling The mass and inertia properties of the body The surface of the body Before starting the modelling exercise it is necessary to decide the definition position of the body with respect to the FRA The body is defined such that the bottom of the box is 40 metres below the X Y plan
84. ies and affiliates Page 54 of 122 AQWA LIBRIUM User Manual Description of Output The topology output also references the Geometry Group numbers used by the user Each Geometry Group may have a range of properties associated with it The number of relevant properties depends on the type of element under consideration The Geometry Group numbers and the various parameters within each group are output as shown in Figure 7 4 Here the Point Mass element has six geometric parameters which are the prescribed inertia values The localised element Drag and Added Mass coefficients are also printed RS UE Gs OUM ES TAR SD 6 P R20 po E LOEO SU Se GEOMETRY INPUT GROUP ELEMENT GEOMETRIC PARAMETER SEQUENCE 3 6253 11 0 0000E 00 0 0000 00 3 4199 11 output line continued below ADDED MASS COEFFICIENT COEFFICIENT 0 0000 00 3 5991 11 Figure 7 4 Geometric Property Output The program having accepted the user prescribed element distribution now outputs the resultant Mass and Inertia characteristics of the first body being modelled An example of output is shown in Figure 7 5 The coordinates of the centre of gravity are with respect to the FRA used in defining the body and the inertia matrix is about the centre of gravity of the particular body The types and total number of elements used to model the body are output The number of elements output is based on the total coverage of the body s wetted surface and n
85. ies and affiliates Page 60 of 122 AQWA LIBRIUM User Manual Description of Output 7 3 3 Drift Added Mass and Wave Damping The added mass and wave damping for drift frequencies can therefore be expressed as single added mass and damping matrices The added mass and wave damping are expressed in matrix form and Figure 7 10 shows a typical added mass matrix for body one at the drift frequency wave damping being output in a similar fashion GI YD ROD YON Ay M T C PARAMETERS Figure 7 10 Added Mass Matrix Output Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 61 of 122 AQWA LIBRIUM User Manual Description of Output 7 4 DESCRIPTION OF STRUCTURE LOADING This section outputs details of the loads on each structure whether due to wind and current thrusters user applied constraints or mooring lines 7 4 1 Thruster Forces and Wind and Current Coefficients The thruster number and associated force vectors relative to the local system axes LSA of the relevant structure along with the point of application expressed in the FRA system are output as shown in Figure 7 11 THRUSTER NODE POSITION OF THRUSTER FRA LOCAL THRUSTER FORCES IN NUMBER NUMBER SURGE X SWAY Y HEAVE 2 45 000 0 000 20 000 2 000 06 0 000 00 0 000F 00 Figure 7 11 Thruster Force Output Contains proprietary and confidential information of ANSYS
86. ion dnd Stiffness Tor C atenarles oe e RR OR ARR RR ERE MA ERRAT MUEVE AN ERR 3 10 3 Translation of the Mooring Line Force and Stiffness Matrix 3 10 4 Stiffness Matrix for a Mooring Line Joining Two Structures 3I WAVE SPECTRA ee eee eae eed D RR ERE 3 12 EQUILIBRIUM AND STABILITY 515 4 14 0000 3 12 1 Solution of the Equilibrium Position s eir Ag ded edenda dul eee denas 312 2 Sto Stability AIO SIS ecdesia r ien iaa i ai fete S Analysis 3 13 LIMITATIONS OF THEORETICAL APPLICATIONS essent CHAPTER 4 MODELLING nennen nennen nenne tenens tenens tenes dL INTRODUCTION 4 2 MODELLING REQUIREMENTS FOR 4 21 Followine am AQWA LINE d dp eo ohh beh Sh 4 3 DEFINITION OF STRUCTURE AND POSITION nnne nne 4 4 STRUCTURE GEOMETRY AND MASS DISTRIBUTION eene nennen Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 4 of 122 AQWA LIBRIUM User Manual Contents SP MP 30 4 4 2 Ele
87. k k COPYRIGHT AND TRADEMARK INFORMATION Copyright 2008 Ansys Inc 11 rights reserved Unauthorized use distribution or duplication is prohibited See the AQWA manuals for the complete Legal Notice k k k He k He k k k k k k k k k k k k k k k k k k k k K k k k JOB TITLE TEST RUN NUMBER 20 FLOATING BOX 40M DRAUGHT 48 FACETS Figure 8 5 AQWA LIBRIUM Header Page used for Identification Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 97 of 122 AQWA LIBRIUM User Manual Example of Program Use 10CUFX 10CUFY 10CURX 10CURY 1OWIFX 10WIFY 10WIRX 10WIRY END10THRS 950 06 2 400E 06 0 000E 00 0 000E 00 0 000E 00 0 000E 00 000 00 2 400E 06 2 950E 06 0 000 00 0 000 00 0 000E 00 000 00 2 250E 07 2 770 07 0 000E 00 0 000E 00 0 000E 00 0 0 1 770 07 2 250 07 0 000E 00 0 000E 00 0 000E 00 0 000E 00 320 03 1 070E 03 0 000 00 0 000E 00 0 000E 00 0 000E 00 000 00 1 070 03 1 320 03 0 000E 00 0 000E 00 0 000E 00 000 00 1 940 04 2 390 04 0 000E 00 0 000E 00 0 000E 00 390 04 1 940E 04 0 000E 00 0 000E 00 0 000E 00 0 000E 00 000 06 0 000E 00 0 000 00 0 000 00 0 000E 00 0 000E 00 O Ww NNOOHNOON T DECK 11 13CURR 0 0 0 800 0 000 0 000 13WIND 0 0 15 000 0 000 0 000 INFORMATION UNIFORM WIND SPEED IS
88. ments and Element ner Ee Rer EE EM Krank aM 30 AS MIO RESON ELEMENTS tpi prp EE 30 4 6STATIC ENVIRONMIENCL eret 32 4 6 1 Global Environmental 32 4 7 LINEAR STIFFNESS aee RR MEM ER REA RERUM UNDA RERUM AME MR EN E UR E AMA RAM RA REDI EAE 32 Mk SUIT RN 32 4 7 2 Additional Linear Stiffness M XR ER REUS 32 4 8 WAVE FREQUENCIES AND DIRECTIONS ie ut qui uv en uta did iu 33 4 9 WAVE LOADING COEFFICIENTS 33 4 10 WIND AND CURRENT LOADING COEFFICIENTS AND THRUSTERS 34 JUL DHERUSTBR POBRES ipee PS S n taeda dave oa oa aa 34 4 12 CURRENT AND WIND VELOCITIES AND DIRECTIONS eere 34 4 13 CONSTRAINTS OF STRUCTURE MOTIONS HH ERR YER RR 34 4 14 WAVE SPECTRA WIND AND CURRENT SPECIFICATION eere 35 T EXNIOORING EINESL Sus cob n a ime imd pre pere p p en 35 2 15 T Linea Non Linear Elastic epa 35 4 15 2 Constant Tension Winch 36 4 155 Constant Forc
89. ments are listed in detail in the later sections of this chapter 6 1 2 Description of General Format The input format of these decks is designed to provide checking of the data for the average user and outputs a suitable message to inform the user if the instructions for data preparation have been misinterpreted or are unusual When running the program for the first time it is recommended that the PRCE option see Appendix A is used This causes the data input in these decks to be output automatically in order that the user may check the program s interpretation of the data before proceeding to the next stage of the analysis 6 1 3 Data Input Summary for Decks 1 to 5 Deck 1 The coordinates of points describing the elements The coordinates of the mooring line attachment points The coordinates of any points whose position or motions are requested by the user specified options Deck 2 Element description of the mass properties Element description of the hydrostatic model Element description of the hydrodynamic model Deck 3 A table of material values associated with each element Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 45 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation Deck 4 A table of geometric values associated with each element Deck 5 Static environmental parameters i e the depth and density of the water and the acceleration due t
