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CASTEM2000

1. force by unit of volume shear modulus identity matrix stiffness matrix mass matrix bending moment membrane effort matrix of shape functions vector of nodal equivalent loadings frequency temperature or shear force time thickness surface 11 CASTEM2000 C E A D M T L A M S V volume U V W displacement components g acceleration of gravity 0 0 null matrix and vector a thermal expansion coefficient A finite increment virtual operator strain vector angle or polar coordinate vector of Lagrangian multipliers or eigenvalues V Poisson s ratio p mass density o stress vector o pulsation i2 CASTEM2000 C E A D M T L A M S UNITS OF MEASUREMENT CASTEM2000 does not have any special system of units of measurement it is up to the user to supply the data to be integrated to a system with appropriate dimensions while defining the model The system coherence will be checked by applying the basic law of dynamics according to which F my Once the units of measurement used in the data are defined all the results will be expressed with these units However there is an exception to this rule the measurement of angles must always be expressed in degrees On the other hand both the values of temperature and the thermal expansion coefficient must be expressed with coherent units A few examples of appropriate systems of units of measurement as well as steel characteristic values
2. Of course creating new operators implies that the developer masters ESOPE the programming language which is a kind of highly efficient FORTRAN Without going into details the user just needs to specify that a computer entity such as a subprogram is written in ESOPE language translated in standard FORTRAN and compiled as usual To remove any ambiguity it is advisable to distinguish between thedeveloper slanguage ESOPE the user s language GIBIANE It is obvious that a user who writes procedures i e super operators becomes a GIBIANE developer 2 5 General aspects for using the program CASTEM2000 can be used both in interactive or batch mode The user should give preference to the mode which will enable him to make the most of the code especially the user program dialogue The running session is in any case fully memorized in a file which can be edited directly before being subjected to the program in the event of another execution 20 CASTEM2000 C E A D M T L A M S The structure of this file is identical to that of the file containing all the controls required for a running in batch mode The user may prepare those controls so that they apply to the definition of the model to the running of the calculation and to the postprocessing of the results However it would be better to proceed following several stages prepare the data in interactive mode perform the computation in batch mode and then return to in
3. Y SOLUTION 30 CASTEM2000 C E A D M T L A M S NEW CHAMELEMS GENERAL PARAMETERS GEOMETRY MATERIAL MODEL MODL CHARACTERISTICS OF ELEMENTS CARB MATERIAL DATA MATR BOUNDARY CONDITIONS LOADINGS Y SOLUTION The logic illustrated in the previous diagrams can be expressed in terms of operators as follows als CASTEM2000 C E A D M T L A M S NEW CHAMELEMS General parameters OPTI DIME 3 ELEM QUA8 Definition of the geometry EE D US ue cs P221 0 0 Ll DROI 2 P1 P2 S8 Ll TRAN 2 0 1 0 Material model and F E MM MODL S8 MECANIQUE ELASTIQUE COQ8 Material data CARMA MATR MM YOUN 2E11 NU 0 3 RHO 7800 xOther characteristics CAR1 CARB MM EPAI 0 01 CARMA CARMA ET CARI Boundary conditions 32 CASTEM2000 C E A D M T L A M S COND BLOQ DEPL ROTA S8 COTE 2 Loading FORT FORC 1E3 0 0 POIN 8 S8 Solution K RIGI MM CARMA KTOT K ET COND DEPL RESO KTOT FORI It is also possible to give additional characteristics while defining the material data CARMA MATR MM YOUN 2E11 NU 0 3 RHO 7800 EPAI 0 01 As a result the following is avoided CARMA CARMA ET CARI 4 1 Definition of the geometrical model In most of the preprocessing moduli of the computer codes by finite elements there are two successive
4. MATR MO YOUN 2E11 NU 0 3 RHO 78000 Rid RIGI MO MA1 RIZ ELI ET OLLI MAS1 MASSE MO MAI SOI VIBR PROC PROG 20 RI2 MAS1 SOI is a SOLUTION type object TABLE type if the key word TBAS is specified which contains the eigen frequency and mode which are closer to 20 Hz Illustration list auto list auto SOLUTION de pointeur msolut 3629 qui contient 1 mode s bis MODE DE RANG 1 DANS L OBJET SOLUTION CE MODE NUMERO 1 ON A AFFECTE LE POINT 13 FREQUENCE 2 41650E 01 MASSE GENERALISEE 3 89119E 00 QX 6 06305 205 QY 1 56670E 01 QZ 0 00000E 00 Mode de rang 1 Frequence 24 165 Masse generalisee 3 8912 1 W 0 A QY 15 667 Champ de deplacements CHPOINT de pointeur 4025 contenant 2 sous champ s Titre Type Option de calcul PLAN Points Inconnue LX LX LX 3 3 41684 197 11 9 02942E 04 10 9 02942E 04 8 3 41684 197 5 1 70833 196 9 02942E 04 6 9 02942E 04 4 1 70833 196 Points Inconnue uy RZ Ux uy RZ 2 0 00000E 00 2 46045E 17 1 00000E 00 3 1 55463 206 3 18385E 01 2 73584E 17 1 4 90476 222 2 48045E 17 1 00000E 00 The algorithms used are for the PROCHE option algorithm of inverse iterations for the INTERVALLE option research in a bandwidth for the SIMULTANE option lanczos algorithm 130 CASTEM2000 C E A D M T L A M S 7 4 Lesson 29 BUCKLING Buckling is processed in the same way as for the calculation of eigen modes apart from the f
5. 1 Lesson 15 HOW TO USE THE RESULTS Having performed a calculation the user is usually left with objects such as a stress field MCHAML type or a displacement field CHPOINT type The best way to proceed would consist in printing these objects but there is a risk of being overwhelmed by the large quantity of data As for the stress MCHAML it is possible to calculate and print a few useful entities such as Von Mises equivalent stress with the VMIS operator the principal stresses with PRIN a given component pertaining to a field may be extracted with EXCO the support of a stress MCHAML or displacement CHPOINT may be turned into a smaller support by means of REDU the numerical value of a component located at a specific point may be retreived by means of EXTR the maximum and minimum values of a field may be obtained with MAXI and MINI the norms of objects may be calculated with the XTX operator and the norm resulting from the difference between two stress or displacement fields may also be calculated to check for instance the discrepancy between the object obtained by calculation and a reference solution the reactions may be estimated at the supports using the REAC operator resultants may be calculated with the RESU operator 111 CASTEM2000 C E A D M T L A M S 5 2 Lesson 16 PLOTTING OF RESULTS There are several types of plots plot of deformed objects It is for in
