Home

NAUTICUS HULL - DNV Exchange

1. and curvatures kK K of the continuous plating In mathematical terms the orthotropic macro material law takes the following form AN Ca Cp Cy Qi Qr Qs Ae AN Ca Cy Cy Qa Qy Q Ae AN Cy Cy Ca Q3 Qy Qs Ae AM Qi Qa Q Dy Dy Dha Ax AM Qo Qa Qz Da Da Dz Ax AM Ox Qa Q D Dy Dy Ax The symbol A indicates incremental properties By accepting local elastic buckling in stiffened panels under extreme loads the panel will behave in a non linear and more flexible way than under the standard linear response hypothesis This local panel flexibility is assessed in the PULS code as a set of reduced orthotropic macro stiffness coefficients defined as L N Cus C C Dog Dup D a B 1 2 3 Qag Qag Quy Each of the coefficients in the stiffness matrix has two contributions i e a linear part and a non linear part The linear part represents coefficients with the full stiffener rigidities smeared out DET NORSKE VERITAS PULS Nauticus User Manual 34 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 N N N over the total plate area The non linear corrections C D Q are assessed using a numerical procedure This and more details about the theory is explained in the Theory Manual Ref 3 The macro model stiffness relation is written on sub matrix notation as mile ole ells lad The bending extension coupling coefficients Q
2. DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 69 6 8 Running the program Standard mode or Capacity Curves The common use of the program is to use the Standard mode The standard mode gives the results by clicking the button on the toolbar or alternatively using the Solve option in the Panel menu The button have to be bold active for a case to be analysed A non bold button indicates a finalised analysis ready for saving In order for the Solve routine to work non zero external loads have to be specified in the input window Non zero external loads are automatically used as the reference load combination through which a proportional load history is prescribed The final result in the standard mode is the actual usage factor which is given in the Input Window as well as in the Detailed Window page see below The program can also be run in an alternative mode giving Capacity Curves This option is given in a separate Menu Capacity curves mean elastic local buckling eigenvalues elastic global buckling eigenvalues and ULS buckling boundaries in 2D load spaces If this mode is used the actual usage factor is not defined and consequently not calculated The 2D load spaces for capacity curve visualisation are i bi axial loads o ii axial shear loads T 3 iii transv shear loads T 3 For pre stress selection
3. Plate material A F 7 material properties Aluminium Modulus of elasticity MPa E proper ties also Poissons ratio v 03 available Shear modulus MPa not input G 80000 Yield strength plate MPa Sfp 355 Geometry Material Boundary conditions Axial stress MPa Cis 0 Cea 0 Transverse stress MPa Gns 0 0 ees oa 22 Specification of Shear stress MPa T 0 applied loads Lateral pressure MPa p 0 M Only pressure computation membrane M Only pressure computatio ding Compression positive Only pre ssure mo de Same computation method for membrane and bending but different stresses are shown in the stress plots membrane and bending Location of panel Integrated panel restrained in plane support all edges Default option Location of panel Choose C Girder panel free in plane support e between integr ated panel or girder panel Girder panel sets restrictions to which load components that can be non Zero Rotational support Rotation stiffness MNm m Left side Simply supported x I Vertical corrugated panel 2 sane Rotational support of plate Right side Clamped x I Horizontal corrugated panel Speci fy ei ther clampe d y U ide Si x Pe MMENnEnenn El simply supported or user Lower side Userdefined E 0 specified Also possible to specify corrugated panel DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6
4. DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 29 Stiffeners EEL 93 K l g Cz NSS SSS SSS SSS NNNnnn RRQ AAVVGAM M Mo Ag qa QA RE SSSSS_LLLHAA Fig 5 External load system Constant axial load and shear and linearly varying normal loads in transverse direction 3 6 Boundary conditions All four edges in the S3 element are taken as simply supported in the global buckling model In the local model the rotational restraint of the plate is determined by the influence from the stiffener The same restraint is implicitly assumed to act at the ends of the stiffened panel The in plane boundary conditions are by default so that all four edges are forced to remain straight This is representative of an integrated panel that is part of a larger structure Alternatively two opposite edges may be specified as free to pull in which is more representative for web girders stringers etc The stiffeners are by default continuous in the axial direction but may alternatively be specified as sniped This will reduce the support from the stiffeners to the plate 3 7 General available results When operated in the standard mode the PULS 2 0 code applies a proportional loading history I load space Along the proportional load history the following strength parameters are calculated i Local eigenvalue LEB SLS
5. ______ _ i Active data windows 6 Panel 2Detailed results T Panel 2 nnnnn nPanel 2_13mm Global eigenmode 8 Panel 2 nnnnn nPanel 2_13mm Local eigenmode Help menu not implemented Contents Search For Help On Check of current PULS version Version 2 0 About DET NORSKE VERITAS Nauticus Hull User Manual ProgramVersion 10 5 PULS Version 2 0 6 September 2006 PULS A toolbar for direct operation of some menu items is implemented as follows New panel same as new panel from File menu EA PULS Pane 1 Save file same as Save project on File menu Animation of Panel Results Capacity Curves Animation Window Help Print report in Word format to printer or to file Input parameters and main results Open project same as open project from File buckling process Direct button for Profile table same as Capacity curves define stiffener under panel menu button same as Solve Panel in Panel menu requires values on input loads DET NORSKE VERITAS Buttons for 3D graphic operations Alternative right hand mouse click when in 3D graphic window PULS Nauticus User Manual 60 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 The tree view control menu operates equal as to Windows Explorer It has the following layout Three view control menu Active Window SEURE Panel 7 Local eigenmode gt file Edit Panel Resu
6. DET NORSKE VERITAS PULS Nauticus User Manual 30 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 il Global eigenvalue GEB iii Ultimate capacity stress UC iv Buckling load minimum of eigenvalues and ultimate load v Usage factor n with reference to ultimate load and buckling load Vi Orthotropic macro stiffness coefficients Cog Dag 1 and 11 The eigenvalue and the corresponding eigenmode are ideal elastic buckling stresses with associated buckling shape for a stiffened panel with perfect flat geometry They are categorised into local LEB and global GEB modes They represent an idealized reference state at which the panel will start buckling deflecting out of plane iii The ultimate stress UC is the maximum nominal stress the panel can carry for the defined proportional load history iv The buckling load is defined as the minimum of the eigenvalues and the ultimate load Applicable if functional requirements are to be imposed SLS with the purpose of avoiding elastic buckling deflections of plates and stiffeners v The UC usage factor describes the margin between the applied loads and the corresponding ultimate capacity stresses The usage factor BS is measured against the buckling load vi Orthotropic macro coefficients represent the in plane and out of plane stiffness of the panel in an unloaded and loaded state They are reduced compared to the linear smeared macro coefficients taking into account
7. DIN YV NU NAUTICUS HULL USER MANUAL PULS DET NORSKE VERITAS NAUTICUS HULL USER MANUAL PULS SEPTEMBER 2006 Valid from Hull program version 10 5 Puls version 2 0 6 Developed and marketed by DET NORSKE VERITAS DNV Report No 2004 0406 Rev 02 Copyright 2004 2006 Det Norske Veritas All rights reserved No part of this book may be reproduced in any form or by any means without permission in writing from the publisher Published by Det Norske Veritas Veritasveien 1 N 1322 H vik NORWAY Telephone 47 67 57 76 50 Fax 47 67 57 72 72 E mail sales dnv software dnv com E mail support software support dnv com Website www dnv com software If any person suffers loss or damage which is proved to have been caused by any negligent act or ommision of Det Norske Veritas then Det norske Veritas shall pay compensation to such person for his proved direct loss or damage However the compensation shall not exceed an amount equal to ten times the fee charged for the service in question provided that the maximum compensation shall never exceed USD 2 million In this provision Det Norske Veritas shall mean the Foundation Det Norske Veritas as well as all its subsidiaries directors officers employees agents and any other acting on behalf of Det Norske Veritas Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 5 Contents 1 IN THOD GC TION sialic chi
8. Q enter due to the eccentricity effect of the one sided welded stiffeners This coupling effect is eliminated using a simple neutralisation procedure The resulting uncoupled moment curvature relation is M Dkx where neutral orthotropic bending stiffness matrix is D D Q Q GF The PULS S3 element calculates the macro model submatrices C Q D D for the linear state for the initial unloaded geometrically imperfect state and for an averaged state secant being representative for the ultimate strength assessment 3 9 Global level Overall elastic eigenvalue of panel GEB Global buckling is associated with an overall mode lifting the stiffeners out of plane together with the continuous plating assuming lateral support along all four outer edges see Fig 8 for illustration DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 35 b Fig 8 Examples of global buckling modes stiffeners lift out of plane together with the plating assessed by PULS GEB a Example for an axially compressed panel b Example for a transversely compressed and shear loaded panel The corresponding global elastic buckling level GEB eigenvalue is assessed using the classical orthotropic plate theory though as explained in chapter 3 6 3 with modified orthotropic macro material coefficients accounting for the local buckling effects With reference to the DNV rules Ref 4 Ref 5
9. All four edges supported laterally in plate plane Long edges locally elastically restrained as along primary stiffeners Transverse edges simply supported Two options for in plane support membrane support I Integrated panel all four edges restrained to be straight decks bottom etc G Girder panel two opposite plate edges free to pull in web girders etc Model imperfections Output Default model imperfections consistent with as welded steel panels and normal production tolerance standards User defined tolerances Damages imperfection sensitivity studies etc Ultimate Capacity UC Buckling Strength BS min of UC LEB GEB Usage factor UC ratio applied loads UC Usage factor BS ratio applied loads BS Local Eigenvalue LEB Global Eigenvalue GEB DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 25 Validity limits Plate slenderness s tp lt 200 s shortest edge between primary and sec stiffeners Max aspect ratio of plate between prim sec stiffeners 0 17 lt L s lt 20 Primary stiffeners Stiffener web slenderness for flat bar stiffeners h ty lt 35 Stiffener web slenderness Angle and T profiles hy tw lt 90 Free flange slenderness for Angle and T profiles fte lt 15 Minimum width of flange for Angle and T profiles b hy gt 0 22 Secondary stiffeners AV Stiffener web slendern
10. ProgramVersion 10 5 PULS Version 2 0 6 conditions iii Sniped primary stiffener option iv Tilted primary stiffener option v Improved imperfection control vi Improved lateral pressure model vii Capacity curves prestress option Unstiffened plate U3 i Rotational restraint may be specified for each edge individually ii Corrugated bulkhead option iii Alternative in plane boundary conditions iv Improved imperfection control Non regular stiffened plate T1 i New linear element formulation for plates with arbitrary oriented stiffeners sub versions will include bug fixing minor relevant improvements etc 1 4 Buckling of hull elements problem identifications A thin walled stiffened panel is the basic building block in ship hulls as illustrated in Fig 2 They are typically located in the bottom ship sides longitudinal and transverse bulkheads and in the deck structure Each stiffened panel is composed of individual component plates joined together along junction lines Depending on where in the structure the stiffened panel is located i e bottom deck shipside girder webs etc it will be subjected to different types of local loads DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 13 Global hull sections iy i a Fig 2 Ship hulls with stiffened panels as main building block Typically the main load c
11. state is used to control the bending and shear capacity of the stiffeners under the influence of combined lateral load and in plane loads Yielding in the stiffener flange at the transverse frames is accepted since stiffeners have significant strength reserves after first yield when subjected to lateral pressure The panel is loaded until the plastic capacity of the stiffeners is reached Two criteria are used for this limit state The first is the capacity of the top and bottom flanges to carry the combined axial force and bending moment resulting from the applied loads and the second is the capacity of the web to carry the shear force and axial force due to the applied loads The value for the four independent in plane stresses at the point of ultimate strength is defined as Oiu A Ozi AO Ozu AyOr gt Ozu A Ox The value of the A factor is calculated as the minimum explicit solution of the six limit states functions The solutions are found using a numerical procedure There exist one A for each limit state and the minimum of these is used as representative for the ultimate strength It follows per definition that it is the inverse of the UC usage factor n as defined in Chapter 3 9 3 10 2 Steel The steel limit states follow the six main stress control points as given above Different material yield stresses can be specified in the plate and stiffeners same in all stiffeners while only one set of values for the Young s modu
12. the lateral buckling mode or column buckling corresponds to the global buckling mode in PULS However in the DNV rules and most other international codes the lateral buckling mode neglects the plate effect altogether i e the column approach assumes lateral support only at two opposite edges typically being at transverse frame supports This is the reason while the column approach is not suited for analysing integrated stiffened panels in ship and offshore structures addressing the problem of combined in plane bi axial and in plane shear loads According to design principle iii Section 3 2 the present S3 element takes the global eigenvalue as the upper limit of the buckling capacity of the panel This is refereed to as GEB cut off in the present code and is consistent the Perry approach much referenced in the literature In the standard program mode the global eigenvalues are found by scaling the simultaneously combined loads 60 0291029 2 039 in proportion until global buckling takes place The global buckling loads are accordingly Sigg Age Ozio Age 201 OaE AgeF 20 2 Ozar Age 30 DET NORSKE VERITAS PULS Nauticus User Manual 36 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 where A is the global eigenvalue of the load parameter A found by the program The nominal Stresses O icz gt O 216E 02 20 gt 03cg are called the global elastic buckling stresses under a combined load situation The eigenvalue