90. merical differentiation Steady wind current and wave drift forces are only functions of the heading angle Therefore their stiffness contributions are found only in changes in the yaw coordinate ie K K At present the effect of changes in global thruster forces or moments with heading has not been implemented The Stiffness Matrix is non linear in general To move the bodies towards equilibrium requires a number of iterative steps In each step the values of the K matrix and the force vector F are re calculated Once the Global System Stiffness Matrix has been formed the program checks and removes any singular degrees of freedom see Section 3 7 Iteration Towards Equilibrium Let the initial guess of the structure positions and orientations be represented by the vector X where t X DX USD god ee ena xyz coordinates of the CG with respect to the FRA and par finite angular rotations which describe the orientation of the bodies The superscripts denote the iteration step and the subscripts denote the body number The displacement required in step 1 is given by and the new position of the body X D is given by Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 21 of 122 AQWA LIBRIUM User Manual Theoretical Formulation x 0 ax 4 x 9 3 12 3 The process is repeated until dX is smaller than the user prescribed limit It is possible to have more
91. n an irregular sea will significantly affect the equilibrium configuration of the system If this is the case the modelling requirements for AQWA LIBRIUM will depend on the type of model used by the AQWA LINE run If the AQWA LINE model includes all non diffracting elements e g Morison elements elements above water line remodelling of the hydrostatic properties is not required by AQWA LIBRIUM unless the user wishes to use a coarser mesh for the AQW A LIBRIUM run Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 26 of 122 AQWA LIBRIUM User Manual poet 4 2 yo us a TT v 2 PA P aa 2 gt lt Figure 4 1a AQWA LIBRIUM Mesh Des qanri of fetal _ bed surface Figure 4 1b AQWA LINE Mesh Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Modelling Techniques Page 27 of 122 AQWA LIBRIUM User Manual Modelling Techniques 4 3 DEFINITION OF STRUCTURE AND POSITION Full details may be found in the AQWA Reference Manual Two sets of axes are used in AQWA LIBRIUM and these are shown in Figure 4 2 They are the FRA Fixed Reference Axes or Global Axes and the LSA Local Axes System or Body Fixed Axes Full details of the axes systems used in the AQWA suite are given in the AQWA Reference Manual In AQWA LINE body motions and fluid forces are with respect to the cent
92. nce Manual 8 1 13 Input Preparation for Data Run Stage 4 The AQWA LINE run see AQWA LINE example has been performed and the following information is contained on the RESTART backing file produced by AQWA LINE input of the node coordinate data input of the model s element topology with associated material and geometry properties input of the static environment the detailed properties of elements used in each body the final mass and inertia properties of each body the preliminary diffraction modelling checks the wave periods and directions the analysis position of each body the secondary diffraction modelling checks hydrostatic calculations for each body diffraction radiation analysis giving wave loading coefficients Page 92 of 122 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates AQWA LIBRIUM User Manual Example of Program Use The decks for the AQWA LIBRIUM DATA run are shown in Figure 8 4 and the input may be described as follows JOB card provides identifier program and type of analysis to be used TITLE card prescribes a title header for the run OPTIONS card containing the selected options PRDL print data list from restart file REST indicates that a restart run is required END indicates the end of the options list RESTART card containing the start and finish stages Note that the current run which starts at the beginning of
93. nd affiliates Page 106 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 15 The Equilibrium Analysis Run Once the data input in Decks 8 to 18 are correct the equilibrium analysis stage is then performed As program restart is being performed the specified restart file of which the name is defined on the RESTART card in this example 20 is used to supply the program with the information contained within Decks 1 to 18 previously input The only data required to be input in card image format is in the preliminary deck This contains only the information to indicate that a Stage 5 analysis is required as shown in Figure 8 14 Note that the PRDL option has been omitted and that there are two additional options PRST Print global stiffness matrix PBIS Print force components at each iteration step JOB T001 LIBR STAT TITLE TEST RUN NUMBER 21 FLOATING BOX 40M DRAUGHT 48 FACETS OPTIONS PBIS PRST REST END RESTART 5 5 20 Figure 8 16 Data Input for Stage 5 Box Example Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 107 of 122 AQWA LIBRIUM User Manual Example of Program Use 8 1 16 Output from Equilibrium Processing Run The output relating to the equilibrium analysis stage i e Stage 5 contains the information shown in Figures 8 17 to 8 23 The results given are for the first spectrum only Figure 8 17 Figure 8 18
94. ndicate the end of the option list Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 121 of 122 AQWA LINE User Manual Appendix B APPENDIX B REFERENCES 1 Berteaux H O 1976 Buoy Engineering J Wiley amp Sons New York 2 Barltrop N D P 1998 Floating Structures a guide for design and analysis Oilfield Publications Limited and Kinematic viscosity of water Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 122 of 122
95. ness calculated by AQWA LIBRIUM or AQWA LINE and linear stiffness terms from any other mechanism or for parametric studies Although all terms in the additional linear stiffness can be included in the hydrostatic stiffness matrix the user is advised to model the two separately The most common applications where an additional stiffness model is useful to have are when modelling facilities for a particular mechanism are not available in the AQWA suite Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 32 of 122 AQWA LIBRIUM User Manual Modelling Techniques the hydrostatic stiffness matrix is incomplete theuser wishes to investigate the sensitivity of the analysis to changes in the linear stiffness matrix N B This facility does not replace but compliments the stiffness due to mooring lines if present as AQWA LIBRIUM includes the mooring line stiffness in its calculations of the total system stiffness matrix In practice it is only in unusual applications that the user will find it necessary to consider the modelling of additional linear stiffness 4 8 WAVE FREQUENCIES AND DIRECTIONS The wave frequencies and directions are those at which the wave drift current and wind coefficients are defined Since they are transferred automatically from backing file when AQWA LIBRIUM is used as a post processor the following notes refer to AQWA LIBRIUM when used as an indepen