6. 2 X SIN 22 5 Pl X 0 28 6699 No operator is required with this object the sign is enough The space dimension must be specified with the OPTION directive before specifying any point If the dimension has been modified during the meshing process a third null coordinate will be added to the existing points or a coordinate will be removed depending on whether one moves from 2D to 3D or from 3D to 2D When a POINT type object is listed an additional quantity comes up at the coordinates it is the density quantity which checks the average size of the sides of the elements that are connected to this point during automatic meshing processes By default the density is null When a POINT type object is listed its number which is exclusively used by the program comes up This number can change using the SORT TASS and SAUV directives Example OPTI DIME 2 OPTI DIME 2 PO 1 0 4 Re FOO EOD T a Ion wg og Point dont le numero est actuellement 2 Coordonnees 1 0000 1 0000 Densite 0 OPTI DIME 3 OPTI DIME 3 P3 0 0 0 P3 0 0 0 LIST P3 LIST P3 Point dont le numero est actuellement 3 Coordonnees D D D Densite 0 LIST P1 CIST PT Point dont le numero est actuellement 2 Coordonnees 1 0000 1 0000 D Densite 0 a The same type of POINT object is used for representing a point or a vector 2692 CASTEM2000 C E A D M T L A M S The PLUS operator not to be mistak
7. 2 the user must therefore explicitely combine the stiffness matrix K of the free system with the matrix C whereas the vector q must be added to the vector of nodal equivalent loadings f In accordance with 1 the definition of the boundary conditions given in CASTEM2000 includes the creation of a RIGIDITE type object corresponding to the vector q Of course this vector equals zero when only the null values of the nodal unknowns u have to be imposed The user can generate as many stiffness objects and as many additional fields by points as there are boundary conditions to be analyzed In CASTEM2000 formula 1 enables the processing of boundary conditions referring to linkages between different portions of a same region whether of absolute or relative type The boundary conditions can be specified by referring to MAILLAGE type objects such as points lines surfaces and volumes and by specifying the degrees of freedom concerned with the boundary conditions 4 4 Definition of loading 4 4 1 Constant mechanical loadings In CASTEM2000 the stage during which external loadings are being defined corresponds to the creation of a vectorial or scalar field by points depending on the application This field corresponds to the vector of the known right hand sides used in the resolution of the system of equilibrium equations without taking into account the boundary conditions described in chapter 4 3 _ 45 CASTEM2000 C E A D M
8. 3 0 1 3 S2 S2 PLUS 1 0 illustration For S1 45 is the angle of rotation in degrees 3 the number of elements to be created around the circumference and P1 the point at the centre of the rotation of the surface For the surface S2 1 0 stands for the translation vector and 3 the number of elements to be created on the side of the translation The mesh fineness is controlled in these 2 surfaces by the length of the segments composing the line LII and by the number of elements to be created on one side or by the density of the extreme points The DALLER operator makes it possible to mesh regularly the inside of a contour defined 97 CASTEM2000 C E A D M T L A M S by 4 sides the opposed sides have the same number of points The REGLER operator constructs a ruled surface lying on two lines The VOLUME operator creates volumes from surfaces The number of elements of a MAILLAGE object can be retreived using the NBEL operator Example NNI NBEL SI 98 CASTEM2000 C E A D M T L A M S 3 4 Lesson 8 GEOMETRICAL ELEMENTS Here is the list of the elements that can be generated by meshing operators out of the context of a finite element formulation There are two categories linear and quadratic elements depending on whether the sides of the elements have a node in the middle or not linear elements elem
9. LIGNE DROI 3 Pl P2 A straight line composed of 3 segments of equal length is created As a result the NOEU operator makes it possible to give a name to the intermediate nodes 3 and 4 N3 NOEU 3 N4 NOEU 4 40 CASTEM2000 C E A D M T L A M S 4 1 3 Creation of surfaces There are three different ways for creating a surface from a certain number of lines which compose its perimeter on a fixed geometrical surface by the translation or the rotation of any type of line from its polynomial equation written in parametrical form In the first case the surface can stem from one of the following five geometrical elements plane sphere cylinder cone or torus The mesh which is automatically constructed on a surface can be composed of triangular or quadrangular elements or both However if the surface is composed of quadrangular elements only either the contour will have to be regular or the sides opposite this contour will have to be subdivided into an equal number of segments The dimensions of the elements created on each surface are defined by the density values at the nodes of the contour The ELIM directive makes it possible to delete within a surface or between two surfaces the nodes whose relative distance is smaller than a certain specified value including double nodes this may prove necessary when several regions of the mesh are generated separately then group
10. T L A M S 4 1 1 Creation of points 4 1 2 Creation of lines 4 1 3 Creation of surfaces 4 1 4 Construction of volumes 4 2 Definition of the characteristics of the material 4 2 Linear elastic materials 4 2 1 1 Constant properties 4 2 1 2 Variable properties in relation to one parameter 4 3 Definition of boundary conditions 4 4 Definition of loadings 4 4 Constant mechanical loadings 4 4 1 1 Eigen weights 4 4 2 Thermal loadings 4 5 Characteristics of elements and selection of the formulation 5 Resolution of the discretized problem 5 1 Static linear elastic analysis 5 1 1 Substructures 5 2 Modal analysis 6 Processing of results 7 Procedures 7 1 Definition of a procedure 7 1 1 During execution 7 1 2 By means of an external file 7 2 Examples of procedures 7 2 1 Procedure reserved for static linear elastic analysis 7 2 2 Procedure reserved for modal analysis 7 2 3 Precoded procedures 36 37 41 41 42 42 42 43 44 45 45 46 48 49 49 50 50 53 53 54 54 55 56 57 57 59 61 CASTEM2000 C E A D M T L A M S ANNEX A 63 ANNEX B 65 ANNEX C T4 CASTEM2000 C E A D M T L A M S TRAINING MANUAL 1 INTRODUCTION 82 2 BASIC NOTIONS 83 2 1 Lesson 0 GENERAL INTRODUCTION OBJECTS AND OPERATORS 83 2 2 Lesson 1 HOW TO ENTER CASTEM2000 PROGRAM 84 2 3 Lesson 2 A FEW ELEMENTARY OBJECTS AND OPERATORS 86 2 4 Lesson 3 NOTION OF NAMED OBJECT 89 2 5 Lesson 4 TYPES OF OBJECTS