13. Basic VB tools Subroutines are programmed in Fortran 2000 Two different user interfaces are available i Advanced Viewer AV Provides 3D graphical presentation of buckling modes membrane stress redistributions load interaction curves etc ii PULS Excel version with compatible input output data files with the AV version 1 3 Revision history The PULS revision history is summarized in the following table Prog Date Theory updates New program Comments Version functionality 1 2 4 April New imperfection model for U1 As for 1 2 3 2002 element 1 3 May New local buckling model Local eigenvalues for Aluminium 2002 implemented for stiffened panels pure shear and shear in option locked S2 comb with normal alu can be stresses shown Shown specified in More correct local buckling DET NORSKE VERITAS PULS 10 September 2006 Nauticus User Manual ProgramVersion 10 5 PULS Version 2 0 6 assessment of slender stiffener webs in steel mode but rotational restraint effects from no HAZ stiffeners detail result window effects Local shear buckling assessment sm PEN eipeimode Moet with rotational restraint effects from Migs stiffeners in capacity curves Improved imperfection modelling as window default user specified imp as option Status bar Recalculate the project option File menu Extended imperfection settings Increased control of change of input values c
14. Fig 13 Capacity Curves in 2D load space bi axial loading all quadrants thin plate DET NORSKE VERITAS PULS Nauticus User Manual 72 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 gt E Global elastic buckling Local elastic buckling ULS Limitstate 1 Limitstate 2 Limitstate 3 F Limitstate 4 Limitstate 5 Fig 14 Capacity Curves in 2D load space bi axial loading all quadrants thick plate Similar capacity curves are available in the other two load spaces where shear stresses are one of the load components Fig 15 shows an example including shear Note the symmetry in the shear load T12 03 gt E Global elastic buckling ULSS Limitstate 4 amp Limitstate 2 amp Limitstate 3 7 Limitstate 4 amp Limitstate 5 Fig 15 Capacity Curves in 2D load space transverse load o2 and shear o3 71 all quadrants DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 73 Elastic buckling s_2 0 amp ULS p 0 s_2 0 Fig 16 Capacity Curves in 2D load space for U3 element unstiffened plate axial stress c and shear stress 63 T12 all quadrants An example of 2D Capacity curves for the U3 element is given in Fig 16 for combined axial nominal stress o and nominal shear stress 63 T12 As can be seen the example is for relatively thin plate for which the UC strength i
15. September 2006 67 6 7 Input window Defining the T1 element triangular plate NB Note that all input numbers entered has to be followed by a tab entry for proper registration A tab reminder is given on the status bar at bottom whenever a new number is entered into a cell Active picture for easy definition E of stiffener location Define new 5 Panel 2 T1 i i General Panel particulars stiffener by clicking on picture Identification eroe nete xxs p Change location of stiffener by Panel 2 Rene clicking on relevant end point stiffener onto f f Allowable usage factor theplate The plate dimensions must be set before the stiffeners can be defined T stowable BS 7 100 Comments Change between moment of inertia input or stiffener x i scantlings input Geometry Material Loads Boundary conditions Actual usage factor maie toni Panel length mm L 3000 DARET Delete stiffener r 2f input ot moment Panel width mm L2 1000 Plate thickness mm tp 10 Identification f3 x 9 arae ernia Buckling strength SCHED Orientation Scantling 0 00 Not OK ui Status No End point 1 X 2443 Stiffener type T profile x End point 1 709 Stiffener height mm h 300 End point 2 X 136 Web thicknegs mm tw 10 End point e414 Flange width mm b 90 Flange thickness mm t 15 Flange eccentricity e Tilt angle degrees g 0 Web sle
16. a given load combination nominal applied stresses load control as specified by the user This corresponds to the standard mode of program operation The results are presented as elastic buckling eigenvalues and ultimate strength nominal capacities and summarized in a detailed result table As a single parameter result the safety margin in the form of usage factor is given both related to buckling BS and ultimate capacity UC The usage factor provides a measure of the difference between the user specified loads and the corresponding ultimate capacity UC or buckling strength BS The PULS AV program also provides capacity curves under combined loads The capacity curves are illustrated in two dimensional load spaces They are to be understood as limit boundaries covering the load space selected by the user They inform about the strength of the plates in the different load directions and under any load combination In this mode the usage factor is not calculated as it is not defined The term capacity curve is demonstrated in Section 5 7 DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 15 2 U3 UNSTIFFENED PLATE ELEMENT 2 1 General The U3 unstiffened plate element applies Marguerre s non linear plate theory geometrical non linearity The elastic buckling eigenvalues and non linear postbuckling problem are solved using a multiple degree of freedom model in terms of
17. aluminium Loads Buckling Strength BS and Ultimate Capacity UC can be estimated for linearly varying longitudinal compression tension linearly varying transverse compression tension and uniform shear and for all possible in plane load combinations of these Lateral pressure can also be specified Boundary conditions For all load combinations simply supported out of plane free to rotate but laterally fixed and constrained in plane straight but movable in plane edges are by default assumed along all four boundaries Alternative boundary conditions may be specified by the user 2 Element S3 Uni axially stiffened plate Field of application Integrated hull element between laterally rigid structures such as frames bulkheads etc Rectangular plate with primary stiffeners in axial direction Based on non linear theory Primary Stiffeners Welded open profiles Angle T bulb or flat bar profiles Secondary Stiffeners option Perpendicular to primary stiffeners simplified theory Material Steel and aluminium Loads Buckling Strength BS and Ultimate Capacity UC can be estimated for uniform longitudinal compression tension linearly varying transverse compression tension and uniform shear and for all possible in plane load combinations Lateral pressure can be specified and is assumed to act across several bays in the continuous primary stiffener direction Boundary conditions For all load combinations simply supported out
18. are given as O 5A Op O2 Adw2 O A Oy O A0n O A Oy where A is the load factor automatically controlled by the program A subscript 0 on the nominal external stresses indicates the values of the input values i e they corresponds to A 1 4 6 Available results The following strength parameters are calculated for the T1 element 1 Eigenvalue ii Buckling load iii Usage factor n with reference to buckling load DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 49 1 The eigenvalue and the corresponding eigenmode are ideal elastic buckling stresses with associated buckling shape for a stiffened panel with perfect flat geometry They represent an idealized reference state at which the panel will start buckling deflecting out of plane ii The buckling load is defined as the load at the onset of yield Since linear theory is used the buckling load is always lower than the eigenvalue iii The usage factor describes the margin between the applied loads and the corresponding buckling load Graphical results available are plots of the minimum eigenmode the model imperfection and the ultimate limit state deflection mode In addition membrane stress plots are produced 4 7 Safety margin The safety margin is presented as the usage factor defined as Gini Gua Gry Gaya 5 2 2 2 2 2 F101 O19 9 021 020 2 O39 Th
19. in the original plate plane This implies full utilisation of normal compressive and DET NORSKE VERITAS PULS Nauticus User Manual 26 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 tension fields Alternatively two opposite edges may be specified as free to pull in for analysis of web girders stringers etc In order not to exceed the range of validity of the theory used in the S3 sub element the following slenderness requirements of component plate elements in a cross section are formulated i General Web slenderness for flat bar stiffeners h t lt 35 Web slenderness for L or T profiles h t lt 90 Free flange for L or T profiles f ft lt 15 Plate between stiffeners s t lt 200 Aspect ration of plate between stiffeners 0 17 lt L s lt 20 Flange width for L or T profiles h h gt 0 22 NB Note that the real validity limit for the plate between stiffeners may well exceed this recommended limit if the actual load condition analysed enforces a wave pattern sufficiently described by less than 20 1 21 half waves in the axial direction x direction The local minimum eigenmode can give a hint of the real validity limit of the ULS capacity calculated by PULS These validity limits are checked by the program An error message is given when limits are exceeded A summary is given on the status bar shown in the bottom of the PULS AV window 3 4 General S3 element design principles The S
20. pressure distribution is uniform all across all bays Theoretically this means that the model includes both symmetric deflection modes CS for assessing the pressure effect and asymmetric modes SS for assessing the buckling effect with respect to the global stiffener bending in x direction as illustrated schematically in Fig 11 below Ni OLEPPEPEPEPEP EPP PPT Titty DET NORSKE VERITAS PULS Nauticus User Manual 42 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Fig 11 Deflection of a stiffener in the simply supported mode SS asymmetric modes top and the clamped mode CS symmetric modes bottom Maximum pressure criteria are introduced representing practical design boundaries for the stiffeners They kick in and present themselves in dialog boxes with stated limits not to be exceeded Two different pressure limits are specified one for controlling the bending stiffness of the stiffener plate unit and one for controlling the shear area of the stiffener web They are based on linear beam theory The bending stiffness pressure limit prs is W nii Prs 12 0p Si where W min is the minimum section modulus of the stiffener plate unit normally being at the stiffener flange position W nin h 0 5t 0 5t z where the moment of inertia of the plate stiffener unit is 1 4b t b t h 0 5t 0 5t z tyh hyt 05h 0 5t z bst3 st z and Zg is the neutral axis measured from the
21. problem is formulated as K AK q 0 K is the small displacement stiffness matrix K is the geometrical stiffness matrix and q is the eigenvector 3 10 Local stress limit states Ultimate strength evaluation 3 10 1 General The S3 element includes non linear elastic models for both the global mode orthotropic plate theory and the local mode isotropic plate theory with plate stiffener compatibility These non linear models are run in sequence with a logging of the response for local stress registration to be used in the subsequent limit state evaluations The limit state evaluations are based on the redistributed membrane stress distributions within the stiffened panel Membrane stresses in this context means stresses in the middle plane of the individual thin walled component plates plating stiffener web stiffener flange of which the stiffened panel is built Thus membrane stresses can be a purely local effect due to local plate stiffener buckling or they arise from global bending effects of the stiffener the latter due to compressive in plane forces or lateral pressure Due to local buckling of the component plates in a cross section the membrane stress will redistribute as compared to neglecting buckling effects For thin plates and stiffeners the redistributions will be significant Typically the stresses in the hard corners critical positions along plate edges plate stiffener junction lines etc will be higher than in mid regi
22. the non linear effect of local elastic buckling of plates and stiffeners They can be used as reduced efficiency elements in linear FE models or as reduced stiffness elements in simple hull girder models Graphical results available are plots of minimum eigenmodes imperfection modes and ultimate limit state deflection modes In addition membrane stress plots are produced The calculated parameters are more thoroughly explained in the following sections 3 8 Local level Elastic Eigenvalue and reduced stiffness properties 3 8 1 General Local buckling is classified as modes associated with pure local deflections of the component plates in the cross section i e as per definition the stiffener junctions to the continuous plating act as nodal lines in the local buckling pattern The local level assesses the eigenvalue and the postbuckling strength of panels buckling exclusively into local modes Local geometrical imperfection effects and residual stress effects are implicitly considered in a set of orthotropic macro material coefficients From an overall point of view the stiffened panel is then considered as an orthotropic panel in which the orthotropic macro material coefficients have reduced stiffness efficiency properties compared to linear elastic values thus accounting for the local buckling on the overall strength DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 31 Fo
23. varying normal stress in x direction Uniform in plane shear stress x x2 plane Materials Isotropic elastic material E v Material yield stress in plate used in buckling strength assessment Boundary conditions Out of plane support bending support All four edges supported laterally in plate plane Rotational restraint control of each edge free to rotate rotationally restrained or clamped Stiffener with rotational spring stiffness to simulate partly restrained edges Model imperfections Automatically set default model tolerances consistent with as welded panels Output Buckling Strength BS Usage factor BS ratio applied loads BS Minimum Eigenvalue Validity limits Max slenderness ee ee f O yield min eigenvalue Max stiffener slenderness Stiffener web slenderness for flat bar stiffeners h t lt 35 Stiffener web slenderness Angle and T profiles hy ty lt 90 Free flange slenderness for Angle and T profiles ftp lt 15 Table 3 Overview of T1 element characteristics DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 47 4 3 Element limitations slenderness requirements The present PULS T1 element has the following range of application Geometry Rectangular stiffened plate with stiffeners oriented in any direction Profiles Open profile type with standard angle shape eccentric angle symmetric T or
24. yet PULS Panel 3 Detailed results Jog gt Fle Edt Panel Animation Window Help a x D osla a lele Biz iu el m vaala bulkcarrier side pane Detailed results summary Standard parameters Pane 1 Cross sectional area Design lateral pressure parameters one stiffeneriplate unit Panel 2 Area of one stiffener mm 2 11566 Max bending stress at design pressure MPa 259 22 Panel 3 Total area for plate and stiffeners mm 2 736260 Max shear stress at design pressure MPa 70 T Detailed result Max von Mises stress in plate at design pressure MPa 164 9 Eigenmodes Cross sectional bending data one stiffener plate unit Max won Mises stress in flange at design pressure MPa 268 a Imperfections Moment of inertia one plate stitfener unit mm 4 1 73609 Neutral iddle plate pl ULS modes eutral axis above middle plate plane mm 3 203 211 _ Maximum lateral pressure parameters one stiffeneriplate unit E Pressure Beclonalimement at midale plate plane IMMO 8 496 08 Lateral pressure at first pure bending stress yield MPa 0215 9 Panel 4 Sectional moment at stiffener top mm 3 3 486 08 Lateral pressure at plastic hinge at support MPa 0 308 E Detailed result Cross sectional capacity parameters one stiffener plate unit Eaei peee St piae collaps
25. 04 16 Steen E Byklum E and Vilming Kjetil G Computer efficient non linear buckling models for capacity assessments of stiffened panels subjected to combined loads ICTWS 2204 Fourth International Conference on Thin Walled structures 22 24 June Loughorough University UK 17 Steen E Byklum E Vilming K G and stvold T K Computerized Buckling Models for Ultimate Strength Assessment of Stiffened Ship Hull Panels PRADS 2204 Lubeck Travemunde Germany 18 Brubak L Hellesland J Steen E Byklum E Aprroximate buckling strength analysis of plates with arbitrarly oriented stiffeners NSCM 2004 Nordic Seminar on Computational Mechanics KTH Stockholm Sweden NOTATION o Nominal uniform stress in stiffener direction i e along x axis compression positive tension negative unit N mm O Nominal uniform stress in perpendicular to stiffener direction i e along x2 axis compression positive tension negative unit N mm Nominal uniform in plane shear stress positive negative unit N mm Tis Shear stress same as Op Characteristic yield stress unit N mm Om Characteristic yield stress of plate unit N mm Oop Characteristic yield stress of stiffener unit N mm E Young s modulus N mm v Poisson s ratio G Shear module not input G E 2 1 v n Calculated usage factor for actual applied load combination DET NORSKE VERITAS Nauticus Hull User Ma