96. nput data Hydrostatic model Panels and tubes No restrictions AQWA LINE LIBRIUM NAUT Hydrodynamic model Diffracting panels and tubes Restricted in geometry AQWA LINE and proximity to each other and to the boundaries Hydrodynamic model Panels and tubes Restricted only AQWA NAUT by size as a function of wavelength In practice this means that there is a hydrodynamic model for AQWA LINE to which other elements are added for AQWA LIBRIUM NAUT If the user wishes and when restrictions allow a more approximate model may be defined with fewer elements to minimise computer costs 4 2 MODELLING REQUIREMENTS FOR AQWA LIBRIUM AQWA LIBRIUM requires models of the inertia hydrostatic and hydrodynamic properties of the bodies the moorings and the environmental loads Some analyses using AQWA LIBRIUM might not require all of these models For example a static analysis would not require the hydrodynamic model In general AQWA programs do not require modelling of all aspects of the system for two reasons 1 The calculations associated with a particular model may have been done previously by one of the AQWA programs and the results can be transmitted either through backing files or manually as card image input Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 25 of 122 AQWA LIBRIUM User Manual Modelling Techniques 2 The mechanics of the system are such that a model is not
97. o be read from the restart file before the hydrodynamics can be read there is no possibility to change the model definition when using this option use ALDB instead PRDL PRINT DATA LIST FROM RESTART FILE This option causes the program to read the data contained within the restart backing file and output it to the user Typically all body modelling information is output together with environmental wave loading details LSTF LINEAR STIFFNESS This option is used to instruct the program to use the linear stiffness matrix calculated by AQWA LINE instead of calculating the hydrostatics by integrating over the wetted surface RNDD Reynolds No Drag C for Morison Elements switched by SC1 CARD This option causes drag coefficients to be set to zero i e switches off the Morison drag calculations on tube elements Together with the SC1 card in Deck 17 this option causes drag coefficients to be calculated using the Wieselburger curve for Reynold s number dependent drag coefficients PBIS Print Force Components at Each Iteration Step This option causes the program to output the component forces acting on each structure e g gravity hydrostatic current and mooring forces for each iteration PRCE Print Card Echo For Decks 1 to 5 This option causes the program to echo the input received by the program in reading Decks 1 to 5 This is the body modelling data and the static environment see Section 6 1 END This is used to i
98. o gravity The above information is required before an AQWA LIBRIUM static dynamic equilibrium calculation can be performed The information contained within Decks 1 to 5 must be input into AQWA LIBRIUM The AQWA Reference Manual gives details of the format for these input data decks 6 2 STAGE 2 DECKS 6 TO 8 THE DIFFRACTION RADIATION ANALYSIS PARAMETERS Input to Stage 2 of the analysis is only necessary if the restart stage at which the analysis begins is 1 or 2 see Chapter 5 If the restart stage is greater than 2 there is no input necessary for Stage 2 of the analysis 6 2 1 Description Summary of Physical Parameters Input The data input in these decks relates to the equation of motion for a diffracting structure or structures freely floating in monochromatic waves The latter are defined for a range of frequencies and directions Note that the structural mass is input in Decks 1 to 5 For a specified range of frequencies and directions the equation of motion can be written as M s X M a X CX KX F d F f F 2 6 2 1 The parameters in the equation of motion are K Linear Stiffness Matrix with associated values of Buoyancy Force at Equilibrium The Global Z coordinate of the Centre of Gravity at Equilibrium and for each frequency M a Added Mass Matrix C Radiation Damping Matrix and for each frequency and each direction X Response Motions or RAOs F d Diffraction Forces Fi Froude Kryl
99. om a previous run in order to DUPLICATE the database for the structure indicated by the deck header see AQW A Reference 4 6 7 To APPEND to the parameters calculated in a previous run additional frequencies which differ from those existing may be input in Deck 6 together with values of the appropriate frequency dependent parameters in Decks 7 and 8 at these additional frequencies Note that as all parameters are defined for a unique range of directions these directions must not be redefined To change the parameters calculated in a previous run these parameters are simply input in Decks 7 and 8 and depending on the type of input see individual deck sections in the AQWA Reference Manual the parameters will be either overwritten with the input values or become the sum of input values and original values 6 3 STAGE 3 NO CARD IMAGE INPUT DIFFRACTION RADIATION ANALYSIS 6 3 1 Stage 3 in AQWA LIBRIUM There is no input for Stage 3 AQWA LIBRIUM as this stage corresponds to the Diffraction Radiation analysis which has either been performed in AQWA LINE or the values from which have been input by the user from a source other than AQWA LINE i e when the program is used independently 6 4 STAGE 4 DECKS 9 TO 18 INPUT OF THE ANALYSIS ENVIRONMENT Input for Stage 4 of the analysis is only necessary if the restart stage at which the analysis begins is a stage not greater than 4 see Chapter 5 If the restart stage is greater than 4
100. on the structure e g the attachment points of each end of a mooring line see also Section 4 15 4 4 2 Elements and Element Properties Each body is modelled by one or more elements which could be a combination of tubes point masses point buoyancies and quadrilateral and triangular pressure plates This facility enables simple modelling of bodies of arbitrary shape With the exception of plate elements each element is associated with a set of material and geometric properties which define the structural masses and inertias of the system When only pressure plates are used to simulate the fluid pressure one or more point mass element with equivalent mass and inertia is needed to model the mass distribution of the body The moment of inertia is required for the dynamic runs only The program allows the user to take full advantage of symmetry in specific problems Up to four fold symmetry is accommodated 4 5 MORISON ELEMENTS Morison elements available within AQWA LIBRIUM are tubes slender tubes and discs Tubes are defined by specifying end nodes diameter wall thickness and end cut lengths over which the forces are ignored Each tube element may have a different drag and added mass coefficient associated with it Drag coefficients can be defined as functions of Reynolds Number Full consideration is given to current variation over the tube length and to partial submersion of members Morison drag is evaluated on all submerged or par