11. UZ CASTEM2000 C E A D M T L A M S 5 3 Lesson 17 BACKUP AND RETREIVAL CASTEM2000 makes it possible to store results and to retreive them by means of the SAUVER and RESTITUER operators Several objects can be saved and one can choose to save and retreive with or without format to avoid problems of compatibility between computers The SAUVER operator saves the objects specified by the user as well as those used to construct these objects see lesson 20 SAUVER and RESTITUER are used as follows Example OPTI SAUV FORMAT data sortgibi SAUV FORMAT MATI DEI Or OPTI SAUV data2 sortgibir SAUV MATI DE depending on whether one saves a formatted or a non formatted file Likewise for RESTITUER Example OPTI REST FORMAT data sortgibi REST Or OPTI REST data2 S5ortgibi REST 114 CASTEM2000 C E A D M T L A M S 6 A FEW DISTINCTIVE FEATURES OF CASTEM2000 6 1 Lesson 18 MCHAML TYPE OBJECTS They replace the CHAMELEM type objects which are connected with the AFFECTE type objects They can store a wide variety of data They are subdivided in several subtypes The main subtypes are GRAVITE NOEUD RIGIDITE MASSE STRESSES DEPLACEM FORCES CONTRAIN DEFORMAT MATERIAU CARACTER MAHOOKE VARINTER TEMPERAT scalar at centre of gravity scalar at the nodes scalar at the stiffness integration points scalar at the mass int
12. VITEUNIL procedure called on by NONLIN and NEWMARK in order to correct the velocities in case of unilateral supports WEYBUL makes it possible to calculate the probability to have an object ruptured by weybul law 80 CASTEM2000 C E A D M T L A M S 2 APART TRAINING MANUAL 81 CASTEM2000 C E A D M T L A M S 1 INTRODUCTION CASTEM2000 is a program with a powerful structure which offers innumerable possibilities to the user The goal of this section is to explain the notions of operators objects and the way they are articulated This guide which is composed of a series of examples grouped together in lessons ranged from the less to the most difficult is intended for beginners The user will be able to imagine by himself more and more powerful combinations of operators It is strongly advised that the user provide himself with the manual of operators before going and settling down in front of his computer and that he enter the instructions presented in the lessons We suggest that he read no more than about ten lessons at once The beginners most common errors are listed at the end of this part this will prevent the beginners from falling into the usual traps 82 CASTEM2000 C E A D M T L A M S 2 BASIC NOTIONS 2 1 Lesson 0 GENERAL INTRODUCTION NOTIONS OF OBJECT AND OPERATOR Solving a problem by means of a computer program consists in following several stages such
13. after the FINP control the user should specify when necessary the list of objects generated during the execution which must be retreived for continuing the execution Let us assume the CILRET procedure allowing the cartesian coordinates of a point P1 to be calculated from its cylindrical coordinates it can have an open or closed definition by means of controls such as DEBP CILRET A FLOTTANT B FLOTTANT C FLOTTANT floating FINP D where A B and C refer to the cylindrical coordinates R o and Z and D the internal 55 CASTEM2000 C E A D M T L A M S name of the point to which the rectangular coordinates are attributed It should be noted that the object corresponding to the coordinate Z has been defined as FLOTTANT because the procedure can be used in both 2D and 3D so it may or may not be regarded as a declared argument Later on this procedure will be found again in the course of the execution by a simple insertion in the same way as for an operator Example PI CILRET RAYON TETA Z 7 1 2 By means of an external file Instead of being defined directly in the execution stage the procedures or controls macro can be defined in advance and be memorized on the appropriate file GIBI PROC for a later use after the processing stage In this case the controls for the procedure definition should include another control for the identification such as 5 name procedure In the aforementioned case
14. as descretizing a region mesh defining a few properties material boundary conditions etc solving systems examining the results As a general rule each stage corresponds to one or several processes that acquire data edit them and create new ones when necessary So performing a calculation amounts to selecting elementary processes to be used and to supplying them with the requested data In CASTEM2000 the processes are called OPERATORS and the sets of data are called OBJECTS Objects are named by the user which enables him to find and use them Objects have been assigned a type which enable the OPERATORS to process them Objects take a part of the memory space allocated to the calculation The GIBIANE language developed from both operators and objects enables the user to specify his problem 83 CASTEM2000 C E A D M T L A M S 2 2 Lesson 1 HOW TO ENTER CASTEM2000 PROGRAM By way of introduction to CASTEM2000 the beginner should refer to the REFERENCE MANUAL chapters DEBU EXEM GIBI INTK MECA MECI MEC20 For running CASTEM2000 at least two directives are needed first the OPTION directive enables the user to declare the program main parameters such as the space DIMENSION the type s of ELEMENT used the type of calculation Example Declaration of parameters OPTION DIME 3 ELEM QUA4 PLAN CONT second the FIN directive enables the user to normally end the program r
15. as follows Example BOL1 VRAI BOL2 FAUX 86 CASTEM2000 C E A D M T L A M S the program recognizes the words VRAI true and FAUX false These objects can also be created with the comparison operators EGA gt EG EG lt gt The following instructions generate a logical object with a FAUX false value Example I1 21 I2 3 BL1 Il EGA 12 LIST BL1 The LOGIQUE SI SINON FINSI type objects are used to control the execution of a block Example SI BOLI X X 1 SINON X X 1 FINSI d LISTENTI or LISTREEL type objects The user can create a collection of integers with the LECT operator and a collection of real numbers with the PROG operator Example X 3 4 K 30 P1 PROG 1 2 2 3 X LI LECT 20 K 40 50 P2 PROG 12 13 L2 LECT 60 70 then they can be joined by means of the ET operator P3 P1 ET P2 L3 L1 ET 25 This joining operator is general it applies to most objects P3 will contain the floatings 87 CASTEM2000 C E A D M T L A M S 1 2 2 3 3 4 4 5 12 13 L3 the integers 20 30 40 50 60 70 Remarks An operator creates at least one object and the name of the result is defined by the user A directive modifies an existing object or produces an output on a logical unit screen printer disk An operator may sometimes generate several objects The COOR operator for instance calculates the coordinates of a point i