26. 3 element applied in an ULS design application is based on the following main principles i Elastic local buckling of any of the component plates in a panel section is accepted Local buckling is classified as all modes where the stiffener plate junction lines act as nodal lines in the buckling pattern For open profiles local elastic buckling means buckling of the plating between stiffeners sideways torsional buckling of stiffeners stiffener web plate buckling and interactions between these modes ii Permanent buckles are not accepted By ensuring the maximum membrane stresses within a panel to stay below the yield stress condition von Mises excessive permanent sets and buckles are prevented DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 27 iii Global overall buckling of the panel is not accepted GEB cut off This principle ensures the panel as a whole to have sufficient out of plane bending stiffness to avoid global buckling overall stiffener buckling see Fig 8 for illustration Sufficient overall bending stiffness of the stiffeners ensures lateral support to the component plates which is a reasonable requirement for accepting local elastic buckling of these principle i In sum the present ULS philosophy predicts an ultimate strength value accepting elastic local buckling deflections of plates and stiffeners while preventing excessive permanent damages
27. 82 3 University of Oslo Department of Mathematics Mechanics Division 1999 Steen E and stvold T K Basis for a new buckling model for strength assessment of stiffened panels DNV Seminar Buckling and Ultimate Strength of Ship structures 20 September 2000 H vik Norway stvold T K and Steen E Windows program implementation of new buckling code DNV Seminar Buckling and Ultimate Strength of Ship structures 20 September 2000 H vik Norway Steen E and stvold T K Simplified treatment of buckling effects in global linear FE ship models using an orthotropic macro material modelling technique DNV Seminar Buckling and Ultimate Strength of Ship structures 20 September 2000 H vik Norway Byklum E and Amdahl J A simplified method for elastic large deflection analysis DET NORSKE VERITAS PULS 88 Nauticus User Manual September 2006 ProgramVersion 10 5 PULS Version 2 0 6 of plates and stiffened panels due to local buckling Thin Walled Structures vol 40 no 11 pp 923 951 2002 14 Byklum E Ultimate strength analysis of stiffened steel and aluminium panels using semi analytical methods Dr ing thesis Department of Marine Technology Norwegian University of Science and Technology 2002 15 Byklum E Steen E and Amdahl J A semi analytical for global buckling and postbuckling analysis of stiffened plates Thin Walled Structures vol 42 no 5 pp 701 717 20
28. For the T1 element the in plane boundary conditions are not relevant since linear theory is used The U3 element is assumed to have uniform plate thickness The S3 element is assumed to have constant plate thickness and stiffener proportions across the panel The T1 element is assumed to have uniform plate thickness but may have stiffeners with different proportions DET NORSKE VERITAS PULS Nauticus User Manual 52 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 The PULS code concept isolates a rectangular panel and prescribes a set of external loads across the panel surface For the S3 element the prescribed external nominal loads stresses have to be uniformly distributed in the axial direction but may be linearly varying in the transverse direction Long edges Short edge 030 N I Snort eage O10 Sie ae _ 010 os oO lt 020 Fig 12 Rectangular panel definition of supported edges and applied loads Limitations and fields of applications of the PULS 2 0 code are summarised in Table 1 in Section 5 2 Usage hints are given in Chapter 6 DET NORSKE VERITAS Nauticus Hull User Manual ProgramVersion 10 5 PULS Version 2 0 6 September 2006 PULS 53 5 2 Applications For overview typical ship hull areas of application for the U3 and S3 elements are tabulated below Short edges Long edges Remark Misc PULS element Edges 1 Edges 2 Applica
29. Fourier expansions The plate can be subjected to combined load situations and the numerical procedure scale the applied loads up to collapse Stress control criteria describe the onset of material yielding in the highest loaded position along the plate edges using the redistributed membrane stress distribution The redistributed membrane stresses consist of the external applied nominal stresses added to the second order stress distribution arising due to elastic buckling and due to presence of geometrical imperfections from production The values of the proportionally scaled loads at the onset of first edge membrane yield is taken as representative for the UC values UC values based on such first yield criteria for thin walled designs are close to the real UC values and on the conservative side In addition to the UC value the ideal elastic buckling stress eigenvalue is calculated Linear Elastic Buckling Using default tolerance settings and boundary conditions and characteristic yield strength as specified in the rules the code predicts UC strength values representative for integrated plates in larger flat plate constructions Alternatively the in plane boundary conditions may be specified as free so that an isolated unstiffened plate is represented User specified tolerance input for the max amplitude is optionally The default tolerance amplitude is specified in terms of a maximum amplitude delta s 200 The tolerance shape is a
30. K Ultimate stress and usage factor for each Table showing the maximum limit state minimum ultimate stress displacement selected locations given in detail result summary above in panel Stiffness coefficients sheet Orthotropic macro stiffness coefficients L linear I initial U ultimate secant DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 77 Standard Parameters sheet The stiffened panel element has also a Standard parameter list Most of these parameters are not a part of the PULS buckling models and they are only meant as general user info They are categorised into Cross sectional data cross sectional data for plate and stiffener x const Cross sectional bending data valid for one stiffener plate unit full plate width s is included Cross sectional capacity parameters standard moment and shear load capacities Numerical parameters number of increments in PULS procedure Design lateral pressure parameters Stresses in single stiffener plate unit according to linear beam theory for the prescribed pressure Maximum lateral pressure parameters one stiffener plate unit pressure limits according to linear beam theory for a single plate stiffener unit Maximum lateral pressure parameters plate reference pressure limit pp based on first edge bending stress limit for a clamped plate unit with length s JTP requirements sheet Not implemented
31. Panel 1 U3 fa Ene Detailed result summary Model imperfection Pressure Applied loads Ultimate loads Buckling loads Eigenvalue Ultimate capacity mode Detailed results Allowable usage factor E Panel 2 T1 9 1 1MPa fi00 00 124 75 75 Panel 3 S3 S Detailed results 1 2MPa 100 00 124 75 75 gt MPa 0 00 0 0 0 Ultimate capacity Status 02 2 MPa 0 00 0 0 81 OK Typ MPa Buckling strength Status p IMPa 1 33 Not OK External Ultimate Elastic nominal prescribed nominal stresses buckling stresses nominal stresses Minimum of eigenvalues stresses elastic buckling stresses and ultimate stress J Ready Plate slend OK Aspect ratio OK Imperfections Default 6 12 Status bar The status tool bar is located at the bottom of the Window Below is given examples for the stiffened panel S3 Ready Plate slend OK Web slend OK Flange slend OK Aspect ratio OK Imperfections Defa lt i L 7 Press Tab key Plate slend OK Web slend OK Flange slend OK Aspect ratio OK Imperfections Defa LI p JE Recalculation needed Plate slend OK Web slend OK Flange slend OK Aspect ratio OK Imperfections Defa Ready program ready Press Tab key a new number has entered a cell tab to next field to register the number Recalculation necessary A new set of data has
32. ULS curves with specified factor Option for cancelling GEB cut off Scaling of axes None axes in MPa actor for scaling the loads pressure will not be scaled Scaling of axes None ai umber of points pa Cancel Number of points Number of points describing the capacity curves in specified Load range number of analyses Max allowable 64 points Alternative non dim axes scaled with yield stress DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 71 A set of capacity curves in the 2D load space according to i classification above is shown in Fig 13 for a constructed S3 element example The red curve indicates the global elastic buckling boundary GEB which always will be the very outer curve according to the adopted design principles see chap 3 3 design principle ii1 The blue curve indicates local elastic buckling LEB and the violet curve is the ULS curve Note that the local elastic buckling boundary LEB is below the ULS boundary in a limited region in load space for this example This is typical for cases where the plate is thin For thicker plates the ULS boundary curve will be the inner curve in the whole load space See Fig 14 for illustration of such a case Global elastic buckling Local elastic buckling ULS Limitstate 1 Limitstate 2 Limitstate 3 Limitstate 4 Fd aool t Limitstate 5
33. ULS design for ships corresponds to an extreme load condition typically the probably largest loading experienced in a 20 years period These ULS design principles are established in order to constrain the panel designs to have some minimum stiffness properties for efficient in plane load transfer The principles are consistent with the present DNV rules and guidelines even though in the latter they are not explicitly stated and not consistently included for combined load situations In some cases it will from serviceability functional reasons SLS not be acceptable that local elastic buckling takes place In such cases the local elastic buckling boundary LEB and GEB cut off can be used as the upper limit of allowable load application The ultimate limit state calculation procedure for the S3 element can be split into three levels i Local level Establishment of orthotropic macro material coefficients and assessment of local eigenvalues Non linear analysis il Global level Eigenvalue calculation of the global overall mode GEB and nonlinear global deflection analysis including knock down effects from local buckling postbuckling and local imperfections residual stresses ili Ultimate limit state Global non linear analysis with explicit solution of different limit state functions for identifying the most critical failure hot spot location and corresponding loads acting on the panel The calculation procedure is illustrated schemat
34. a ue Zs ule Applied nominal stresses loads reference nominal stresses loads 000 DET NORSKE VERITAS
35. also be specified covering a special application of local pressure on a plate NB Capacity curves involves a sequence of non linear calculations for different load paths and may require some computer time number of load paths number of points in load space number of fixed stress values S3 element i Detailed results summary The applied nominal stresses are listed together with the ultimate stresses the eigenvalues in local and global mode and the usage factor The results are based on a proportional load path for the in plane stresses meaning the same ratio between each nominal stress component applied at the point of elastic buckling eigenvalues and ultimate state The lateral pressure is as specified in the input i e it is kept fixed The results for each of the five limit states are listed The critical limit state is picked out and given in the detailed summary list A set of orthotropic stiffness coefficients are given indicating the degree of reduced stiffness increased flexibility of the panel due to local buckling from the plate between stiffener and sideways buckling of stiffeners The stiffness coefficients given in PULS 1 5 represent linear values sub superscript L and tangent values for zero load sub superscript I and at the secant values as representative for the ultimate state sub superscript U A superscript N symbolises neutral relevant for the bending stiffness about the instaneous neutral axis of plate an
36. ar tdesie A E A atte 7 1 1 General 7 1 2 Approach 9 1 3 Revision history 9 1 4 Buckling of hull elements problem identifications 12 2 U3 UNSTIFFENED PLATE ELEMENT ssicaiseccapardiiaiunanaraiaers 15 2 1 General 15 2 2 Overview of element characteristics 15 2 3 Element limitations slenderness requirements 17 2 4 General U3 element design principles 17 2 5 External prescribed loads 17 2 6 Boundary conditions 19 od Available Results 20 2 8 Safety margin 20 2 9 Capacity curves 21 2 10 Lateral pressure 21 3 S3 STIFFENED PANEL ELEMENT iiccudsncavasteaste aia autores 23 3 1 General 23 3 2 Overview of element characteristics 23 3 3 Element limitations slenderness requirements 25 3 4 General S3 element design principles 26 3 5 External prescribed loads 28 3 6 Boundary conditions 29 3 7 General available results 29 3 8 Local level Elastic Eigenvalue and reduced stiffness properties 30 3 8 1 General 30 3 8 2 Local eigenvalue LEB 31 3 8 3 Orthotropic material coefficients 32 3 9 Global level Overall elastic eigenvalue of panel GEB 34 DET NORSKE VERITAS PULS Nauticus User Manual 6 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 3 10 Local stress limit states Ultimate strength evaluation 36 3 10 1 General 36 3 10 2 Steel 38 3 10 3 Aluminium 39 3 11 Safety margin 39 3 12 Capacity Curves 41 3 13 Lateral pressure 41 4 T1 STIFFENED PLATE ELEMENT NON REGULAR GEOMETRY 45 4 1 General 45 4 2 Overview of element
37. as shown in the example DET NORSKE VERITAS Nauticus Hull User Manual ProgramVersion 10 5 PULS Version 2 0 6 September 2006 PULS 85 2 Delete save old results Delete or save the results already written to the output sheet KRN PULS 2 0 Unstiffened panel U3 input DNY Clear input sheet Import unstiffened panels from file Define corrugated panel Calculate panel s Panel illustration figure Calculate and export panels to file Analysis options Allowable usage factor a Delete old Ultimate capacity puc 1 Rowbyrow onis Buckling strength as 1 Save od c c Combinations of input ts Please see comment boxes cells marked with red triangles for further explanation of features input Pressure In plane Rotational support Identification Length of Width of Plate Modulus of Poisson s Yield st Axial Axial Transversal Transversal Shear of panel plate plate thickness elasticity ratio plate stress stress stress stress stress fixed support L1 2 tp E v ey Os Bi Dz Ons Ty P Left Right Upper Lower mm mm mm MPa MPa MPa MPa MPa MPa MPa MPa MNmm _MNmm __ MNmm _MNmm test panel 3000 1000 10 208000 0 3 315 100 100 0 0 0 Ojint 0 0 0 4000 12 0 0 1001 100 0 0 14 7 5 Result sheets All parameters regarding each panel are written to the output sheet A Set extent button is made so that the user easily can hide and show the desired columns An alternati
38. ate tab high and slender stiffeners added a S strip under detailed short wave local pattern for axially 5 3 result folder It gives compressed panels having a min linear parameters such as eigenmode in local 1 1 mode cross sectional data Consequence Predicts more RF f ne moment of inertia of conservative and realistic ULS stitfenerfnl te unit et strength than 1 4 for axially p compressed panels with very high Animation of non webs and flanged profiles linear buckling v Updated aluminium model with response separate i menu on tool bar for HAZ corrections A i animation of non linear vi aspect ratio of plate between buckling response NB stiffeners from 14 PULS 1 4 to may take long time for range 0 25 10 for covering cases thin plates and cases with closely spaced secondary with much elastic stiffeners buckling 10 15 inut Improvements of unstiffened plate mintes U1 theory Lateral pressure as ce J d bl it i Updated aluminium model with Le oe Diets fare HAZ corrections i Separate option in capacity curves settings GEB cut off and scaling of ULS capacity curve as allowable usage factor This gives the capacity curves as required strength envelope 2 0 April Stiffened panel S3 2004 i Linearly varying load in the transverse direction ii Alternative in plane boundary DET NORSKE VERITAS PULS 12 September 2006 Nauticus User Manual