101. or JONSWAP form or numerical values supplied by the user The equilibrium position of each of the bodies is described by six coordinates of each structure s centre of gravity i e three translational and three rotational The static stability of the complete system is assessed through an eigenvalue analysis of the global stiffness matrix at equilibrium The global stiffness matrix is non linear and comprises hydrostatic pressures mooring tensions and stiffness due to the heading variation in wind current and wave drifting forces and moments Given an initial guess of the equilibrium configuration AQWA LIBRIUM moves the bodies in steps towards the final position via a series of finite displacements The displacements in each step are determined by summing the residual forces and moments acting on the bodies and forming the stiffness matrix of the system at its latest position Only time invariant forces and moments are permitted in the analysis Once equilibrium is reached the program reports all the mooring forces the local mooring stiffness matrices the global stiffness matrix and examines the stability of the system The equilibrium configuration determined by AQWA LIBRIUM may be used as a starting point for analyses carried out by other modules in the AQWA suite e g AQWA DRIFT AQWA FER and AQWA LINE and of course as input to the dynamic stability part of AQWA LIBRIUM The drift frequency dynamic stability of the system is assessed th
102. orces at each position The program also has no capacity to model internal compartments within a structure and hence neither internal compartment free surfaces nor damage effects on the hydrostatic stiffness nor small angle stability parameters are included These facilities will be included in a later version Drag effects on mooring cables are ignored if without the cable dynamics option Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 23 of 122 AQWA LIBRIUM User Manual Modelling Techniques CHAPTER 4 MODELLING TECHNIQUES This chapter relates the theory in the previous section to the general form of the input data required for the AQWA suite The sections are closely associated with the sections of the input to the program All modelling techniques related to the calculations within AQWA LIBRIUM are presented This may produce duplication between manuals where the calculations are performed by other programs in the suite Other modelling techniques which are indirectly related are included to preserve subject integrity these are indicated accordingly Where modelling techniques are only associated with other programs in the AQWA suite the information may be found in the appropriate sections of the respective manuals the section numbers following correspond to those in the other manuals as a convenient cross reference Users formulating data from sources other than progr
103. ot the number input when utilising the program symmetry facilities Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 55 of 122 AQWA LIBRIUM User Manual Description of Output MASS AND INERTIA PROPERTIES STRUCTURE L ORS NUMBER OF ELEMENTS WEIGHT 3 3210 08 3 2566E 09 0 0000 00 0 0000 00 CENTRE OF GRAVITY 0 000 10 620 INERTIA MATRIX 3 625E 11 0 000E 00 0 000E 00 0 000E 00 3 420E 11 0 000E 00 0 000E 00 0 000E 00 3 599 11 Figure 7 5 Resultant Mass Inertia Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 56 of 122 AQWA LIBRIUM User Manual 7 2 DESCRIPTION OF ENVIRONMENT This information is output only if the program is starting at Stage 1 or the PRDL option is used to print this information from backing file The environmental parameters within AQWA LIBRIUM consist only of the water depth and density and the gravitational acceleration The static environment is output as shown in Figure 7 6 and is seen to contain these values eG hO B A LL PARAMETER WATER DEPTH a ama ama AmA 8 W a CS 250 000 DENSITY OF WATER 2 1025 000 ACCELERATION DUE GRAVITY 9 806 Description of Output Figure 7 6 Static Environment Contains proprietary and confidential information of ANSYS Inc and it
104. ov Forces FO Second Order Drift Forces Of these parameters only the linear stiffness matrix with the associated values of the buoyancy force and the second order drift forces are applicable to a static analysis using AQWA LIBRIUM For dynamic stability the added mass and damping matrices for drift frequency motion are also required Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 46 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation 6 2 2 Description of General Format The input format and restrictions in these decks are designed to provide maximum cross checking on the data input when the more advanced facilities are used This ensures that the program is able to output a suitable message to inform the user if the instructions for data preparation have been misinterpreted In any event the interpretation of the data input in these decks is output automatically in order that the user may check the results before proceeding to the next stage of the analysis It is important to recognise the different function of the specification of the frequencies and directions when using AQWA LINE which calculates the diffraction radiation analysis parameters than when using other programs to perform an analysis using these parameters Thus for AQWA LINE the range of frequencies and directions specified are those at which the parameters are to be calculated for AQWA LIBR
105. performs the search for equilibrium and therefore requires NO INPUT Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 51 of 122 AQWA LIBRIUM User Manual Description of Output CHAPTER 7 DESCRIPTION OF OUTPUT This chapter describes the comprehensive program output provided by AQWA LIBRIUM The various program stages perform different types of analyses and the output for each stage of the analysis is described in detail in the following sections Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 52 of 122 AQWA LIBRIUM User Manual Description of Output 7 1 STRUCTURAL DESCRIPTION OF BODY CHARACTERISTICS This information is only output when starting at Stage 1 or the PRDL option is used to print this information from backing file 7 1 1 Properties of All Body Elements The body surface geometry and mass characteristics are input to AQWA LIBRIUM through input Decks 1 to 4 see Section 6 1 These data decks define the following parameters see AQWA Reference Manual Node numbers and positions Elements used to model the body Material properties of the various elements Geometry group properties of the elements The information received by AQWA LIBRIUM to define the body characteristics is output for checking and the body s resultant centre of mass and inertia matrix are also output The nodal coordinates are outp
106. r bodies e g AQWA LINE mean drift force coefficients being input to AQWA LIBRIUM for an equilibrium analysis Efficiency when using any of the AQWA programs The restart facility allows the user to progress gradually through the solution of the problem and an error made at one stage of the analysis does not necessarily mean that all the previous work has been wasted The programs within the AQWA SUITE are as follows AQWA LIBRIUM Used to find the equilibrium characteristics of a moored or freely floating body or bodies Environmental loads may also be considered to act on the body e g wind wave drift and current AQWA LINE Used to calculate the wave loading and response of bodies when exposed to a regular harmonic wave environment The first order wave forces and second order wave drift forces are calculated in the frequency domain AQWA FER Used to analyse the coupled or uncoupled responses of floating bodies while operating in irregular waves The analysis is performed in the frequency domain AQWA NAUT Used to simulate the real time motion of a floating body or bodies while operating in regular or irregular waves Non linear Froude Krylov and hydrostatic forces are estimated under instantaneous incident wave surface Wind and current loads may also be considered If more than one body is being studied coupling effects between bodies may be considered AQWA DRIFT Used to simulate the real time motion of a floating body or bodies