16. be constructed from a strain field allows the mesh of an imperfect ring to be generated ANNOIMP BOA CALCULEI interactive mesh of lines of pipes procedure called on by CALCULER if former chamelems CALCULE2 CALCULER procedure called on by CALCULER if new chamelems allows an assisted input of the data required for performing a 2D calculation in linear elasticity CH THETA CRITLOC determines a THETA type field which is called on by the G_THETA procedure in postprocessing enables the user to apply a damage criterion for rupture analysis CRITLOCI1 CRITLOC2 procedure called on by CRITLOC if former chamelems procedure called on by CRITLOC if new chamelems 77 CASTEM2000 C E A D M T L A M S name DENL description procedure called on by NONLIN used in the calculation of plastic correcting forces DYNAMIC allows a step by step dynamic calculation to be performed DYNAMOD2 procedure called on by DYNAMODE DYNAMOD3 procedure called on by DYNAMODE DYNAMODE allows the dynamic response of a structure to be calculated FACTORIE allows the factorial of an integer to be calculated procedure called on by FLAMBAGE if former chamelems FLAMBAGE procedure called on by FLAMBAGE if new chamelems allows buckling calculations to be performed G THETA G THETAI allows the energy restitution rate to be calculated by the G 0 method proc
17. degrees 48 CASTEM2000 C E A D M T L A M S Im CPT MANU CHPO GEO 1 T 100 calculation of the stresses equivalent to the temperature field SIGT THETA MMODEL MATERIAU CPT FEN BSIG MMODEL SIGT DEPL RESO K FEN SIG SIGM MMODEL MATERIAU DEPL SIGT 4 5 Characteristics of elements and selection of the formulation The appropriate formulation must be chosen during the last stage of definition of the calculation model In other words the user must select the type of finite elements and specify if necessary the geometrical characteristics which can be directly infered from the geometry shell thickness properties of the beams transverse sections The operator used for selecting the formulation geometry material model type of finite elements creates an AFFECTE or MODL type object Additional characteristics of the elements are selected by means of the CARA or CARB operator if the latter are not specified by MATR as for new chamelems CARA and CARB generate a CHAMELEM or MCHAML type object Resolution of the discretized problem By resolution of the discretized problem we understand all the mathematical operations required for calculating the vector of the unknows in the system of discretized equations to which any formulation applies To reach this stage it is required that one first calculates the matrices stiffness mass conductivity obtained by an integration on the studied discre
18. in the next stage while defining the calculation model This means that a plane surface for instance is automatically generated and discretized into 3 node triangular elements apart from the fact that afterwards these elements will be used with a plane or shell modelization CASTEM2000 has another important distinctive feature the numbering relating to both the nodes and the elements is transparent The notion of object to which the name directly refers and the possible automatic creations actually allow the analyses to be developed using only the reference terminologies defined by the user Figure 1 shows the geometrical elements which can now be used automatically in the stage of creation It also implies that F E formulations can be associated with each geometrical element Geometrical support Type Finite elements SEG2 oe COQ axisymmetrical POUT TUYA BARR beam pipe bar TRIB e TRI3 COQ3 DKT QUA4 Le COQ4 QUAM S 34 CASTEM2000 C E A D M T L A M S Geometrical support Tvpe Finite elements TRI6 mw TRI6 COQ6 QUAS o QUAS COQ8 TET4 LN TET4 PYRS ZS PYRS PRI6 Z PRI6 CUB8 SS CUB8 TE10 LN TE10 239 CASTEM2000 C E A D M T L A M S Geometrical support Type Finite elements PY13 S PY13 PR15 Z PR15 CU20 A CU20 figure 1 In order that the user learn easily the incremental method used in CASTEM2000 for the creation of geometrical models we have described below the proces
19. language GIBIANE GIBIANE is an advanced language enabling the user to communicate directly with the program through data exchange All the operations performed with GIBIANE consist in handling existing objects with a view to modifying them or creating new ones The syntax of an elementary operation can require several objects it takes various forms depending on whether the result obtained consists of one or several modified objects or of newly created ones In the first case the instruction is as follows OPERAND DIRECTIVES ELIM 0 001 GEOM for instance in which ELIM DIRECTIVE refers to the name of the function to be run and OPERANDS GEOM 0 001 to the objects to be used In the second case the instruction is as follows RESULTSZOPERANDS OPERATOR LIGNE DROI P1 P2 S for instance in which OPERATOR DROI refers to the name of the function to be run OPERANDS P1 P2 S stands for the objects supplied as arguments in the operator syntax and RESULTS LIGNE refers to the objects resulting from the operation Operations are performed by operators which apply directly to objects supplied as arguments Operands can be already existing objects containing information characteristic of the analysis to be carried out or specific objects defined only to facilitate the execution of the 18 CASTEM2000 C E A D M T L A M S requested operation Allocating a name to an integer or a r
20. meeting condition 2 equals M order In a partly or totally free structure non constrained the stiffness matrix is singular and there are as many null eigenvalues as there are possible stiffness motions 6 Processing of results It usually proves vital to process the results of an analysis carried out with CASTEM2000 they are contained in the CHPOINT or SOLUTION type object and are obtained by solving the equations corresponding to the phenomenon studied this processing should enable the calculation of derivative magnitudes that will then be processed more easily it should also allow the results to be displayed in order to be interpreted as rightly as possible Hence the two categories of operators of the program one of which is intended for postprocessing whereas the other is destined for graphic display In principle the postprocessing operators are used for calculating magnitudes to be displayed in graphs These magnitudes are always defined in appropriate objects provided on input to the TRAC operator This operator serves as a driver for the graphic display of both the geometry during its creation and the results in the form of deformed shapes symbols for 53 CASTEM2000 C E A D M T L A M S I vectorial magnitudes arrows line contours or color bands Besides the potentialities of the TRAC operator it is possible to get graphs in the X Y plane and three dimensional diagrams It should be remembered that all th