39. been registered recalculation is necessary for updated buckling and ULS strength DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 79 6 13 Program hints The usage hints are given here for overview It refers both to program operation and how to address special problems and applications cases General 1 User specified model tolerances can be specified for the plate and stiffener U3 and S3 see under Panel menu on tool bar In current version only model imperfection amplitudes not imperfection forms can be specified Default settings correspond to normal fabrication standards of steel structures ii Excel Report can be printed see under File menu Always remember to press the solve button before printing in order to avoid mismatch between input data and results This is controlled also by the status bar information at the bottom of the PULS Windows General Eigenmode Imperfection Pressure and ULS mode windows i The windows figures and plots can be copied and pasted into other programs such as Word etc ii By clicking the right mouse bottom a property menu for the graphic is available iii By holding the pointer over the panel a tool tip box appears and shows the displacement or stress depending on plot in the selected point General Capacity Curve Windows i The capacity curves elastic buckling and ULS can be copied and pasted as numbers int
40. characteristics 45 4 3 Element limitations slenderness requirements 47 4 4 General T1 element design principles 48 4 5 External prescribed loads 48 4 6 Available results 48 4 7 Safety margin 49 4 8 Capacity curves 49 5 PULS CODE APPLICATION USAGE HINTS 0 ccccccccscesseeseeseeeeneeeeseneeseeeees 51 5 1 General assumptions Boundary conditions 51 5 2 Applications 53 6 USING THE PULS 2 0 ADVANCED VIEWER PROGRAM 55 6 1 Program structure 55 6 2 Menu Toolbars and Tree view control menu 56 6 3 Tolerance specifications 60 6 4 Opening and Saving files 61 6 5 Input window Defining the S3 element stiffened panel 61 6 6 Input window Defining the U3 element unstiffened plate 65 6 7 Input window Defining the T1 element triangular plate 67 6 8 Running the program Standard mode or Capacity Curves 69 6 9 3D plots of buckling modes UC modes and UC membrane stresses 74 6 10 Output window Detailed result S3 element stiffened panel 76 6 11 Output window Detailed result U3 element unstiffened plate T11 6 12 Status bar 78 6 13 Program hints 79 7 PULS EXCEL SPHEADSAEE FE niria ereer E E E AAEE agneaiee 83 7 1 Introduction 83 T2 Input columns 83 71 3 Buttons in input sheet 84 7 4 Option buttons 84 DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 7 7 5 Result sheets 8 REFERENCES sniatininpeissnnonanpi eian a e A RRD 87 1 INTRODUCTION 1 1 General The present repor
41. d stiffener combination DET NORSKE VERITAS PULS Nauticus User Manual 82 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 ii Eigenmodes Shows the minimum ideal elastic buckling mode according to linear elastic buckling theory in the local and global mode separately The global eigenvalue is calculated based on an orthotropic plate theory with the reduced bending stiffness coefficients in the ultimate state The eigenmodes are normalised to unity iii Imperfection mode Shows form of geometrical imperfections used in the non linear analysis Deflection Wimp in mm iv Pressure The pressure plot shows the displacements in the plate caused by the applied pressure Both the solution for regular and only pressure mode is linear iv UC mode Shows the deflected form in the UC state separated into local and global modes The ULS deflection shown in the figure is the total deflection Wiot including the geometrical imperfection and the displacements due to pressure Wrot Wimp Wload Wpressure v UC membrane stresses The membrane stresses is shown at the local UC state This is not exactly as the same as the real UC state but for qualitative illustration of non linearly redistributed stresses the 3D graphics may be useful The graphical presentation is only an added feature it has no influence on the UC results which consider interaction between local and global buckling effects vi Capacity curves Capacity c
42. e ara pan op in Eigenmodes Elastic moment at first yield kNmm 124600 Lateral pressure at first pure shear yield MPa 0 409 0 Imperfections Plasti momant capaci Kimm Tyro Lateral pressure at pure shear squash MPa 0 486 9 ULS modes Plastic neutral axis above middle plate plane mm 650 Pressure Shear load at first shear yield kN 1600333 Maximum lateral pressure parameters plate Panel 5 Shearsquash load pure shear kN 1903765 Lateral pressure at first pure bending stress yield MPa 0 188 Detailed result fa Elgenmodes Numerical parameters Number of increments local 0 E Imperfections Number of increments global T ULS modes lt n gt Ready Plate slend OK Web slend OK Flange slend OK Aspect ratio OK Imperfections Default BO Ginbox microso Gaciisteentpursy PRA ETER een Gb 5 Microsoft Ww gt DNV PULS Bu MOE RA 17 10 ja pJeus 1 a 6 11 Output window Detailed result U3 element unstiffened plate DET NORSKE VERITAS PULS Nauticus User Manual 78 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 In the standard mode a Detail results Window is available by selecting Detailed results from the Result menu The output parameters are commented on figure below a Pus PE x File Edit Window Help oela a lele e EIE el m Slelelalol gt Project 1 5 Panel 1 U3 Detailed results Jeg
43. e calculated usage factor n is to be measured against the allowable Natiow or called Nmax as specified in the relevant Rules and Standards 4 8 Capacity curves Capacity curves under combined loads are available for the T1 element The capacity curves are illustrated in two dimensional load spaces The notation of capacity curves and buckling boundaries are described more in detail in Section 6 7 Pre loading is handled for any of the three in plane load components 1 Bi axial load space 6 62 for fixed t12 shear il Axial shear load space T12 for fixed transverse 62 stress ili Transverse shear load space 62 t12 for fixed axial stress DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 51 5 PULS CODE APPLICATION USAGE HINTS 5 1 General assumptions Boundary conditions The current U3 and S3 elements by default assess the buckling and ultimate strength of integrated thin walled panels in ship and offshore structures The strength characteristics of an integrated element in larger structures depend on the structural geometry and profile type nature of prescribed loads and not at least the boundary conditions Two sets of boundary conditions are of particular importance for buckling and ultimate strength assessment 1 e 1 out of plane bending boundary conditions and ii in plane membrane boundary conditions 1 ii Out of plane bending boundary co
44. ed plate NB Note that all input numbers entered has to be followed by a tab entry for proper registration A tab reminder is given on the status bar at bottom whenever a new number is entered into a cell Unstiffened plate figure automatically adjusted with correct aspect ratio proportion f Ele Edit Panelsettings Solve panel Capacity Curves Animation Window Help n la S elel ele SE eel l eala gt iat S Panel 2 U3 a ane l He General Panel particulars Identification O11 Panel 2 a 22 Allowable usage factor n T allowable uc 7 n tH T atowable BS 1 00 Comments a la 4 i L ia Y i Input O21 7 F F tn S11 Allowable S12 S11 le L gt l usage 2 Material Loads Boundary conditions factor Actual usage factor defined in i Panel length mm 0 imate capacity the rules SET 0 00 ET Not OK Panel width mm L2 0 Plate thickness mm t 0 Buckling strength n 0 00 status Not OK Geomtry input plate length L plate width Ly plate thickness tp Ready Plate slend OK Aspect ratio OK Imperfections Default DET NORSKE VERITAS PULS Nauticus User Manual 66 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Geometry Material Properties Loads Material classification X Specification of
45. elastic buckling ULS p 0 eta 1 00 Limitstate 1 Limitstate 2 6 Limitstate 3 F Limitstate 4 che fpinto i Limitstate 5 Limitstate 6 1 MPa Fig 18 Capacity Curves in 2D load space with associated 3D visualization of ULS modes for two different points in load space DET NORSKE VERITAS PULS Nauticus User Manual 76 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 6 10 Output window Detailed result S3 element stiffened panel Detail result summary sheet In the standard mode a detailed results window is available by selecting Detailed results from the Result menu The output parameters are commented in figure below Ultimate loads with GEB cut off do Minimum local eigenvalue LEB Buckling loads Applied loads not accept global GEB and LEB cut mapped from stiffener buckling off input window Minimum global eigenvalue GEB JA PULs nlala aj siele 2L NCE H el a SNP a SACR A oe B Panel 3 53 Detailed results global stiffener E Panel 2 T1 Details results summary Stiffness coefficieyts Nominal parapfeters JTP requifements buckling 5 Panel 3 S3 a a tee z ae Detailed results summary gplied loads Ultimate loads Bucklinglfads Local eigenvgyfe Global eigenval Ultimate loads Allowable usage factor a MPa 100 00 170 126 126 2577 0 1 00 aji MPa 0 00 0 0 0 0 0 Ult
46. ell control 1 4 Sept Improvements of stiffened panel S2 Automatic Profile Aluminium 2002 theory Table Bulb profiles L option locked i Generally more degrees of freedom P rops cee rom alucan De Ia Nauticus Hull specified in for local buckling description steel mode but Consequences Button for switch i no HAZ between ULS estimates Max allowable aspect ratio plate isad bearing capacity effects between stiffeners from 8 to 14 ont eae included and SLS buckling estimates w r t usage fact t ii Modified imperfection model AE OE PULS ver 1 4 Consequence New application of supports ver dialog box f lecti 1 3 data fil Predicts more conservative ULS ee tat ne i e i Saara MIER strength than 1 3 for some rare P YP geometry s and loading Typical very Two options for high stiffeners and dominating secondary transv transverse compression stiffeners sniped or tripping stiffeners Extended 3D hi Improvements of unstiffened plate P EPEa U1 th for S2 element similar to cory U1 element i Generally more degrees of freedom _ All 3D graphics sorted for plate buckling description into panel tree menu Consequences eigenmodes Max allowable aspect ratio plate imperfections ULS from 6 to 20 modes ULS stresses ii Modified imperfection model Automatic Word Report Consequence generator Updated to Predi Pn support both S2 and U1 redicts more smooth bi axial elerients capacity curves ULS u
47. er Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 55 6 USING THE PULS 2 0 ADVANCED VIEWER PROGRAM 6 1 Program structure The PULS program has a multi document MDI layout for easy input and output All parameters are given in cells with text identification and unit assignment The program has two levels of organising data The highest level is the Project typically being a specific ship identification or similar The level below is the Panel level typically being a specific panel in the ship Any number of Panels can be specified but it is recommended not to exceed 15 especially when there are generated graphics for most panels The Project with the corresponding Panels organised as subfolders are saved in a file with a format notation of pbp The Project name will automatically be updated to be the same as the name given to the file using the Save as option in the File menu The Panel can be given any name by directly editing in the Tree view control menu or using the identification text box The program features and the project control is facilitated using the Menubar Toolbar Tree view control menu and the Window Project 1 Panel 1 Detailed results 9 Eigenmodes 9 Imperfections E Pressure ULS modes DET NORSKE VERITAS PULS Nauticus User Manual 56 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 6 2 Menu Toolbars and Tree view contr
48. ess for flat bar stiffeners h ty lt 15 Stiffener web slenderness Angle and T profiles hy ty lt 33 Free flange slenderness for Angle and T profiles fte lt 15 Table 2 Overview of S3 element characteristics 3 3 Element limitations slenderness requirements The present PULS S3 element has one local macro material routine with the following characteristics Geometry Profiles Sec stiffeners Loads Edge Support and range of application Uni axially stiffened plate with open continuous profiles welded to plating The stiffeners may also be specified as sniped The stiffeners may have a tilt angle relative to the plate normal Open profile type with standard angle shape eccentric angle symmetric T or flat bar shape Standard profile table included Profiles run continuously across several spans Bulb profiles are modelled as equivalent angle profile Secondary stiffeners perpendicular to continuous stiffeners option for sniped stiffeners continuous stiffeners or tripping brackets Uniform membrane stresses in axial o direction linearly varying stresses in transverse O direction and constant shear stress All combinations of bi axial compression tension and shear can be analysed Uniform lateral pressure acting across several bays is included All four edges are assumed to be straight free to move in plane and free to rotate out of plane simply supported edges and constrained to be straight and stay
49. ffener direction plate middle plane X2 Cartesian in plane co ordinate perp continuous stiffener direction plate middle plane X3 Cartesian co ordinate perpendicular to plate plane E1 Normal strain in plate middle plan in x direction E2 Normal strain in plate middle plan in x2 direction E3 Engineering shear strain in plate middle plan in x1 x2 plane 3 2 12 12 Shear strain tensor in plate middle plan in x1 x2 plane K Curvature in plate middle plan in x direction K w K2 Curvature in plate middle plan in x2 direction K W K3 Twisting curvature in plate middle plan in x1 X2 plane K W DET NORSKE VERITAS PULS Nauticus User Manual 90 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 A Load proportionality factor unit load factor A 1 corresponds to applied loads 9 19 gt 929 gt 9 30 Ag Load proportionality factor at ideal elastic buckling for U3 eigenvalue Ace Load prop factor at ideal elastic buckling in global mode global eigenvalue GEB Arg Load prop factor at ideal elastic buckling in local mode local eigenvalue LEB Au Load proportionality factor at ideal ultimate load Lo Load effect Sa Ds Characteristic resistance Rx Sa Load effect Lo Rx Characteristic resistance Ly Yi Material factor offshore rule notation Superscripts or subscripts Linear properties Non linear properties Ultimate limit state Initial properties for zero load Transposed Oni
50. flat bar shape Standard Profile table included Bulb profiles are modelled as equivalent angle profile Loads Linearly varying membrane stresses in axial o and transverse direction and constant shear stress All combinations of bi axial compression tension and shear can be analysed Edge Support All four edges are assumed to be supported laterally Rotational constraint may be specified In plane boundary conditions is not necessary to define due to the use of linear theory The theory for stiffeners is simplified in sense that they are not considered to carry any axial stress This means that buckling of stiffener web is not checked and thus a certain max slenderness of the stiffener web has to be ensured The T1 stiffener model is similar to the secondary stiffener option in the S3 element and the web proportions should fulfil the table 2 requirements at least if the stiffeners are continuous across the boundaries For sniped stiffeners the stiffener web requirement can be relaxed As an upper max slenderness limit the following ratios are implemented 1 General Web slenderness for flat bar stiffeners h t 35 Web slenderness for L or T profiles h t lt 90 Free flange for L or T profiles ff ft lt 15 These validity limits are checked by the program An error message is given when limits are exceeded A summary is given on the status bar shown in the bottom of the PULS window Another alternative option for modelli
51. h usage factor calculation Plate slend OK Flange slend OK Aspect ratio OK Web Flange slend OK Input Plate dimensions and number Tab strips for material load and of continuous stiffeners Ns boundary condition specification Secondary transverse stiffener option see next page own dialog if different from zero DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 63 Profile table for flat bars bulbs angles and T bars same as in DNV Nauticus Hull Stiffener scantlings Profile category Profile type 20 HPBulb 7 T lj Dimensions Profile view a A Code h t 20 aon fi 6 h t A Profile table directory 4 C Program Files DNYANAUTICUS SN auticus Hull data OK Cancel Secondary transverse stiffeners three options 1 Sniped stiffeners ii continuous stiffeners 111 tripping brackets amp Define secondary stiffener Type of secondary stiffener stiffener restrained local Tripping bracket Stiffener restrained local Dimensions Flatbar Height mm h C Angle Web thickness mm T bar Flange width mm b Flange thickness mm DET NORSKE VERITAS PULS Nauticus User Manual 64 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Geometry Material Properties Loads Material classification Ma