107. re of gravity of the particular body see Section 3 3 and Figure 4 1 The AQWA suite employs a single common sign convention with the axes defined as in the AQWA Reference Manual Translations of a structure in the X Y and Z direction are termed SURGE SWAY and HEAVE and are positive in the positive direction of their respective associated axes The rotational freedoms are termed ROLL PITCH and YAW and are positive in a clockwise direction when looking along the coordinate axes from the origin The direction of wave or wave spectra propagation is defined relative to the positive X axis of the FRA and is positive in an anticlockwise direction when seen from above E g the heading angle is zero when the propagation is along the positive X axis and 90 degrees when along the positive Y axis of the FRA The position of each body is defined by the coordinates of its centre of gravity with respect to the FRA The orientation of the body is defined by three successive rotations about the OX OY and OZ axes in that specific order Within the program the orientation is defined by the direction cosines of the BODY FIXED AXES LSA with respect to the FRA Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 28 of 122 AQWA LIBRIUM User Manual Modelling Techniques PRA uses Figure 4 2 Axes Systems Contains proprietary and confidential information of ANSYS Inc and its su
108. required The models used by AQWA LIBRIUM follow closely the form used by the rest of the AQWA suite In most cases the same model should be applicable to all AQWA programs However the user may choose to adopt different models of the same system A typical example is the modelling of the hydrostatics of a wall sided pontoon In AQWA LIBRIUM the hydrostatic calculation is not affected by mesh size Therefore the complete side of a pontoon may be accurately modelled by one flat quadrilateral pressure plate In AQWA LINE the mesh size is governed by the wave length but only the wetted part of the hull requires modelling Hence the user may choose either to use two different meshes for the two programs or to use a mesh which is acceptable to both The former will lead to cheaper AQWA LIBRIUM runs while the latter will save the user from the labour of remodelling See Figure 4 1 for an illustration of the differences between an AQWA LINE and an AQWA LIBRIUM mesh The general modelling requirements for AQW A LIBRIUM are Analysis Models Static mass hydrostatics moorings current wind wave drift thrusters constraints Dynamic the same as above plus mass distribution hence inertia hydrodynamic properties The following subsection describes an exception to the above requirements 4 2 1 Following an AQWA LINE Run An AQWA LINE run is performed before an AQWA LIBRIUM run ONLY if it is considered that the second order mean wave drift forces i
109. rough an eigenvalue analysis of the equations of small perturbations from the equilibrium position In addition to the wind current mooring thruster and steady drift forces the analysis also accounts for the mass moment of inertia added mass and damping of the bodies at drift frequencies where drift frequencies in AQWA means frequencies lower than the start frequency defined for each wave spectrum Note the general dynamic stability analysis of the system in which the added mass and damping are frequency variant can be carried out in AGS inline calculation Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 9 of 122 AQWA LIBRIUM User Manual Program Description 22 THE COMPUTER PROGRAM The program AQWA LIBRIUM may be used on its own or as an integral part of AQWA SUITE of rigid body response programs When AQWA LINE has been run a data base is automatically created which contains full details of the forces acting on the body Another backing file called the RESTART FILE is also created and this contains all modelling information relating to the body or bodies being analysed These two files may be used with subsequent AQWA LIBRIUM runs The concept of using specific backing files for storage of information has two great advantages which are Ease of communication between AQWA programs so that different types of analyses can be done with the same model of the body o
110. rted on a structure by the mooring line P may therefore be written as P e ao ate t ase it 3 10 2 Notice that the constant term may be produced when the unstretched length is continually reset to the actual length i e e 0 The direction of this force will be given by the vector joining the two attachment points of the mooring line The elastic stiffness in the direction of the force is given by S e P e a 2a5e 3 10 3 If this elastic stiffness for a given extension is 5 and the tension is P then the 3X3 stiffness matrix relating the force to the translational displacements at the attachment point of the structure may be expressed as l K PNd N z h l5 l3 x L L 1 2 5 3 2 l3 3 10 4 where 1 1 13 unit vector joining the attachment points of the cable I 3x3 unit matrix L stretched length of the mooring line Note that K and the direction vector of the force P must be defined in the same axis system If the axis system chosen has the X axis coincident with the direction of P then the stiffness matrix will be diagonal with S as the value of the leading diagonal term corresponding to the coincident axis and the other two leading diagonal terms equal to P L e g for the X axis coincident Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 17 of 122 AQWA LIBRIUM User Manual Theoretical Formulation S
111. rties of Composite line information number non linear stiffness each section 1 1 order polynomial Weight length Miminum expected vertical coefficient distance between two ends 2 2 order polynomial Equivalent cross sectional Maximum expected vertical coefficient area distance between two ends 3 3 order polynomial Stiffness in terms of EA Sea bed slope at anchor coefficient point 4 4 order polynomial Maximum tension coefficient 5 5 order polynomial Unstretched length coefficient Note i Non linear moorings can have group properties whereas the linear moorings have specific individual properties 1 structure number of zero means that the mooring is attached to ground e g a pier sea bed etc The Equivalent Cross Sectional Area is equal to the Volumetric Displacement per unit Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates length of the Catenary In general this area is not the same as the Cross Sectional Area e g a chain will have a varying Cross Sectional Area along its length It is used to calculate the buoyancy force on the catenary which is assumed to be constant along its length Page 65 of 122 AQWA LIBRIUM User Manual Description of Output CABLE MOORING LINE C FT G U RSA T ION S ukum CABLE ATTACHMENTS STRUCTURE 0 IS GROUND COMBINATION CABLE ATTACHED TO NODE LINKED TO NODE UNSTRETCHED STIFFNESS WINCH FRICTI