21. nnn the absolute value will be taken into account but the memory management algorithms will be those previous to the 9 1 release of GEMAT To make sure that the space in this memory overflow file is enough the user will allow a requirement of nnn x lll words this corresponds to twice the maximum requirement of all the segments existing at a given moment of the program execution OFILE The OFILE parameter sets the fortran number of the memory overflow file when the value of NTRK is different from zero DUMP During the execution of an ESOPE subprogram the memory management subprograms may detect an abnormal situation and stop the execution after having printed a diagnosis For getting a DUMP at that very moment the DUMP parameter will be used VERACT During the execution of an ESOPE subprogram it will be difficult to detect the error made while using the variable of a disabled segment Most of the time such a situation will entail a 125 CASTEM2000 C E A D M T L A M S serious failure relative to the program execution adressing error domain error violation In order to avoid these reactions the option VERACT NON no should be used temporarily By default VERACT OUI yes Example of a PARAM file ESOPE 1000000 NTRK 2000 LTRK 2048 Only the first line of the PARAM file is taken into account It is checked whether the PARAM file parameters have been taken into account at the start of the prog
22. of the CILRET procedure the memorization should therefore be performed as follows KSSSS CILRET DEBP CILRET A FLOTTANT B FLOTTANT C FLOTTANT FINP D Whenever he classifies a new procedure in the proper corresponding file the user should not forget to run a series of operations enabling him to use it directly The basic operation consists in turning the formatted procedure file into a non formatted file by means of the secondary program creproc so as to be accessible to CASTEM2000 IF gibi procedure is the name of the formatted file containing all the procedures one will have to proceed as follows for creating a direct access file 56 CASTEM2000 C E A D M T L A M S assign gibi procedure to the logical unit 20 GIBI PROC to the logical unit 10 run the creproc program 7 2 Examples of procedures 7 2 1 Procedure reseved for static linear elastic analysis In accordance with the schematization of an approach by finite elements and the logic adopted in CASTEM2000 it is possible to carry out a static linear elastic analysis in several stages 1 interactive definition of a MAILLAGE GEO type object or retreival of this object on a stack file 2 definition of the elastic linear behavior model of the material in a MMODEL MODI type object containing also the geometric type data and data on the finite element formulation 3 definition of the material characteristics and of possible addit
23. or is named PARAM On CRAY the parameter file is replaced with a string placed at the beginning of the set of data It contains data written as follows KEY WORD KEY WORD value If there are several parameters the separating character is a comma Example BUF 20000 NTRK 100 LTRK 2048 DUMP Two types of parameters must be supplied Execution parameters Translation parameters 6 8 1 1 Execution parameters ESOPE and BUF 2124 CASTEM2000 C E A D M T L A M S The ESOPE parameter fixed eee in number of words eee size of the memory space which must be available for GEMAT If eee words are not available the program running will be stopped If there is no ESOPE parameter the maximum number of words available will be allocated to GEMAT if necessary the value bbbb of the parameter BUF bbbb will be substracted from GEMAT The parameter BUF bbbb stores bbbb words in memory By default BUF 0 ZERMEM The parameter ZERMEM NON no prevents GEMAT at the time of initialization from setting back to zero the memory space which has been allocated to it This option will be used only if it is certain that this memory space is already at zero By default ZERMEM OUI yes LTRK and NTRK The memory overflow file GEMAT is direct access it includes NTRK nnn blocks of LTRK Ill words each If there is no NTRK parameter or if it equals 0 there will be no disk memory overflow If nnn is negative in NTRK
24. reduced by static condensing The static condensing procedure enables the removing of a few unknowns of the system arising from equilibrium equations by replacing them in the remaining equations As a result the loadings and equivalent stiffnesses are obtained in relation to the selected nodal points and both the gathering and the resolution of these values allow the initial problem to be solved The degrees of freedom of each substructure according to which the matrices are reduced are usually those located on the contour in order to ensure the continuation with the adjacent substructures In the static area the solution obtained by means of this technique is either correct or equals that which would be obtained if the structure had been studied as a whole Nevertheless when this technique is used advisedly the matrices of each substructure are usually far smaller than those of the complete structure and they demand shorter periods of time for being solved and less memory space for each stage of resolution 50 CASTEM2000 C E A D M T L A M S An analysis by substructure consists of three basic distinct stages 1 Reduction of substructure matrices The degrees of freedom of each substructure are reduced so as to generate a stiffness and some loadings equivalent to the contour If u j stands for the external degrees of freedom and u j the internal degrees of freedom of the ju substructure the system of linear equilibrium equati