52. ically in Fig 4 DET NORSKE VERITAS PULS Nauticus User Manual 28 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Local level Global level Ultimate limit state y Orthotropic macro material Open profiles T L bulb flat bar Closed trapezoidal profiles OVERALL Open corrugations ORTHOTROPIC PLATE BUCKLING MODEL PANEL STRENGTH Fig 4 Calculation procedure in PULS S3 element A Rayleigh Ritz expansion of the out of plane displacements using trigonometric functions is used both at the local and global level Different types of simplifications are introduced in order to limit the degrees of freedoms These are not discussed here 3 5 External prescribed loads The S3 sub element can be subjected to a combined external load situation covering uniform in plane load in the axial direction linearly varying load in the transverse direction and constant in plane shear The four in plane loads are given as o AOp O A0 O AOn 0 Ady where A is the load factor automatically controlled by the program A subscript 0 on the nominal external stresses indicates the values of the input values i e they correspond to A 1 For strength assessment the in plane loads are scaled proportionally until elastic buckling and ULS strength is identified The considered external loads typically takes the form as illustrated on Fig 5
53. icks in for tension loads will also kick in for transverse compressive loads for panel with small stiffeners i e large global effects Plate compression criterion Stress control in plate at midspan x L 2 in plating for global panel deflecting towards stiffener flange compression criterion PI collapse Stiffener compression criterion Stiffener criterion Stress control in stiffener at midspan x L 2 in stiffener flange for global panel deflecting towards plating compression criterion SI collapse typical for pure axial load Plate tension criterion Stress control in plate at midspan x L 2 in plating for global panel deflecting towards plating tension criterion rare for compressive loads but kicks inn for tension loads DET NORSKE VERITAS PULS Nauticus User Manual 38 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Note that the limit state criteria i 2 5 is not always evaluated at midspan Maximum curvature in x direction and thereby the highest bending stress could be closer to the ends for certain geometrical proportions of stiffened panels Typical are cases with small stiffeners for which the panel behaves more as a plate than a column with a global buckling mode pattern flattening in the mid regions i 6 Stiffener bending stress criterion at support Stress and capacity control at support x 0 compressive or tension criterion kicks in for cases with lateral pressure This limit
54. imate capacity Status Oy MPa 0 00 0 0 0 0 0 0 59 OK oy MPa 0 00 0 0 o ol 0 Buckling strengi Status p MPa 0 000 0 000 0 000 NA NA 0 000 0 79 OK Ultimate loads panel capacity accepting local and global buckling Buckling loads minimum of local eigenvalue global eigenvalue and ultimate loads no buckling accepted Ultimate loads minimum of global eigenvalue and ultimate loads global buckling not accepted C l l t d Stress control limit states Stress control usage factor limit state Pets Pu oy Oz4u O22u Tru usage 1 5 15 0 000 515 0 0 0 0 19 Tree 2 1 84 0 000 184 0 0 0 0 54 3 1 93 0 000 193 0 0 0 0 52 view 4 1p 0 000 170 0 0 0 0 59 5 99 0 000 199 0 0 0 0 50 control 6 177 0 000 177 ol 0 0 0 57 Weakest lin displacements at ultimate capacity Maximum flate displacement between stiffeners at ultimate capacity local mode mm 9 24 Maximfn lateral stiffener displacement global mode mm 0 22 Mayfmum sideways displacement in top of stiffener local mode mm 1 04 faximum sideways displacement across stiffener web height local mode mm 2 04 Failing stress control limit state 4 The imperfection amplitude is not included Ready Plate slend OK Web slend OK Flange slend OK Aspect ratio OR Web Flange slend O
55. ion in the PULS approach the ULS state Some more capacity may be expected for thin plates involving spread of plasticity and consequently involving permanent sets but the extra capacity is marginal DET NORSKE VERITAS PULS 75 Nauticus Hull User Manual ProgramVersion 10 5 PULS Version 2 0 6 September 2006 S3 stiffened plate element The stiffened plate shows similar results as for the unstiffened plate The difference is with respect to categorisation of modes 1 e stiffened panels buckles into local and global modes respectively General 3D plots of LEB and GEB eigenmodes and ULS modes are available for the capacity curves The 3D visualisations are generated by double clicking on the corresponding point in the capacity curve Window figure 3D plots are shown in Fig 18 for a S3 element example subjected to bi axial loading in two different points in load space illustrating different types of collapse modes TAT 5 pi ULS mode plot elk ULS mode plot BE Displacement mm Displacement mm Sii ANPE E E PA Ultimate buckling stresses G 261 cS 0 p 0 000 Se c 22 Beir 62 tT 0 p 0 000 Local and global displacement at ULS sum of imperfeftion lateral pressure effect and load effect magnified Locg 4nd global displacement at ULS sum of imperfection lateral pressure effect and load effect magnified cere este cre ne e a E gt Global elastic buckling Local
56. ions Ea Initial deflection tolerances Plate mm 3 65 tbo Stiffener mm dog 5 28 User specified Stiffener tilt mm oo 52 Cancel Default values The model imperfection shape is not operated by the user only the imperfection amplitude Imperfection models combining eigenmodes for constructing relevant imperfection modes are pre set in the program They can be viewed in the tree control menu after a calculation has been carried out Both amplitude and shape is defined by the program for the T1 element 6 4 Opening and Saving files Opening an existing file is done by clicking the Open button on the toolbar or by using the Open option in the File menu A new blank input page is generated by clicking the New file button on the tool bar or using the New option in the File menu After an analysis is run the results are saved by clicking the Save button or using the Save or Save as in the File menu Save as will provide a dialog box for setting of file name which is automatically set to be the same as the Project name The Panel identification names can be edited and given any name by clicking on the corresponding labels in the Tree view control menu 6 5 Input window Defining the S3 element stiffened panel NB Note that all input numbers entered has to be followed by a tab entry for proper registration A tab reminder is given on the status bar at bottom whenever a new number is ente
57. itstate 2 Limitstate 3 7 Limitstate 4 Limitstate 5 Li i Usage factor l N Lo Lu Fig 10 Definition of safety margin usage factor capacity curve example for bi axial loading DET NORSKE VERITAS PULS Nauticus User Manual 40 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 For the single load cases the definition of usage factor becomes N 0 0 i 1 2 3 as is the familiar form used in the DNV steel ship rules For the present PULS code approach the final rule acceptance criterion will be in the form L u lt N allow 1 n lt N atow where Nowy or also called 1 is to be specified in the rules and y is calculated by the PULS allow code In the offshore marked the LRFD format is used i e the acceptance criterion is on the form Sa lt Ra where Sais the load effect and Rg is the design resistance The design resistance is related to the characteristic resistance as Ra SR Ym For offshore application of the PULS code the following definitions applies Characteristic resistance R 6 2 ton 55 L Load effect Sa Mow ome Ci Ly The offshore strength format is then Daeg R en which in Ship rule terminology is 1 S i e lt where t n 3 n R The ratio S R is the same as the actual Ship Rule usage factor 7 and is calculated by the PULS code Load factors are to be included in load effect parameter Sa since it repre
58. itude input is optionally The tolerance shape is always automatically taken to harmonise with some critical modes being most influential for the ultimate strength The latter is called the imperfection model and can not be controlled by the user 3 2 Overview of element characteristics The main characteristics of the S3 element are summarized in Table 2 DET NORSKE VERITAS PULS Nauticus User Manual 24 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 S3 element stiffened plate regular geometry Theory Non linear Structural Rectangular stiffened plate configuration lt a Uniform plate thickness N equal constantly spaced main stiffeners in x dir Continuous or sniped Secondary stiffeners perpendicular to x dir a Sniped between main stiffeners b Supporting stiffener sideways Secondary stiffeners only strengthening the plate between main stiffeners carry no axial stress Loads Materials Boundary conditions Uniform normal stress in main stiffener direction x direction Linearly varying normal stress perpendicular to main stiffeners x2 direction Uniform in plane shear stress x1 X2 plane Uniform lateral pressure p fixed Isotropic elastic material E v Steel different yield stress in plate and stiffeners optionally Aluminium different yield stress in plate and stiffeners HAZ correction option Out of plane support bending support
59. l pressure is kept fixed while the in plane loads are increased until subsequent collapse is reached Alternatively a plate subjected to lateral pressure alone may be analysed In this case results are presented for the specified pressure magnitude and no ULS assessment is performed It is remarked that the U3 plate element by default assumes all four plate edges to be simply supported out of plane and constrained to be straight in plane For application on say bottom panels in ships having uniform lateral pressure acting across many plate spans between stiffeners and frames this SS assumption is not fully consistent and clamped boundary conditions may be more appropriate Option for any rotational edge restraint is available When using the PULS program an indicator warning always pops up as a dialog box for pressure beyond a fixed limit This fixed limit is based on a linear clamped plate unit strip model i e pp is defined as t Py 20 0 which corresponds to first material yielding in extreme fibre along the long edges due to pure bending stress across the plate thickness DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 23 3 S3 STIFFENED PANEL ELEMENT 3 1 General The S3 element code applies Marguerre s non linear plate theory geometrical non linearity in combination with stress control criteria for ultimate strength assessment The stiffened panel may be s
60. lates second order bending stresses adds to the second order membrane stresses The resulting surface stress is generally accepted to exceed the yield condition in local areas This is not considered critical for the ULS strength of plates and it will not induce permanent sets beyond what is normally accepted in ship designs In some cases it will from serviceability functional reasons SLS not be acceptable that elastic buckling takes place In such cases the local elastic buckling stress LEB cut off can be used as the upper limit of allowable load application In effect a SLS type of strength assessment allows no elastic buckling and may prove to be a useful approach in particular for girder webs webs frames i fore and aft ship etc and in general for designs that are not accepted to buckle elastically nor plastically 2 5 External prescribed loads The U3 element can be subjected to a combined external load situation covering linearly varying in plane loads in bi axial directions and constant in plane shear The five in plane external nominal stresses are given as O A 01 A Oz 5A Oy O21 AOn gt 6 A Oy DET NORSKE VERITAS PULS Nauticus User Manual 18 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 where A is the proportional load factor automatically controlled by the program A subscript 0 on the nominal external stresses indicates the values of the input values i e they corresponds to A 1 This correspond
61. lick on the selected point and the buckling mode window pops up The corresponding co ordinates in load space are given in the inserted frame above always given in MPa Several points may be called up and moved around inside the window for comparison purposes illustrating different type of failure modes as function of the load combination U3 element i Detailed results summary The applied nominal stresses are listed together with the ultimate stresses buckling loads the eigenvalues and the usage factor The results are based on a proportional load path for the in plane stresses meaning the same ratio between each nominal stress component applied at the point of elastic buckling eigenvalues and ultimate state The lateral pressure is as specified in the input i e it is kept fixed ii Eigenmode The eigenmode shows the minimum ideal elastic buckling mode according to linear elastic buckling theory The deflections are normalised to unity iii Imperfection mode Shows form of geometrical imperfections used in the non linear analysis Deflection Wimp in mm iv Pressure The pressure plot shows the displacements in the plate caused by the applied pressure The plot generated by a regular solution is non linear while the plot generated by the only pressure mode is linear The shown stresses are bending stresses or membrane stresses depending on the users choice in the load tab strip v UC mode Shows the deflected for
62. lts es Animation Window Help nela S tlele el elo amp m SlalelQiol animation e 5 02 200 Panel 1 Detaildd results Panel 2 E Detailed results 9 Panel 3 E Detailed results Panel 4 Detailed results Panel 5 E Detailed results Panel 6 Panel 7 Detailed results Eigenmodes Local LEB E Global GEB Imperfections ULS modes E Pressure E Panel 8 Detailed results 9 Panel 9 Panel 10 isplacement gt Normalised minimum local elastic eigenmode LEB Eigenvalue 1 35 Plate slend OK _ Web slend OK Flange slend OK Aspect ratio OK Imperfections User Ee Inbox Microsof uj 5 Microsoft Word j DNV New soft S PULS Panel 7 Ea 2 Microsoft Excel NC E Sr 17 29 6 3 Tolerance specifications Explicit geometrical model tolerances can be specified For the unstiffened element U3 there is only one model tolerance amplitude available i e the maximum initial plate amplitude 550 For the stiffened panel S3 three independent imperfection amplitudes can be specified i e see figure below dpo dso and dro Default model tolerances correspond to ULS code strength values according to normal fabrication standards of welded integrated structures used in the shipbuilding and offshore industry DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 61 ia Imperfect
63. lus E and Poisson ratio v is possible The geometrical imperfection size and shape effect and the residual stress effects are implicitly considered in the ULS values when using default tolerance values The imperfection values used as default values are typical for welded and fabricated steel plates used in ships and offshore constructions DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 39 3 10 3 Aluminium A special option for analysis of aluminium panels including HAZ effects for NV 5082 T6 is implemented in PULS 2 0 A first membrane yield criterion in the HAZ zone is added to the limit states used for steel This first HAZ yield criterion will be conservative but reasonable as a design limitation since limited knowledge is available for soft HAZ zones strained beyond the material yield level Crack initiations and fracture can be the result if the HAZ zones around welds frequently are loaded beyond the first yield level 3 11 Safety margin The calculated UC usage factor n in the PULS code represents the ratio between the applied combined loads and the corresponding ultimate strength It is defined as H L L 1 A where the radius vectors Lo and L in load space are defined as 2 2 2 L o 0 03 2 2 2 Lo o O Oz see Fig 10 for illustration A a oe aa pa ee ee 52 sasad bssdeeeesesecest Applied loads Lim