112. s Page 63 of 122 AQWA LIBRIUM User Manual Description of Output Ree COON PIR AL PON Se CARS es CONSTRAINT JOINT DEFINED ON AT IN DIRECTION AND DIRECTION LINKED TO AT IN DIRECTION AND DIRECTION STRUCTURE NODE OF NODE OF NODE STRUCTURE NODE OF NODE OF NODE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER STRUCTURE ACTIVE FREEDOMS TABLE NUMBER Figure 7 13 Structure Constraints Table Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 64 of 122 AQWA LIBRIUM User Manual 7 4 3 Cable Line Mooring Configurations Description of Output The mooring line configurations table as shown in Figure 7 14 consisting of the individual mooring type and properties is output along with the mooring combination and group number The location of the line is identified by a pair of structure numbers and node numbers In the case of linear moorings i e linear lines winch loads and constant forces the properties are included in the general output either as stiffnesses or forces However in the case of non linear moorings i e a non linear hawsers or composite catenary mooring the properties are output in an additional table as shown in Figure 7 15 The parameter list depends on the mooring type and is defined in the following table Table 7 1 Parameters List for Non linear Moorings Parameter Polynomial curve fit of Catenary prope
113. s of the FRA are on the free surface Small Angle Stability Parameters These parameters are output in standard naval architectural terms They include the vertical distance between the centre of gravity and the centre of buoyancy measured w r t the centre of buoyancy The metacentres are also output together with the metacentric heights These allow the restoration per unit degree of rotation to be calculated and output Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 73 of 122 AQWA LIBRIUM User Manual Description of Output HYDROSTATIC PROPERTIES FREE FLOATING POSITION 0 629 GY 0 205 Gz HEAVE 2 8 141E 07 2 249 05 004 06 ROLL RX 2 249 05 2 441 10 922 04 PITCHIRY e 1 004 06 1 922 04 441 10 HYDROSTATIC DISPLACEMENT PROPERTIES MESH BASED DISPLACEMENT 24000 05 MASS BASED DISPLACEMENT 220 555 24000 05 POSITION OF THE CENTRE OF 621 203 000 AN INCOMPLETE ELEMENT DESCRIPTION OF F 000 THE HULL GIVES OUT OF BALANCE FORCES F 000 AND MOMENTS IF THE C O B IS NOT F 000 BELOW THE C O G THIS GIVES OUT OF 002 BALANCE MOMENTS FORCES ARE DIVIDED 009 BY THE WEIGHT AND ARE W R T AXES 000 PARALLEL TO THE FIXED REFERENCE AXES CUT WATER PLANE AREA PROPERTIES CUT WATER PLANE AREA oXov Www wow 8 100E 03 CENTRE OF FLOATATION I E CENTROID 0 617 POSITION IN THE FIXED REFERENCE AXE
114. s subsidiaries and affiliates Page 57 of 122 AQWA LIBRIUM User Manual Description of Output Following the static environment data the wave environment is output and AQWA LIBRIUM may have up to 50 wave frequencies periods and 41 associated wave directions for each body in the analysis The output summary of wave frequencies and directions is shown for structure 1 in Figure 7 7 The output also shows details of other wave related parameters Wave number i e 2 0 wavelength Maximum element size applicable to AQWA LINE NAUT Depth ratio The final piece of information given in Figure 7 7 relates to the frequency dependent parameters i e Drift Forces If these parameters have not already been input for certain frequencies then these frequencies are listed as having undefined parameters Wow FREQUENCIES PERIODS STRUCTURE FREQUENCY FREQUENCY PERIOD WAVE WAVE MAX ELEM DEPTH RATIO PARAMETERS RAD SEC HERTZ SECONDS NUMBER LENGTH SIZE Figure 7 7 Wave Particulars Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 58 of 122 AQWA LIBRIUM User Manual Description of Output 7 3 DESCRIPTION OF FLUID LOADING This information is output only when starting at Stage 1 or 2 or the PRDL option is used to print this information from backing file from AQWA LINE The output detailing the various types of fluid loading will now be describe
115. ser may either model the component body forms or provide their hydrostatic stiffness properties and specify a mooring configuration and environmental conditions The method of data preparation and modelling is fully described and reference is made to the AQWA Reference Manual The Reference Manual contains a complete guide to the format used for input of data into the AQWA Suite It is necessary that the AQWA LIBRIUM User Manual and AQWA Reference Manual be available when running the program AQW A LIBRIUM Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 8 of 122 AQWA LIBRIUM User Manual Program Description CHAPTER 2 PROGRAM DESCRIPTION AQWA LIBRIUM gives the equilibrium configuration and the stability properties both static and dynamic of a system of one or more floating bodies under the influence of mooring lines steady wind current thrusters and wave drifting forces 2 1 PROGRAM CAPABILITIES The program can accommodate up to 50 bodies 20 sea spectra and 100 mooring lines The mooring lines may be grouped together in not more than 25 combinations The program loops over the mooring combinations and sea spectra with the latter being the inner loop A mooring line can be modelled as a linear or non linear elastic weightless hawser a force with constant magnitude and direction a constant winch force or a composite catenary chain The sea spectra may take the Pierson Moskowitz
116. spended length w submerged weight per unit length AE stiffness per length X horizontal distance between fairlead point on the structure and contact point on seabed Z vertical distance between fairlead point on the structure and contact point on seabed H horizontal tension V vertical tension force at the fairlead point T total tension force at the fairlead point A non linear composite mooring line in terms of one or more elastic catenaries can be defined in AQWA with intermediate buoys or clump weights between catenaries Page 18 of 122 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates AQWA LIBRIUM User Manual Theoretical Formulation A numerical approach is used to calculate the stiffness matrix of composite mooring line 3 10 3 Translation of the Mooring Line Force and Stiffness Matrix The formulation of a vector translation may be applied directly to a force and displacement in order to translate the stiffness matrix K from the point of definition to the centre of gravity It should be noted however that if the stiffness matrix is defined in a fixed axis system which does not rotate with the structure an additional stiffness term is required This relates the change of moment created by a constant force applied at a point when the structure is rotated The full 6x6 stiffness matrix K for each mooring line relating displacements of the centre of gravity to