25. resolution of the system of linear equilibrium equations e STAGE 3 ANALYSIS AND POSTPROCESSING OF RESULTS that can either be local quantities such as displacements stresses strains or global quantities such as strain energy or else maximum strain Usual computer programs are rigorously structured according to this logic each stage being associated with a definite modulus specific to the code a preprocessor for defining the complete model which transmits the data to the computer program proper as soon as the data are elaborated 2 the computer program which sends a series of processes which the user is compelled to use in black box as soon as a procedure of resolution has been selected 3 a postprocessor which carries out the required processings as soon as it has received the results from the above processes It is obvious that the user does not have to intervene with this type of structure in any of the stages to bring about modifications meeting his own needs However more flexibility would be of benefit to the user who sets out to solve various problems located at different 16 CASTEM2000 C E A D M T L A M S points of the resolution process The user could indeed come up against great difficulties when modeling the structure geometry usually composed of several complex parts in a way best suited to the requirements of the analysis Besides the process of discretization requires that the elem
26. stages in the creation of the geometrical model definition of the geometry using basic geometrical elements such as points lines surfaces and solids generation of the mesh from the geometries and a series of parameters types of elements and distribution of these elements on the sides for instance In CASTEM2000 on the contrary a geometrical object whatever it may be only exists in discretized form So the region of analysis is discretized into elementary geometrical elements as soon as the geometry has been defined the objects defined in this way are stored in the Ed s CASTEM2000 C E A D M T L A M S MAILLAGE type object The stage during which the geometrical model is generated corresponds to the creation of a series of MAILLAGE type objects which once grouped together compose the discretized region as a whole The MAILLAGE type objects are points lines surfaces or solids some operators enable their construction others allow geometrical operations such as rotations translations intersections to be performed on them It is also possible to call on other operators the functions of which are not limited to the geometrical area and which can be used in other stages of the analysis see chapter 3 The elements defined while the geometry is being constructed constitute the geometrical support of the finite elements that will be used later on in the analysis The characteristics of these elements will be specified
27. the materials are being defined corresponds to the creation of a field by element MCHAML type object This field can be single for the whole area of analysis if the latter is composed of one type of material If it is composed of several types of materials the user will define as many fields by elements as there are regions of materials with different characteristics With former CHAMELEMS the structure complete mathematical model is obtained as soon as the geometrical model is constructed by associating the corresponding physical characteristics with it or by defining the type of behavior and the material properties With new CHAMELEMS the field of properties material and geometrical is constructed once the geometrical model the material behavior and the finite element are associated 4 2 1 Linear elastic materials 4 2 1 1 Constant properties Four operators MODL MODELE and MATR MATER are used to define linear elastic materials MODL and MODELE are used to define an isotropic or orthotropic behavior within the framework of linear elasticity 42 E CASTEM2000 C E A D M T L A M S As for MATR and MATER they give the material properties such as Young s modulus Poisson s ratio the density the thermal expansion coefficient the directions of orthotropy etc Operators construct fields by elements with several components 4 2 1 2 Properties varying with a parameter Combining appropriate sequences of gen
28. the objects saved on a file RESU calculation of the resultant of a CHPO type force field RIGI construction of the stiffness matrix RIMP conversion of a complex SOLUTION type object ROTA contruction of a surface by the rotation of a line or a surface RTENS reorientation of a field by elements for massive and shell elements in a new and direct orthonormal basis SAUF modification of a list of real numbers or integers SAUT skip of line s or page s 73 CASTEM2000 C E A D M T L A M S name description SAUV backup of one or several objects on a file SEIS construction of a loading from a seism modal basis SI logical test SIGM calculation of a stress field from a displacement field SIGN gives the sign of a real number or integer SIGS calculation of stresses from a SOLUTION type object SIN sine of objects SINO alternate condition SOLS construction of static solutions SOMM calculation of the integral of a SOLUTION type object SORT writing of a MAILLAGE type object on a file SOUR imposes a volumic source of heat SPO calculation of oscillator spectra STRU creation of a STRUCTURE type object SUBS program temporary interruption and return to the CMS system IBM VM only SUIT creation of a list of CHPO objects SUPE creation of one super element SURF construction of a surface inside a contour SYME construction of a symmetrical object SYMT imposes
29. 2 UX 1 UY 3 A field by point with two components named UX and UY and the values of which are 1 and 3 are created on the point C1 A name of component cannot exceed 4 letters A CHPOINT type object can also be created from a set of points as follows Example CHP2 MANU CHPO C1 ET C2 ET 2 UX PROG 1 2 UY PROG 1 2 In this case the names of the components must be followed by a progression containing as many floatings as there are points in the considered set of points The usual operations such as sums and substractions are possible whatever the geometrical supports the number and the names of components of the CHPOINTs may be Example FIN DE FICHIER SUR L UNITE 3 LES DONNEES SONT MAINTENANT LUES SUR LE CLAVIER OPTI DIME 2 OPTI DIME 2 C1 0 0 H T CHP1 MANU CHPO C1 2 UX 1 2 UY 2 3 CHP1 MANU CHPO C1 z ux 1 2 UY 2 3 CBS MANU CHPO C1 51 CHP2 MANU CHPO C1 1 T 51 CHTOT CHP1 CHP2 CHTOT CHP1 CHP2 LIST CHTOT LIST CHTOT COCOLNT de pointeur 1857 contenant 1 sous champ s Titr CHPOINT CREE PAR CRECHP Type Option de calcul PLAN Points Inconnue uv T 1 1 20000E 00 2 30000E 00 5 10000E 01 102 CASTEM2000 C E A D M T L A M S It is also possible to multiply divide these CHPOINT type objects by a floating or to raise them to a power Example CHP5 CHP1 2 CHP6 CHP1 2 CHP7 CHP1 2 Moreover two fields by points