64. m in the UC state The UC deflection shown in the figure is the total deflection Wio including the geometrical imperfection and the deflections due to pressure Wiot Wimp Wioad Wpressure DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 81 By clicking on the UC figure a yellow frame pops up showing the co ordinates of the point and the corresponding UC out of plane deflection in mm vi UC membrane stresses Shows membrane stresses in the UC state By clicking on the figure a yellow frame pops up showing the co ordinates of the point and the corresponding UC membrane stresses stress in MPa The membrane stresses for any required load level can be visualised by adjusting a fictive material yield stress in the input cell such that the applied nominal stresses becomes equal to ultimate stresses A bit tricky approach but it is necessary to limit the storage of data Only membrane stresses are given However bending stresses are easily calculated from the method but not included in the current PULS versions due to storage limitations vii Capacity curves Only uniform nominal stresses 61 62 and 63 are possible for capacity curve calculations Capacity curves can be generated in load space 6 62 with fixed 03 6 63 with fixed 62 O2 63 with fixed 62 Five levels of the pre stress may be specified using the add button in the dialog box Lateral pressure can
65. mped edges This is equivalent to using a buckling factor from C 4 for unstiffened plates to C 5 The in plane boundary conditions are by default so that all four edges are forced to remain straight This is representative of an integrated plate that is part of a larger structure Alternatively two opposite edges may be specified as free to pull in which is more representative for web girders stringers etc DET NORSKE VERITAS PULS Nauticus User Manual 20 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 2 7 Available Results The numerical results from the U3 element are i Local Elastic buckling stresses minimum eigenvalue LEB ii Ultimate stresses UC iii Buckling load BS minimum of ultimate load and minimum eigenvalue iv Usage factor n with ultimate load or buckling load as reference Graphical results available are plots of the minimum eigenmode the imperfection mode and the ultimate limit state deflection mode Membrane stress plots for the ultimate limit state are also available For pure lateral pressure computation it is possible to request bending stress output rather than membrane stress output For a given prescribed load combination the code calculates the value Ag of the load factor at ideal elastic buckling The elastic buckling stresses follow as Sips Ag Oioi Sinn Ag S02 Oop Ag On Oop Ag On Oz Ag Oy The corresponding UC strength values are On Ay Oio Sing Ay S102 So
66. nd OK Flange slend OK Aspect ratio OK Imperfections Default Defining the end Buttons for defining and Profile data for points of each deleting stiffeners each stiffener stiffener Stiffeners can be defined or individually deleted with buttons or directly in picture DET NORSKE VERITAS PULS Nauticus User Manual 68 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Geometry Material Loads Boundary conditions Material classification Steel X Plate material SteelNVNS Material input Modulus of elasticity MPa E 208000 Poissons ratio ve 03 Shear modulus MPa not input G 80000 Yield strength plate MPa Sfp 235 Geometry Material 7 Boundary conditions Axial stress MPa enS 0 10 0 Transverse stress MPa ie 0 Chal 0 Soa cer airs te 0 Load input The loads are only acting on the plate Compression positive and not the stiffener S Positive shear stress as defined on figure Note the difference The loads are only acting on the plate No load transfer through stiffeners between po sitive and negative shear stresses Geometry Material Loads Boundary conditions Rotation stiffness MN m m A Leftside Simpy supponed z Rotational spring Rightside Simply SUpporied E support for plate from Upper side Smp eue zl surrounding structure Lower side Simply supported
67. nditions The U3 S3 and T1 elements by default assume the plate edges to be rigidly supported out of plane along all four edges with the edges are geometrically physically free to rotate simply supported boundary conditions This is a conservative set of boundary conditions For the U3 and T1 elements alternative rotational restraints may be specified by the user for each edge individually For the S3 element the rotational restraint at the outer edges is less important than the restraint from the stiffeners which is automatically accounted for Out of plane boundary conditions are important for the buckling load eigenvalue but not so much for the elastic postbuckling behaviour which controls the amount of incremental ULS margin beyond elastic buckling In plane membrane boundary conditions In plane boundary conditions are important with respect to elastic post buckling behaviour and they therefore dictate to a large extent the ULS strength margins In other words they control the available strength beyond ideal elastic buckling overcritical strength Plates compressed beyond the minimum eigenvalue develop second order membrane stresses which need to be transmitted to neighbouring plate fields and surrounding structures By default both the U3 and the S3 elements are assumed to be integrated elements Alternatively two opposite edges may be specified as free to pull in which may be more representative for girders and stringers
68. ng stiffeners is also available using directly a user defined effective moment of inertia and rotational spring stiffness This option enables the user to specify his own preferred stiffener efficiency properties DET NORSKE VERITAS PULS Nauticus User Manual 48 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 4 4 General T1 element design principles The T1 element applied in an design setting is based on the following main principles i Elastic buckling of the plate and or stiffener is not accepted ii Permanent buckles are not accepted By ensuring the maximum membrane stresses along the plate edges and the plate stiffener connections to stay below the yield stress condition von Mises excessive permanent sets and buckles are prevented principle 11 above In plates second order bending stresses adds to the second order membrane stresses The resulting surface stress is generally accepted to exceed the yield condition in local areas This is not considered critical for the strength of plates and it will not induce permanent sets beyond what is normally accepted in ship designs Since linear theory is used the ULS strength calculated will always be below the local elastic buckling load 4 5 External prescribed loads The T1 element can be subjected to a combined external load situation covering linearly varying in plane loads in bi axial directions and constant in plane shear The five in plane external nominal stresses
69. nsverse direction sniped stiffener continuous stiffener or tripping bracket Solve panel curtain Solve panel Calculates results for a given load combination standard Solve panel _ mode of program operation external stresses have to be ee specified different than zero proportional load history for all in plane loads assumed Lateral pressure fixed Result curtain Results Capacity Cury Windows for Eigenmodes Imperfection modes ULS Eigenmodes modes deflections and stresses Detailed results Pressure Imperfections deflections All results activate all available windows Pressure ULS modes Detailed results All results DET NORSKE VERITAS PULS Nauticus User Manual 58 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Capacity curves curtain Capacity Curves Generate capacity curves in 2D load spaces local and global Generate eigenvalues and ULS boundaries Prestress option third Settings load component fixed zero or non zero S3 and U3 also Eorsi sii support lateral pressure Add gesiqnigads Curve settings type of curve number of points in 2D load space scaling against accept levels scaling of axes etc Also available from dialog box under Generate Window curtain Magee Help New Window Cascade Tile Horizontal Arrange data windows Tile Vertical Arange Icons v 1 Panel 2 2 All curves 3 Panel 1_15mm 4 All curves 5 All curves
70. nual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 89 Nallow Allowable usage factor defined in rules L Plate length in x direction stiffener span between rigid lateral supports distance between transverse frames L2 Plate length in x2 direction total pane width for S3 not input Lz Ns 1 s N Number of stiffeners for S3 Ngec Number of sniped stiffeners perpendicular to continuous stiffeners for S3 s Stiffener spacing for S3 h Stiffener height including flange thickness for S3 tw Stiffener web thickness for S3 br Total flange width for S3 tf Flange thickness for S3 tp Plate thickness ef Flange eccentricity distance from centroid of flange to web plate middle plane for S3 Dj Bending stiffness coefficients macro material coefficients ref plate middle plane D Ci Membrane stiffness coefficients macro material coefficients ref plate middle plane C Qij Coupling bend memb stiffness coeff macro material coeff ref plate middle plane Q D Neutral bending stiffness coefficients macro material coefficients ref centroid D N Line load in x direction unit N mm N2 Line load in x2 direction unit N mm N3 In plane shear load x1 x2 plane unit N mm M Line moment about x2 axis ref plate middle plane unit N M Line moment about x axis ref plate middle plane unit N M3 Twisting line moment ref plate middle plane unit N X1 Cartesian in plane co ordinate in continuous sti
71. o e g Microsoft Excel for comparison purposes Procedure Click once with the left mouse button on the curve to be copied This marks all points on the curve Then follow the standard copy and paste procedure for transferring the numbers into Excel for recreating the capacity curve NB When clicking the first time on a capacity curve the marked points black may seemed moved somewhat relative to the coloured continuous curve This error is eliminated by e g a slight drag on the outer curve frame before clicking on the curve or e g by a stretch or move operation on the axes described above ii The axes can be stretched compressed and the origin can be moved by a drag option using the mouse Stretching compressing axes Press the shift key on the keyboard and drag the mouse with left button pressed Moving origin Press the shift key down and drag the mouse with the right button pressed DET NORSKE VERITAS PULS Nauticus User Manual 80 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 iii The text box in the capacity curve figures can be resized and moved in the window iv Graphical visualisation of buckling or ULS mode mode from any point in load space laying on the capacity curves Procedure A point in load space is selected by first select the whole curve all points visualised by coloured marks and then click once more on the point of interest only this point is to be marked by colour symbol Then double c
72. of plane free to rotate but laterally fixed and constrained in plane straight but movable in plane edges are by default assumed along all four boundaries When lateral pressure is specified a symmetric clamped boundary constraint is introduced at transverse frame supports by adding an extra set of deflection forms on top of the regular asymmetric regular simply supported forms Alternative boundary conditions may be specified by the user 3 Element T1 Stiffened plate with non regular geometry Field of application Hull element between laterally rigid structures such as frames bulkheads etc Rectangular plate with arbitrary oriented stiffeners The model is based on linear theory Stiffeners Welded open profiles Angle T bulb or flat bar profiles Material Steel and aluminium Loads Buckling strength BS can be estimated for linearly varying axial and transverse compression tension and uniform shear and for all possible in plane load combinations DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 9 Boundary conditions For all load combinations simply supported out of plane free to rotate but laterally fixed edges are by default assumed along all four boundaries Alternative boundary conditions may be specified by the user 1 2 Approach The PULS buckling models for the S3 and U3 elements apply the non linear large deflection plate theory of Marguerre and von Ka
73. of the ULS collection in the dialog box see next page will put all ULS curves into one diagram The S3 and U3 elements assess capacity curves for preloading w r t a set of specified lateral pressure levels and stresses In girder mode the prestress option is limited The T1 element supports prestresses but not lateral pressure The dialog box for capacity curves is given under Capacity Curves on the menu or separate button and it takes the form DET NORSKE VERITAS PULS 70 September 2006 Nauticus User Manual ProgramVersion 10 5 PULS Version 2 0 6 amp Generate capacity curves 2D load space RE alternatives o Ptestluatspace s for capacity curve generation fa Fixed prest loads ATRSEFE SSS Prestresses Prestresses i Jda T Rea Add Remove _Add Remove Rk te os 2 EAE 0 0 0 0 7 0 0 02 20 0 D 0 30 0 20 0 30 0 Generate curves Te T Generate Cancel Curve Settings For the S3 element the Curve settings for the 2D curves are given in the following dialog box for the U3 and T1 elements the dialog box is similar but no distinction between global and local elastic buckling is necessary Curve selection Type of curve or all in one chart selection by arrows or double clicking Curves to be generated genvalues and ultimate ca Ultimate capacity collection Load range extent of load combination in 2D load spaces three options Scale
74. ol menu The following roll down curtains are available File curtain Specification of new panel geometry Also possible to copy data from idem Edit Panel Results Ca existing panels New Panel Ctrl N New Project Ctrl P o aye New project definition top level identification saved as separate file Save Project Ctrl S Save Project As Recalculate Project Open existing project existing saved file Save project default name equal to project Save project as any name can be used on file preferred equal to project Print Word report or data Windows directly or to file Recalculate all panels Edit curtain N A p Cut eee Remove all graphics Copy and paste Data Windows into Word documents implemented for 3D graphics and capacity curves Remove all 3D graphics in the project Useful for saving response time for large files with many panels and graphics DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 57 Panel settings curtain Panel settings Solve panel Set model imperfections Defi imary stiffe ma mess i Set tolerances default or user specified U3 one plate parameter only S3 three independent parameters Default values correspond to acceptable code strength estimates Define secondaxy stiffener Define stiffener from Profile table Bulb profiles etc Define secondary stiffeners in tra
75. omponents acting on a local stiffened panel plate are i In plane load in the direction of the stiffener compression or tension ii In plane load in the direction perpendicular to the stiffener compression or tension iii In plane shear iv Lateral pressure from sea or cargo Buckling and ultimate strength of plates depends on the nature of the locally applied loads and the boundary conditions enforced from the surrounding structure The boundary conditions can be categorised in two groups i e out of plane support and in plane support Out of plane support In most codes the out of plane support along the outer plate edges is assumed to be rigid in the lateral direction while free to rotate This corresponds to the classical simply supported boundary conditions This is also the default for the present PULS elements but alternative boundary conditions may be specified See also description for each element type for more details In plane support The in plane membrane support is also important particularly with respect to the elements ability to carry loads beyond the elastic buckling load LEB and GEB eigenvalues level i e the nature of in plane support influences the postbuckling and ultimate capacity behaviour UC of thin plates DET NORSKE VERITAS PULS Nauticus User Manual 14 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 The PULS elements U3 and S3 are by default assumed to be integrated elements Fig 2 Integ