117. t all accelerations are zero in AQWA LIBRIUM Full account is taken of fluid velocity variation over the tube length The force arising from components of velocity in line with the tube axis is assumed to be zero and forces acting on the tube end discs are ignored Forces and Moments are calculated with respect to the local tube axis system as shown in Figure 3 1 then transformed to the global axis system Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 13 of 122 AQWA LIBRIUM User Manual Theoretical Formulation In general a partially submerged tube which is arbitrarily inclined may have a section which is either completely submerged partially submerged or completely out of the water Each tube element is classified as above and the forces and moments for each section are summed to obtain the total fluid load For static stability calculations only the tube drag force term in the above equation is considered since the structure and fluid accelerations are not included Figure 3 1 Local Tube Axis System 3 3 DIFFRACTION RADIATION WAVE FORCES Not applicable to AQWA LIBRIUM see AQWA LINE Manual 3 4 MEAN WAVE DRIFT FORCES This section is applicable only if it is considered that the mean wave drift force significantly affects the equilibrium configuration and the mooring loads The mean wave drifting forces and moments are calculated from a set o
118. than one equilibrium position For instance a capsized ship can still float in equilibrium if buoyancy is preserved Therefore it is important to start off the iteration with an approximation close to the required solution Also because of the non linearities in the system it is possible to overshoot and miss the intended equilibrium position Hence in practice dX can be scaled by a user defined under relaxation factor to ensure stability in the iteration scheme 3 12 2 Static Stability Analysis The program extracts the eigenvalues of the linearised stiffness matrix at equilibrium by the standard Jacobi successive rotation method Positive eigenvalues imply stable equilibrium and zero eigenvalues imply neutral stability If any of the eigenvalues are negative in sign it means that the body will not return to its equilibrium position after a small disturbance in any of the corresponding modes These eigenvalues are analogous to the meta centric height GM in transverse stability analysis of ships 3 12 3 Dynamic Stability Analysis Given the static equilibrium position of the floating system the equations of small motions X of the system about its equilibrium position can be written as MX Fw Fy Fp Fy 3 12 4 where overdot time derivatives Fy wave exciting force Ez hull drag force P damping force mooring force and M F did and F evaluated at the position X Expanding and neglecting
119. the structure in the wave spectra are calculated by AQWA LINE for each wave frequency and direction These mean wave drift forces are proportional to the square of the wave amplitude and only the horizontal wave forces and yaw moment are calculated if the far field solution is employed in AQWA LINE Page 88 of 122 Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates AQWA LIBRIUM User Manual Example of Program Use 8 1 7 Drift Frequency Added Mass and Damping The dynamic stability analysis requires that the drift frequency added mass and damping are defined It may be assumed that at low frequency the added mass and damping remain constant The values of added mass often used are those of the lowest wave frequency input in AQWA LINE This is normally a good approximation However for damping empirical values may be input based on either the experience of the user or experimental results For this example values of added mass at a frequency 0 349 period 18 secs will be used whilst hydrodynamic damping is set to be zero by default 8 1 8 Current and Wind Force Coefficients Data for the force coefficients for wind and current in this example are based on the projected area through the centroid in the three directions specified in Deck 6 as well as the drag coefficients at each heading Wind and Current forces per unit velocity acting on the body are given by Force 0 5 Density Are
120. the centre of gravity of the structure at equilibrium but does not include the stiffness contributions generated by the structure moorings RS DRO SoA IE STIFFNESS OF SP R U GC TURE Figure 7 24 Structure Hydrostatic Stiffness Matrix Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 77 of 122 AQWA LIBRIUM User Manual 7 7 3 Mooring Forces and Stiffness An output of the mooring forces and stiffness for a component mooring is shown in Figure 7 25 Note that LENGTH RANGE in the figure is the difference between the distance of two mooring line ends and the unstretched length of mooring 1 These are output for every mooring line and contribute additional stiffness to the global stiffness matrix see Figure 7 26 ine SPECTRUM NUMBER 1 MOORING COMBINATION TYPE LENGTH LENGTH NODE TENSION VERT ANGLE 64 05 18 06 38 06 77 06 FORCE X 64 05 16 03 93 02 15E 03 18 06 36 02 38 06 64 03 22 03 09 04 77 06 05 02 5 0 0 44 0 0 0 44 0 X 1 NUMBER OF LINES AT NODE TENSION STRUC VERT ANGLE LAID LN 64 05 18E 06 38E 06 77 06 4 FORCE X 64 05 16 03 93 02 15E 03 18 06 36 02 38 06 64 03 1 22 03 09 04 77 06 05 02 Description of Output NOTE STRUC
121. the user to output complete details of each element used in the body modelling All important details of the body elements are output together with the resultant properties of the bodies It should only be used when running AQWA LIBRIUM as an independent program ALDB READ AQWA LINE DATABASE Read the hydrodynamics database from the hydrodynamics HYD file created by a previous AQWA LINE run This option is used 1 if the user wishes to modify the hydrodynamic data calculated in a previous AQWA LINE run without having to re run the AQWA LINE radiation diffraction analysis 1 if the user is setting up an analysis with several structures and wishes to pick up the hydrodynamic data for one or more structures calculated in a previous AQWA LINE run Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 120 of 122 AQWA LIBRIUM User Manual Appendix A RDDB READ DATABASE Read the hydrodynamics database from the restart RES file created by a previous AQWA LINE run This option is used if the user wishes to modify the hydrodynamic data calculated in a previous AQWA LINE run without having to re run the AQWA LINE radiation diffraction analysis Note Normally this would be done using the option ALDB see above The RDDB option is only needed if the hydrodynamics file from the previous AQWA LINE run has been accidentally deleted Note that as the model definition has t
122. there is no input for Stage 4 of the analysis 6 4 1 Description of Physical Parameters Input The data input in these decks relates to the description of the analysis environment and the structure coefficients associated with the environment as follows Drift frequency added mass and damping NB Drift frequency is a frequency less than the start frequency in the wave spectrum definition If the dynamic stability in sea conditions is required from the analysis it is optional to input the added mass and damping which are assumed constant associated with the drift frequency motion Otherwise the program will obtain these values from the corresponding database in wave frequency range Wind and current loading coefficients and thruster forces These coefficients which are defined at directions specified in Deck 10 or in Deck 6 if a DIRN card is not present in Deck 10 are associated with the hull drag forces and are proportional to the square of the wind Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 49 of 122 AQWA LIBRIUM User Manual Data Requirement and Preparation current velocity These coefficients also contribute indirectly through the stiffness matrix i e rate of change of wind or current force with yaw Linearised current damping on hull is ignored see Section 4 10 in the dynamic stability calculation The thruster forces are maintained at both constant magnitud