30. 4 6 1 Or OPTI ELEM SEG3 Type Definition Examples DROIT 2 points LIGNE DROI P1 P2 CERCLE 3 points ARC CERC P1 CENTRE P2 CER3 3 points ARC CER3 PI P2 P3 PARABOLE 3 points ARC PARA P1 PINT P2 CUBP 4 points ARC CUBP PI P2 P3 P4 CUBT 2 points and 2 vectors ARC CUBT PI V1 P2 V2 COURBE n points polynomial curve of order n 1 QUELCONQUE n points broken line passing by the n given points INTERSECTION 2 points and 2 surfaces ARC PI INTE S1 S2 P2 Table A type definition examples DROIT 2 points LIGNE DROI P1 P2 P2 M d CERCLE 3 points ARC CERC Pl CENTRE P2 P2 P1 CENTRE CASTEM2000 C E A D M T L A M S type definition examples CER3 3 points ARC CER3 P1 P2 P3 PI d P3 PARABOLE 4 points ARC PARA P1 PINT P2 P1 o Pint CUBP 4 points ARC CUBP P1 P2 P3 P4 p P4 P1 P3 CUBT 2 points ARC CUBT V1 P2 V2 2 vectors 2 PI V P2 VI 39 CASTEM2000 C E A D M T L A M S type definition examples COURBE n points Polynomial curve of order n 1 QUELCONQUE n points LIG1 QUEL SEG2 P1 PN P2 pl INTERSECTION 2 points ARC P1 INTE S1 S2 P2 2 surfaces pif S2 S1 figure 2 As mentioned previously the internal points of a created line are accessible only through the number that the program attributed to them for instance with the following instructions OPTI DIME 2 ELEM SEG2 PL 0 0 ge Eee NS E
31. 91 3 MESH 92 3 1 Lesson 5 POINT TYPE OBJECTS 92 3 2 Lesson 6 CREATION OF LINES 94 3 3 Lesson 7 CREATION OF SURFACES OR VOLUMES 96 3 4 Lesson 8 GEOMETRICAL ELEMENTS 99 3 5 Lesson9 THE CONFONDRE AND ELIM DIRECTIVES 100 3 6 Lesson 10 THE SORTIR AND LIRE DIRECTIVES 101 4 ELASTIC CALCULATION 102 4 1 Lesson 11 FIELD REPRESENTATION 102 4 1 1 Field by points 102 4 1 2 Field by elements 103 4 2 Lesson 12 ELASTIC CALCULATION 105 4 3 Lesson 13 CALCULATION IN IMPOSED DISPLACEMENTS 107 4 4 Lesson 14 OTHER CHARACTERISTICS 108 CASTEM2000 C E A D M T L A M S 5 USE OF RESULTS del 5 2 5 3 Lesson 15 HOW TO USE THE RESULTS Lesson 16 PLOTTING OF RESULTS Lesson 17 BACKUP AND RETREIVAL 6 A FEW DISTINCTIVE FEATURES OF CASTEM2000 6 1 6 2 6 3 6 4 6 5 6 6 6 7 6 8 7 1 1 2 7 3 1 4 Lesson 18 MCHAML TYPE OBJECTS Lesson 19 ELEMENTARY AND COMPOSED OBJECTS Lesson 20 RELATIONS BETWEEN OBJECTS Lesson 21 REPETITIVE AND ALTERNATE RUNNINGS 6 4 1 Repetitive runnings 6 4 2 Alternate runnings Lesson 22 PROCEDURES Lesson 23 TABLE TYPE OBJECTS Lesson 24 MANIPULATION OF COMPONENTS Lesson 25 HOW TO USE THE GEMAT 9 3 release 6 8 1 The Parameter file 6 8 2 The running parameters 6 8 3 The translation parameters MORE MECHANICS Lesson 26 BOUNDARY CONDITIONS Lesson 27 THERMAL LOADINGS Lesson 28 EIGEN FREQUENCIES AND MOD
32. C modification of the name of a component of a field by point NON logical negation NORM calculation of the norm of a vector NOTI printing of GIBI or CASTEM2000 manual OBTE interactive acquisition of objects OPTI definition of the calculation general options ORDO sorting out of a list of objects z7 CASTEM2000 C E A D M T L A M S name description ORIE orientation in the same direction of all the sides of a mesh ORTH orthogonalization of an object with respect to other objects OSCI calculation of an oscillator response OU or logical OUBL clears the name of an object from the memory PARA construction of an arc of a parabola PAVE creation of volumic elements inside a parallelepipedic surface PERM construction of a permeability matrix for elements in porous medium PICA conversion of a Piola Kirschoff stress field into a Cauchy stress field PJBA calculation of the force projection onto a modal basis PLAC gives the size of the available memory space PLAS calculation of a field of plastically acceptable stresses PLUS translation of an object PMIX vectorial product POIN extracts one or several points from a geometry extracts the maximum or minimum point s of one or several components from a field PRCH conversion of a field by points into a field by elements by an interpolation based on the form functions of the finite element formulation PRES calculation of the field of noda
33. CASTEM2000 C E A D M T L A M S CASTEM2000 USER S GUIDE NOVEMBER 1993 CASTEM2000 C E A D M T L A M S PREFACE This manual of CASTEM2000 is composed of two parts the first part consists of a user s manual in which CASTEM2000 general principles as well as the proper way of performing the calculation of an elastic structure are described the second part consists of a training manual which includes several lessons it is meant to help the beginners first steps There are essential additional pieces a collection of annotated examples classified by subject a reference manual in which the functions and the way to use each operator directive and procedure are described CASTEM2000 C E A D M T L A M S CONTENTS USER S MANUAL FOREWORD 9 NOTATION 10 UNITS OF MEASUREMENT 13 References 14 1 Introduction 15 2 General remarks concerning CASTEM2000 15 2 1 Organization of the F E calculation process 15 2 2 CASTEM2000 distinctive features 17 2 3 CASTEM2000 language GIBIANE 18 2 4 CASTEM2000 potentialities 19 2 4 Notion of procedure 19 2 4 2 Development of new operators 20 2 5 How to use the program general aspects 20 2 6 General syntactic rules 21 3 Structures data and general operators 22 3 1 Classification of objects 22 3 2 Classification of CASTEM2000 main operators 25 4 Preparation of the calculation model 28 4 1 Definition of the geometrical model 33 CASTEM2000 C E A D M
34. D M T L A M S c definition of the structure stiffness The RIGI operator is used Example RI1 RIGI MO MA1 d boundary conditions Example CL1 BLOQU DEPL Cl The BLOQU operator constructs the stiffness associated with conditions of imposed values on the unknowns of a discretized problem The DEPL key word constrains all the displacement d o f of the point C1 This stiffness will be added to the structure stiffness e loading The loading can be defined by means of the FORCE and CHARGEMENT operators Example FOL FORC 0 1 C2 f resolution of the linear system The RESOU operator can then be used as follows Example RI2 RI1 ET CL1 DEL RESOU RI2 FOI The result of RESOU is a displacement CHPOINT Once calculated this field must be handled to deduce the stresses Example SIl SIGMA MO MA1 DEl 106 CASTEM2000 C E A D M T L A M S 7 3 Lesson 13 CALCULATION IN IMPOSED DISPLACEMENTS Instead of applying a force it is possible to impose a displacement It is required to call on the DEPI operator Example MO MODL MA1 MATR MO RI1 RIGI CL1 BLOQUE C1 DEPL CL2 BLOQUE C2 UX FO2 DEPI CL2 1 DEPI creates a force field which imposes the value 1 to the displacement UX of the C2 object This field must be added to the other existing forces The system is solved in the same way as in lesson 12 Example RD RII ET CLI ET CL2 DEI RESOU RI2 FO2 Remark