76. ons of local buckles The degree of redistributions depends on the slenderness plate thickness of each component plate and on geometrical imperfections shape size and residual stresses present The current PULS version apply six limit state functions f s i 1 2 3 4 5 6 for identifying critical conditions in different locations in the panel A function fi gt 0 corresponds to applied loads less than the critical condition in the corresponding point Moreover fi 0 solved explicitly give the values for the applied loads corresponding to the ultimate limit state The ultimate strength is found from the minimum of all defined limit states The six limit states are formulated for capturing critical stress conditions in selected critical positions see Fig 9 DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 37 Fig 9 Stress control points in critical positions in a panel defining the ultimate limit states The six limit states fj s are stress controls in the following positions i 1 i 2 i 3 i 4 i 5 Plate criterion Stress control along plate edges based on max edge stresses along supported edges typical transverse load when local buckling dominates Stiffener tension criterion Stress control in stiffener at midspan x L 2 in stiffener flange for global panel deflecting towards stiffener flange tension criterion rare for compressive loads but k
77. plate middle plane This limit correspond to first bending stress yield at support for a clamped stiffener with span L The prs value is tabulated in the PULS output detailed result standard parameter list for info The lateral pressure which gives shear stress yielding in the web is wv Prs sL where the shear force which gives shear stress yield is DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 43 where the moment of area about the neutral axis where the maximum shear stress occurs is 2 S 802 O50 z 0 002 This pressure limit correspond to first pure shear yield in the stiffener web as calculated for a clamped stiffener with span L The p value is tabulated in the PULS output detailed result standard parameter list for info Another pressure limit of practical interest is the first onset of surface yield due to pure local bending of the plate between stiffeners This limit is simply t Pr 200 and is based on a clamped plate unit strip formulation This limit is not included as design limit in the present PULS 2 0 version as it will be too strict for practical applications For ship bottom designs pressure level significantly beyond this pr is normal It is also documented using advanced elasto plastic FE analysis that pressure levels well beyond pr can be carried for plates supported by typical solid stiffener frame structures It is also well documen
78. r all buckling and deflection modes the stiffener flanges are considered locally strong and they bend and twist like a beam constrained to follow the stiffener web deflections 3 8 2 Local eigenvalue LEB For panels stiffened by open profiles the following three categories of local buckling modes are typical in stiffened ship panels 1 plate buckling ii torsional stiffener buckling iii stiffener web plate buckling interaction with plate buckling Interactions between these mode categories are typical for stiffened panels Fig 6 illustrates the three main categories as assessed by PULS i plate buckling strong stiffener sideways LEB ii torsional stiffener buckling typical for tall profiles and flat bar profiles in particular LEB DET NORSKE VERITAS PULS Nauticus User Manual 32 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 iii stiffener web plate buckling interaction with plate buckling and some torsional stiffener buckling LEB Fig 6 Examples of local buckling modes junction line between stiffener and plate straight assessed by PULS The values for the in plane stresses at the instant where local elastic buckling starts are defined as Oire Ape Sou AEO So orp AO Oye AEO where A is the eigenvalue of the load proportionality parameter A calculated by the program The values oirt Oz211 gt 02216 gt 031g are called the local elastic buckling stresses under a combined load sit
79. r the Puls GUI or the Puls file spreadsheet Only steel panels are opened Calculate and S3 U3 All panels are calculated and written to a pbp file export panels to file Define corrugated U3 The spreadsheet sets the necessary options to generate a panel corrugated panel successfully Calculate panel S3 U3 Calculate all panels in the input file and writes all input and output into the output sheet If an error occurs during the computation an error message is written in the output sheet Profile table S3 Lets the user pick profile types from a table Hide Show S3 Hides shows the columns for the secondary stiffener secondary stiffener properties properties S3 Displays message box containing release date and Program info PulsComClasses version 7 4 Option buttons There are two groups of option buttons in the input sheet 1 Row by row combinations of input These options let the user choose how the panels are generated from the input sheet The row by row option makes a panel out of each row one row one panel two rows two panels The combination of input combines input from every cell in each column with every other multiple cell colums The figure below shows an example of a combination of input input There are specified two lengths three thicknesses and two load sets which results in 12 panels All parameters can be combined this way When combining loads all loads in each row must be specified
80. rated elements mean that the plate edges can transfer second order normal membrane stresses to neighbouring elements compressive as well as tension i e tension fields In a theoretical language this means that the plate edges are constrained to remain straight but free to move in plane This is a constraint that is very much used both in the analytical and numerical published literature on plate buckling In practise this constraint means that the present PULS elements are relevant for dimensioning and strength control of internal plates and panels such as in bottom and deck structures bulkheads shipsides etc Weaker free to pull in edges membrane conditions may be specified as an alternative being more relevant for plate girders etc For some type of structures and type of loadings e g serviceability loads SLS it may be that elastic buckling and thereby large deflections are not acceptable This philosophy implemented in a design code means that the plate thickness and stiffener proportions are to be increased as compared to a ULS philosophy For girders in particular such a SLS philosophy will be very reasonable and ensure robust designs with extra margins to take additional redistributed loads coming from accepting elastic buckling of surrounding structures i e typically inner and outer bottom plating in ship hulls For all elements the present PULS code gives a buckling control BS and ultimate capacity control UC under
81. rated on Fig 3 DET NORSKE VERITAS Nauticus Hull User Manual PULS f ProgramVersion 10 5 PULS Version 2 0 6 September 2006 19 YY O BU ULG ARG 22 ya Uy Yy YY Ui a Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy __ yy yyy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy DAA JAAA Uy Yy Uy Yy Uy Yy Uy Yy gt A AN Uy Yy Uy Yy Uy Yy i Z Uy lg Uy Yy Uy Yy Uy Yy Uy Yy I Uy Yy ty yyy 1 Uy Yy Uy Yy i Uy e Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Yy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy __ yy Gy lt Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Uy Yy Yy Yy yy yyy Uy Yy Uy Yy gt LZ MA la 7 Fig 3 External load system linearly varying normal loads in perpendicular directions and constant shear 2 6 Boundary conditions All four edges in the U3 element are supported in the lateral direction By default the rotational restraint of the edges is set to zero representing a plate simply supported on all edges The rotational restraint may be set for each edge individually The edges may be specified either as simply supported clamped or as a specified spring stiffness A corrugated bulkhead option is included The rotational restraints of the edges are then set to a value that increases the eigenvalue of the plate with 25 but limited to that of cla
82. red into a cell Having defined a Panel identification name the input parameters are added most conveniently by stepping through the cells using the tab key on the keyboard Alternatively the cursor may be used It is important that the tab key is pressed upon entering new data in a cell in order for data to be registered DET NORSKE VERITAS PULS Nauticus User Manual 62 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 The Input Window for stiffened panels takes the following form Profile table see Stiffened panel figure automatically adjusted next page with correct proportions and number of stiffeners PULS File Edit Panel settings Results Capacity Curves Animation Window Help osal a elel el 2 2 k m vle E APRA a 5 Panel 1 53 S Panel 52 General Panel Particulars Identification max uols of Panel 1 O22 EN EF TT 4 S22 pel Allowable usage factor T allowable Uc 7 1 00 Input Allowable Doss oc EE Comments usage factor is defined in the rules Dimensions Panel length mm Actual usage factor Ultimate capacity Number of secondary stiffeners Nsec ya 0 58 Status OK Plate thickness mm Output result Primary stiffeners Calculated actual usage factor Both ultimate capacity and buckling strengt
83. rman Discretizations of the buckling displacements follow the Rayleigh Ritz method using Fourier series expansions across the plate and stiffener surfaces Energy principles are used for establishing the algebraic non linear equilibrium equations and incremental perturbation techniques are used for solving these Hot spot stress control using the redistributed membrane stresses in a selection of critical locations determines the ultimate strength allowing for overcritical strength For stiffened panels S3 element an orthotropic version of the same theory is used for the global buckling mode The local buckling model treats the plate and stiffeners as discrete elements including all relevant effects such as buckling of the plate between the stiffeners buckling of the stiffener web plate as well the rotational restraints between plate and stiffeners The interaction between local and global lateral stiffener buckling is coped with using modified orthotropic stiffness coefficients reduced stiffness modulus coefficients For the T1 element plates with stiffeners in arbitrary direction linearized plate theory is used not overcritical strength This means that the buckling capacity predicted for this element is maximum the minimum eigenvalue The incremental approach and hot spot stress control is used also for this element for assessing the strength of geometrical imperfect plates The PULS code is programmed in a Windows environment using Visual
84. s beyond the elastic buckling stress for most of the load combinations NB The Capacity Curve Windows has some extra features The axis can be stretched compressed and the origin can be moved by a drag option using the mouse Stretching compressing axes Press the shift key on the keyboard and drag the mouse with left button pressed Moving origin Press the shift key down and drag the mouse with the right button pressed The Window frames can be moved and resized in a standard Windows manner The capacity curves can be copied and pasted as numbers into e g Microsoft Excel for comparison purposes DET NORSKE VERITAS PULS Nauticus User Manual 74 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 6 9 3D plots of buckling modes UC modes and UC membrane stresses In the standard mode of program operation 3D plots of the eigenmode model imperfections pressure plots ULS mode and ULS membrane stresses is available These data can be found under the Result menu U3 unstiffened plate element For illustration Fig 17 below shows 3D plots for an U3 element subjected to pure in plane bending a elastic buckling mode b ULS mode and c ULS membrane von Mises stresses Fig 17 a U3 sub element LEB eigenmode b UC mode c UC von Mises membrane stresses In particular the ULS membrane stresses show the non linear redistributed stress distribution at the first edge membrane yield condition This is then as per definit
85. sage factor estimates marginally changed compared to 1 3 1 5 Feb Improvements of stiffened panel S2 New functionality Comments theory DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 11 2003 i Improvements of local shear New 3D graphics PULS ver 1 5 p srap buckling model visualizing cont supports as stiffeners in S2 element version 1 3 ii New non linear global buckling Ge R x direction and 1 4 data model with lateral pressure option funk files but not Consequence For most geometries 3D graphics in panel ie eranhies new model gives same in plane tree menu eigenmodes R lation ULS strength prediction than imperfection modes hecessary for version 1 4 for default ULS modes stresses S2 ndated y imperfections settings However lateral pressure aohicsand new model gives improved and graphics pure global grap P detailed result more realistic ULS estimates for pressure deflections Sinamay tolerance exceed New Three options for iii lateral pressure included secondary transv iv Modified local buckling theory sere SHIP ey stiffeners tripping for coping with three types of Boos roe stiffeners or tripping secondary transverse stiffening brackets sniped stiffeners tripping stiffeners and tripping brackets New Standard v Modified imperfection model for parameter output a i placed in a separ
86. sents the actual load situation to be checked against buckling DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 41 3 12 Capacity Curves The PULS code can also assess 2D capacity curves under combined loads The capacity curves are illustrated in two dimensional load spaces The notation of capacity curves and buckling boundaries are described more in detail in Section 6 7 Pre loading of pressure and for the in plane uniform stresses is handled for any of the three in plane uniform stress components i Bi axial load space 1 2 for fixed shear 03 t12 and fixed p MPa ii Axial shear load space 1 T12 for fixed transverse stress o2 and fixed p MPa iii Transverse shear load space 62 t12 for fixed axial stress o and fixed p MPa Limits for acceptable lateral pressures are set in the program and capacity curves generation will be aborted if these limits are exceeded The pressure limits are summarised in the detailed result menu under standard parameters 3 13 Lateral pressure Lateral pressure can be prescribed acting uniformly across the panel In the Ultimate Capacity analysis the specified lateral pressure is kept fixed while the in plane loads are increased until subsequent collapse is reached It is remarked that the S3 stiffened panel element assumes the main stiffeners to be continuous across several bays to match typical ship bottom side designs and the
87. t gives a User s guide to the Windows program PULS 2 0 with a brief review of theoretical background design principles and purpose Main emphasis is on program features and functionality input description results and example illustration PULS is a computerised buckling code for thin walled plate constructions It assess the elastic buckling stresses and ultimate load bearing capacities under combined loads of stiffened and unstiffened plates used as building blocks in larger plated constructions such as ships and offshore constructions The PULS element library is illustrated in Fig 1 below PULS 2 0 ELEMENT LIBRARY U3 S3 T1 Unstiffened plate Stiffened plate Stiffened plate Non linear theory Regular geometry Non regular geometry Non linear theory Linear theory Fig 1 PULS element library The present PULS 2 0 version has three elements which are briefly summarized in the following A detailed description of each element is given in separate chapters For more theoretical details see publications given in the reference list at the end of this report DET NORSKE VERITAS PULS Nauticus User Manual 8 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 1 Element U3 Unstiffened plate Field of application Integrated hull element between laterally rigid structures such as frames bulkheads etc Rectangular plate without stiffeners Based on non linear theory Material Steel and
88. ted below Input parameter Relevant Description Input options element Stiffener type S3 Choose stiffener profile by L Angle profile entering either L T or F User 7 i defined stiffener profile is not PEE an option F Flatbar Stiffener S3 Stiffener end support C Continuous stiffener Doundaly S Sniped stiffener Tilt angle S3 Angle between plate normal Any angle between 45 and 45 and the undeformed stiffener Default is 0 degrees In plane support S3 U3 In plane membrane support In Int Integrated panel girder mode Loads can not be Gy 1 eft rioht edges f specified for free edges yg a R GT Upper lower edges free Rotational U3 Specifying rotational support SS Simply supported support of plate Both numerical values and strings can be specified CL Clamped Corr Corrugated left right or upper lower must be specified DET NORSKE VERITAS PULS 84 September 2006 Nauticus User Manual ProgramVersion 10 5 PULS Version 2 0 6 as corrugated Numerical values can also be specified 7 3 Buttons in input sheet A summary of the buttons in the input sheets are tabulated below Button Relevant Description element Clear input sheet S3 U3 Removes all input data in sheet Panel illustration S3 U3 Opens a window displaying a general panel Import panels from S3 U3 Opens a pbp file generated of eithe