123. tially submerged tubes but if the user wishes to Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 30 of 122 AQWA LIBRIUM User Manual Modelling Techniques suppress these calculations the drag coefficient on any or all tubes of a given structure may be set to zero Slender tube STUB elements differ from TUBE elements in the following respects 1 STUB elements permit tubes of non circular cross section to be modelled by allowing the tube properties diameter drag coefficient added mass coefficient to be specified in two directions at right angles 2 Longer lengths of tube can be input as the program automatically subdivides STUB elements into sections of shorter length for integration purposes 3 An improved second order version of Morisons equation is used to calculate the drag and inertia forces on STUB elements This is particularly useful in the study of dropped objects 4 STUB elements should however only be employed if the mean diameter is small compared with the length A DISC element DISC has no thickness and no mass users can define a PMAS and attach it to a disc if necessary but has drag coefficient and added mass coefficient in its normal direction Therefore a DISC does not have Froude Krylov and hydrostatic force A DISC element has only a drag force and an added mass force Reynolds number effects on drag can be important at model scale Drag coeffici
124. ucture returns to the equilibrium position by an exponentially decreasing oscillation at the specified fishtailing period excessively large fishtailing periods indicate a non oscillatory exponential decay 2 UNSTABLE There is a steady exponential drift away from the equilibrium position 3 FISHTAILING There is an exponentially increasing oscillation about the equilibrium position at the fishtailing frequency SPECTRUM NUMBER 3 FREQUENCY 0 0524 RADIANS SEC PERIOD 120 00 SECONDS FREQUENCY RADIANS SEC PERIOD SECONDS 186 7461 129 3943 91 9647 26 5247 25 9680 16 5292 DAMPING PER CENT CRIT 0 0061 1 3099 0 8796 0 0020 0 0018 0 1089 STABILITY STABLE STABLE STABLE STABLE STABLE STABLE TYPE OF MOTION STRUCTURE NUMBER FREEDOM AMP PHASE AMP PHASE AMP PHASE SURGE X SWAY Y HEAVE 2 ROLL RX PITCH RY YAW RZ 28789 YT79 Figure 7 28 Moored Vessel Dynamic Stability Characteristics Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 81 of 122 AQWA LIBRIUM User Manual Example of Program Use CHAPTER 8 EXAMPLE OF PROGRAM USE In this chapter an example problem using AQWA LIBRIUM is illustrated The problem is one in which AQWA LINE has been used to perform the analysis Stages 1 to 3 All steps in the subsequent analysis procedure are clearly shown from the problem definition through the data preparation to the final analysis run itself The method used in t
125. unstretched length The attachment points are specified as nodes and determine the direction of the constant tension The line is allowed to go slack when the distance between the nodes is less than the unstretched length If the user requires constant tension at all times a zero unstretched length may be input 4 15 3 Constant Force Line The program allows the user to input a force of constant magnitude and direction The direction of the force is specified by a node on the body and a second node chosen such that the force vector is directed from node 1 to node 2 Once the direction is defined the program maintains the magnitude and direction despite movement of the body This facility can be used to input environmental forces where details of the forces e g wind coefficients are not available a9 Extension e Figure 4 3 Load Extension Characteristics 4 15 4 Composite Catenary Line The composite catenary model admits elastic catenary lines Current drag on the line itself is ignored if without cable dynamics option The line is specified by the end nodes length weight in air per unit length and equivalent cross sectional area The equivalent cross sectional area is numerically equal to the volume of water displaced by a unit length of the chain The user may specify maximum tension in the line and possible highest and lowest vertical relative positions between the two attachment points
126. ut in the FRA and the format is shown in Figure 7 1 SR D DNA DA qu Bowen oem INPUT NODE SEQUENCE Figure 7 1 Nodal Coordinate Output Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 53 of 122 AQWA LIBRIUM User Manual Description of Output Following the nodal coordinates each body s element topology is output The body topology describes the elements used in the model of the body see Section 4 4 2 Details of each element are also output as seen in Figure 7 2 The bodies used each have a specific structure number associated with their output and this appears in the title of the output The element topology output may be enhanced by more detailed information This is obtained by using the PPEL program option i e Print Properties of Elements BOOK 4 D E MU E N SP T OQ P Q Ts Q G X ELEMENT NODE NODE MATERIAL GEOMETRY NUMBER TYPE NUMBER NUMBER NUMBER NUMBER NUMBER NUMBER Figure 7 2 Element Topology Output The body topology output references the material group number which has a mass or density value associated with it The material group numbers are output as shown in Figure 7 3 FO BOT BR oT As D PROPERTIE MATERIAL GROUP NUMBER DENSITY PARAM 1 3 3210E 08 0 0000 00 0 0000 00 Figure 7 3 Material Property Output Contains proprietary and confidential information of ANSYS Inc and its subsidiar
127. while operating in irregular waves Wave frequency motions and low period oscillatory drift motions may be considered Wind and current loading may also be applied to the body If more than one body is being studied coupling effects between bodies may be considered AQWA WAVE Used to transfer wave loads on a fixed or floating structure calculated by AQWA LINE to a finite element structure analysis package Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 10 of 122 AQWA LIBRIUM User Manual Theoretical Formulation CHAPTER 3 THEORETICAL FORMULATION The topic headings in this chapter indicate the main analysis procedures used by the AQWA suite of programs However detailed theory is given here only for those procedures used within AQWA LIBRIUM The theory of procedures used by other programs within the AQWA suite is described in detail in the appropriate program user manual References to these user manuals are given in those sections of this chapter where no detailed theory is presented Contains proprietary and confidential information of ANSYS Inc and its subsidiaries and affiliates Page 11 of 122 AQWA LIBRIUM User Manual Theoretical Formulation 3 1 HYDROSTATIC LOADING AQW A LIBRIUM calculates the hydrostatic forces and moments directly from the integral of hydrostatic pressure on all the elements which make up the submerged part of the body The cut waterplane area tog

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