89. ted that the in plane uls capacity for stiffened panels is not very influenced by local surface yielding along stiffener plate supports The pr value is tabulated in PULS output detailed result standard parameter list for info Conclusion The present S3 lateral model has practical pressure limits implemented reflecting reasonable design requirements to the stiffener plate unit These are based on the philosophy that the stiffeners shall carry the pressure and transfer these to the supporting transverse frame bulkhead structures without significant plastic deformations Input pressures beyond these limits are not accepted by the program and warnings are given in dialog boxes DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 45 4 T1 STIFFENED PLATE ELEMENT NON REGULAR GEOMETRY 4 1 General The T1 stiffened plate element applies a linearized version of Marguerre s non linear plate theory Linearized in this context is means that the theory do not assess the non linear postbuckling strength no overcritical strength i e loads beyond the ideal elastic buckling level eigenvalue is not possible The elastic buckling eigenvalue is found using a multiple degree of freedom model in terms of Fourier expansions of lateral deflections Stress control criteria checking the onset of material yielding in hot spot stress locations along the plate edges and in the stiffeners are used as me
90. teel panels and normal production tolerance standards User defined tolerances Damages imperfection sensitivity studies etc Ultimate Capacity UC Buckling Strength BS minimum of UC LEB Usage factor UC ratio applied loads UC Usage factor BS ratio applied loads BS Minimum Eigenvalue LEB Validity limits Plate slenderness Lghortest tp lt 200 Max aspect ratio of plate Liongest Lshortest lt 20 DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 17 2 3 Element limitations slenderness requirements A limited number of degrees of freedom is used in the PULS code in order to achieve high computational efficiency Therefore some limitations are put on the geometric proportions of the plates that are to be analysed The limitations set in the PULS 2 0 version are Aspect ratio limit Lj L2 lt 20 for L gt L or equivalent L L lt 20 for Li lt L2 Plate slenderness ratio Li tp lt 200 Li minimum of L and L2 2 4 General U3 element design principles The U3 element applied in an ULS design setting is based on the following main principles i Elastic buckling is accepted ii Permanent buckles are not accepted By ensuring the maximum membrane stresses along the plate edges to stay below the yield stress condition von Mises excessive permanent sets and buckles are prevented principle ii above In p
91. terial class Steel or Plate material Stiffener material aluminium aE m v Modulus of elasticity MPa E Poissons ratio v 02 Input Material Shear modulus MPa not input G 80000 parameters Yield strength plate MPa 3 5 IE NB Gnot input Yield strength stiffener MPa Loads Axial stress MPa a 100 Only pressure Transverse stress MPa i 0 27 computation Linear computation of deflections for specified pressure No ULS computation Shear stress MPa AT 0 Lateral pressure MPa P Only pressure computation Negative pressre is on the stiffener side Compressn positive Input Applied loads average nominal stresses bi axial and shear Scaled proportionally for assessing Input Pressure fixed Negative pressure is on stiffener side elastic buckling and ULS Sign convention Positive normal stresses loads in compression sence oh pane Location of panel Choose between intgrated panel or girder panel Girder panel sets Integrated panel restrained in plane support all edges Default option Free upper lower edges ESE ARE edges restrictions to which load components that can be non Both the integrated panel and the girder panel are simply supported Zero DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 65 6 6 Input window Defining the U3 element unstiffen
92. thod for the buckling strength assessment The stiffened plate can be subjected to combined load situations and the numerical procedures implemented scale the applied loads up to buckling The results are presented in terms of a single parameter called the usage factor The numerical algorithms are based on the linearized load deflection solution using the minimum eigenvalue in the amplification factor The element can be used for assessing the buckling strength of panels where the stiffener can have variable geometry and arbitrary orientations This means it is suitable for non regular stiffener arrangement and triangular plates More details concerning the T1 element can be found in ref 18 4 2 Overview of element characteristics The main characteristics of the T1 element are summarized in Table 3 DET NORSKE VERITAS PULS Nauticus User Manual 46 September 2006 ProgramVersion 10 5 PULS Version 2 0 6 T1 element stiffened plate non regular geometry Theory Linear Structural Rectangular stiffened plate non regular stiffeners configuration Uniform plate thickness N arbitrary oriented stiffeners N 1 2 25 The stiffeners may have different proportions Stiffener input direct input of scantlings as springs with lateral and or rotational stiffness The stiffeners are secondary in the sense that they carry no axial stress Loads Linearly varying normal in x direction Linearly
93. tion Deck Transverse Long BHDs S3 ULS OK webs or deck girders U3 ULS OK Inner bottom Floors Girders S3 ULS OK U3 ULS OK Bottom shell Floors Girders S3 ULS OK U3 ULS OK BTM girder Floors Inner and outer S3 SLS OK bottom U3 SLS OK BTM floor Girders Inner and outer Check areaby Variable S3 SLS OK bottom area as thickness No U3 SLS OK thickness varies Side shell Deck and Transverse Variable S3 ULS OK bottom webs thickness U3 ULS OK Impl in Midship Section model Side shell Transverse Upper and Variable S3 ULS OK bulk carrier BHDs lower sloping thickness U3 ULS OK BHD Impl in Midship Section model Long BHD Deck and Transverse Variable S3 ULS OK vertical bottom webs thickness U3 ULS OK Impl in Midship Section model Long BHD Shell or inner Transverse Variable S3 SLS OK hopper skin and inner webs thickness U3 SLS OK bottom Impl in Midship Section model Transverse Horizontal Inner skin and Check areaby Variable S3 ULS OK BHD girders Longitudinal area as thickness No U3 ULS OK BHDs thickness varies Table 1 PULS application matrix ULS OK means that local elastic buckling is accepted i e a GEB cut off is implemented ensuring sufficient stiffener proportions but plate between stiffeners can buckle elastically SLS OK means that not any type of elastic buckling is accepted i e both GEB and LEB cut off are implemented DET NORSKE VERITAS Nauticus Hull Us
94. to a proportional load history control up to elastic buckling LEB and beyond to final collapse UC Lateral pressure can also be specified However it should be noted that by default the plate is assumed to have simply supported boundary conditions along all four edges i e a type of single span model in both directions This is not relevant for analysing cases where the lateral pressure is acting across several spans i e several stiffener and girder spans since then symmetric clamped deflection modes needs to be included on top In order to analyse this case more realistic a multi span plate model is needed Multi span unstiffened plate model is not available in the current PULS version Alternatively the boundary conditions should be prescribed so that all four edges are clamped if this can be documented to be realistic boundary conditions In practical cases the stiffeners will be designed to carry the lateral pressure and thus the S3 model will ensure all relevant failure modes For strength assessment the lateral pressure p is kept fixed equal to the input value while the in plane loads are scaled proportionally until elastic buckling and UC strength is identified Alternatively a plate subjected to lateral pressure alone may be analysed In this case stress and deflection results are presented for the specified pressure magnitude and no UC assessment is performed The considered external loads typically take the form as illust
95. u1 A Oy Soyo Ay F292 63 A Oa u u 2 8 Safety margin The safety margin is presented as the usage factor defined as Gini 2 Gry Gaya Cu g 2 2 2 2 2 Jwa 010 2 0201 020 2 G50 DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 21 The calculated usage factor n is to be measured against the allowable Natiow or called Nmax as specified in the relevant Rules and Standards 2 9 Capacity curves The PULS code can also assess 2D capacity curves under combined loads The capacity curves are illustrated in two dimensional load spaces The notation of capacity curves and buckling boundaries are illustrated in Section 6 7 Current version handles pre stress for any of the three independent in plane load component and lateral pressure p i e 2D capacity curves can be generated within limits set in the program i Bi axial load space 61 02 for constant shear say T 2 10 20 30 MPa and for fixed p 0 0 0 1 MPa etc il Axial shear load space 61 T12 for constant transverse compression say 62 10 20 30 MPa and for fixed p 0 0 0 1 MPa etc iii Transverse shear load space 62 T12 for constant axial compression say o1 10 20 30 MPa and for fixed p 0 0 0 1 MPa etc 2 10 Lateral pressure Lateral pressure can be prescribed acting uniformly across the whole plate surface In the buckling analysis the specified latera
96. uation The local elastic buckling stresses are not critical with respect to the ultimate load bearing capacity of integrated panels Higher loads can be carried due to a positive postbuckling effect In an ultimate strength context the local buckling stress LEB can be viewed as a reference state beyond which there exist extra load bearing capacity typically for thin plates or high local slenderness in general The local elastic buckling stress can be useful as an upper limit for panels constrained to follow strict functional requirements SLS i e for design where elastic buckling deflections are not accepted 3 8 3 Orthotropic material coefficients In a simplified mathematical model the stiffened panel can be considered to be equivalent to an orthotropic material where the stiffeners are smeared out over the plate surface The PULS code is based on a six dimensional orthotropic macro material law e g Brush and Almroth 1975 Ref 1 Fig 7 DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 33 N N3 D2 xy go N3 x Nyy N3 X2 e as YM Pa 3 PM M3 M tY P NE Sl 4 4 Brn pa UNIT WIDTH Fig 7 Six dimensional macro model for stiffened panels According to non linear plate theory this macro material law takes the form of an incremental relation between the in plane loads N N N and moments M M M and the corresponding strains
97. ubjected to combined loads The model calculates the ideal elastic buckling loads eigenvalues as a separate procedure A non linear model is used for assessing the elastic postbuckling strength while stress control criteria covers the inelastic response and is used for determining the ultimate strength The stress control criteria describes the onset of material yielding in a selection of critical positions in the panel hard corners and are called limit state functions The stresses in the hard corners are calculated as the sum of the direct applied membrane stresses added to the second order membrane stress due to buckling The second order membrane stresses have contributions from the local buckling of the plate between stiffeners sideways torsional buckling of the stiffeners and global buckling of the stiffeners out of plate bending of stiffeners Membrane stresses are mid plane stresses of each component plate in the cross section Bending stresses across any component plate thickness are not included in the limit state yield criteria The limit states solved explicitly gives the ultimate strength Using default tolerance settings and characteristic yield strength as specified in the rules the code predicts UC strength values as being representative for integrated plates in larger flat plate constructions consistently including redistribution of stresses between primary stiffeners and the plate User specified tolerance for the maximum ampl
98. urves can be generated in load space o1 62 with o3 fixed o 63 with o2 fixed o2 03 with O02 fixed NB Capacity curves involves a sequence of non linear calculations for different load paths and may require some computer time number of load paths number of points in load space number of fixed stress values vii Secondary stiffeners The standard UC and buckling check in present 2 0 version control the strength of the secondary stiffeners by using a simplified theory The secondary stiffeners are modelled as lateral springs and their strength are controlled by a max deflection criterion Thus their bending stiffness is considered but not their axial nor their rotational torsional stiffness DET NORSKE VERITAS Nauticus Hull User Manual ProgramVersion 10 5 PULS Version 2 0 6 PULS September 2006 83 7 PULS EXCEL SPREADSHEET 7 1 Introduction The PULS Excel spreadsheet and the PULS GUI use the same computational routines The spreadsheet offers easy input of a large number of panels and therefore makes parameter studies easy to perform The spreadsheet is organized in input sheets and output sheets for the S3 and U3 elements The input and output parameters are the same as in the Puls GUI The Puls spreadsheet is able to read and write pbp files which are compatible with the Puls GUI 7 2 Input columns Most of input columns are self explanatory The input parameters that are found necessary to explain are tabula
99. utomatically taken to harmonise with the minimum eigenmode with some added trigger modes for safe UC strength assessment The latter is called imperfection model and is not possible to control by the user 2 2 Overview of element characteristics The main characteristics of the U3 element are summarized in Table 1 DET NORSKE VERITAS PULS 16 Nauticus User Manual September 2006 ProgramVersion 10 5 PULS Version 2 0 6 Table 1 Overview of U3 element characteristics U3 element unstiffened plate Theory Non linear Structural Rectangular unstiffened plate configuration Uniform plate thickness Loads Linearly varying normal stress along long edge Linearly varying normal stress along short edge Uniform in plane shear stress x x2 plane Uniform lateral pressure p fixed Materials Isotropic elastic material E v Steel Aluminium HAZ correction option Boundary conditions Out of plane support bending support All four edges supported laterally in plate plane Rotational restraint control of each edge free to rotate rotationally restrained spring or clamped Two options for in plane support membrane support I Integrated panel all four edges restrained to be straight decks bottom etc G Girder panel two opposite plate edges free to pull in web girders etc Output Model imperfections Default model imperfections consistent with as welded s
100. ve to this button is to manually hide or unhide the columns It is written an error message for the panels that were not solved successfully DET NORSKE VERITAS Nauticus Hull User Manual PULS ProgramVersion 10 5 PULS Version 2 0 6 September 2006 87 8 REFERENCES 10 11 12 13 Brush and Almroth Buckling of Bars Plates and Shells McGraw Hill 1975 Washizu K 1975 Variational methods in elasticity and plasticity Pergamon Press Second Edition Bath Great Britain DNV RP C201 Buckling Strength of Plated Structures October 2002 DNV Rules for Classification of Ship Part 3 Chapter 1 Sec 14 January 2000 DNV Classification Note No 30 1 July 95 Steen E stvold T K and Valsgard S A new design model for ultimate and buckling strength assessment of stiffened plates PRADS 2001 Shanghai China Byklum E and Amdahl J Nonlinear Buckling Analysis and Ultimate Strength Prediction of Stiffened Steel and Aluminium Panels The Second International Conference on Advances in Structural Engineering and Mechanics Pusan 21 23 August 2002 Steen E Application of the perturbation method to plate buckling problems Research Report in Mechanics No 98 1 ISBN 82 553 1149 1 University of Oslo Department of Mathematics Mechanics Division 1998 Steen E Buckling of Stiffened Plates using a Shanley Model Approach Research Report in Mechanics No 99 1 ISBN 82 553 11

NAUTICUS HULL - DNV Exchange

Contents

Download Pdf Manuals

Related Search

Related Contents