35. ES Lesson 29 BUCKLING 8 LIST OF COMMON ERRORS 111 111 114 115 115 116 117 118 118 118 120 122 123 124 124 12 126 128 128 129 130 131 132 CASTEM2000 C E A D M T L A M S 1 PART USER S MANUAL CASTEM2000 C E A D M T L A M S FOREWORD This material is not guaranteed on delivery Neither the C E A nor the companies involved in activities of development distribution and maintenance will ever be regarded as responsible for possible damages spendings or loss of profit tied to the use of the CASTEM2000 program even if they are aware that such events might occur CASTEM2000 C E A D M T L A M S NOTATION The symbols used mainly in this manual are given below The other symbols and notations are defined when they are used General conventions Each matrix is symbolized by a capital letter underlined with a bold single line Vectors are referred to by underlined small letters The T exponent refers to a transposition whereas lis used to refer to an inverse matrix Examples A square or rectangular matrix b vector A inverse matrix A transposed matrix Symbols used B matrix of congruence connecting strains and displacements C damping or boundary conditions matrix d d l degrees of freedom u vector of nodal displacements 10 CASTEM2000 C E A D M T L A M S Iz x I iz M N Z laur modulus of elasticity Hooke s matrix
36. LLs VERCALL NON no No checking of the CALLs VERSEG Makes it possible to generate a fortran language containing or not the characteristics for producing at the time of the execution improved error messages for failures occurring during the execution of SEGxxx instructions VERSEG OUI yes Default possible improved messages VERSEG NON no possible non improved messages NORM See chapter CISI extensions of the Development Guide Report CEA DMT 92 300 in which extensions to the Esope language are described NORME DEDR Default option The CISI extensions are refused by the ESOPE translator NORME CISI The CISI extensions are accepted Example of PARAM file ESOPE 1000000 FORT SUN 127 CASTEM2000 C E A D M T L A M S 7 MORE MECHANICS 7 1 Lesson 26 BOUNDARY CONDITIONS It is possible to impose various boundary conditions with the following operators the BLOQUE operator allows the specific degrees of freedom to be constrained in the given directions the SYMT operator allows boundary conditions of symmetry to be specified with respect to a plane or a straight line the ANTI operator allows boundary conditions of antisymmetry to be specified with respect to a plane or a straight line the RELA operator makes it possible to impose any linear combination of displacements at different points this operator is especially useful when you will have the displacements of two
37. PA containing the nodal components of the acceleration vector gp multiplication of the mass matrix M by the field CPA NEW CHAMELEMS model definition MM MA MATR MM c Eee II Z O J E calculation of the stiffness matrix K RIGI MM MA ET C L calculation of the mass matrix M MASS MM MA construction of the acceleration field by point CPA MANU CHPO GEO 1 UZ 9 81 nodal equivalent forces POIDSPR M CPA system solution K DEPL POIDSPR DEPL RESO K POIDSPR 47 CASTEM2000 C E A D M T L A M S 4 4 2 Thermal loadings The generic vector for the thermal loading temperature field imposed on a constrained structure is expressed as follows f B xDxaxN x T xdV V where amp is the vector of thermal expansion coefficients NTT is the temperature punctual vector defined by interpolating nodal values T The loading vector corresponding to the application of a thermal loading can thus be calculated in three stages definition of a scalar field by point CPT containing the temperature nodal values calculation of the field by elements containing the stresses equivalent to the thermal distribution defined by o D a N Ty calculation of nodal equivalent forces f B xoxav V It is advisable to input the following control sequence NEW CHAMELEMS definition of the field by point containing the temperature values here the whole structure is at 100
38. PROJ RACC REGE SYME TASS TOUR VERS Materials MATE MATR MODE MODL Displacement conditions ANTI APPU BLOQ CONV DEPI FLUX RELA SOUR SYMT Loadings BSIG CHAR DEBI FORC MOME PRES SEIS THET 2 CASTEM2000 C E A D M T L A M S Characteristics of elements and formulation AFFE former elementary fields CARA CARB OPERATORS USED FOR SOLVING THE DISCRETIZED PROBLEM ACTI CRIT DEVO DSPR DYNE ELAS EXCE HOTA KP KSIG KTAN MASS MOTA OSCI PJBA PLAS PROI PSMO RECO RESO RIGI SIGS SPO SUPE SYNT VIBR OPERATORS USED FOR PROCESSING THE RESULTS Postprocessing operators DFOU ENER EPSI GRAD INVA JACO PRIN REAC RTEN SIGM SOLS TAGR TOTE TRES VMIS Operators used for graphic display DEFO DESS TRAC VECT 4 Preparation of the calculation model By computer model we understand all the data that the user must prepare for describing in full the characteristics of the problem to be analyzed The calculation model is usually defined by the general parameters defining the working medium and the basic characteristics of the global or local model on which one wishes to operate the data describing in discretized form the geometry of the region to be analyzed the characteristics of the materials composing the area of analysis the boundary conditions expressed in terms of displacements imposed on the values of the unknown function and in term
39. QU ARGU DETR INFO LIRE LIST MENA MESS NOTI OBTE OUBL PLAC RESP REST SAUT SAUV SORT TEMP Execution of arithmetic operations ABS ATG COS ENTI EXP FLOT LOG MULT SIGN SIN Execution of logical operations lt EG gt EG EGA EXIS FINS MULT NEG NON OU SI SINO Execution of mathematical operations COLI COMB CONC ET INTG IPOL NNOR NORM ORDO ORTH PMIX PSCA PVEC RESU SOMM XTMX XTX XTY YTMX Retreival or processing of data in objects CMOY COMT COOR DIAG DIME DIMN EXCO EXTR INDE MAXI MINI NBEL NBNO QULX TIRE TYPE VALE VALP Modification of data in objects CAPI CHAM CHAN CHSP ENLE INSE NOMC PICA PRCH PRHC REDU REMP RIMP RTEN SAUF Calculation of functions FONC GREE IFRE TFR TFRI Loops instructions with conditions and procedures DEBP FIN FINP FINS ITER QUIT REPE RESP SI SINO 226 CASTEM2000 C E A D M T L A M S OPERATORS USED FOR THE PREPARATION OF THE CALCULATION MODEL General parameters DENS OPTI TITR Geometrical model points BARY CONF NOEU POIN lines CER3 CERC COMP CONG COTE COUR CUBP CUBT DROI INTE PARA QUEL surfaces COUT DALL ENVE FACE GENE REGL ROTA SURF TRAN volumes GENE PAVE VOLU colors AFCO COUL mesh processes AFFI CHAN CONF CONT COOR DEPL DIFF ELEM ELIM HOMO INCL INVE MANU MODI MOIN NBEL NBNO NOEU ORIE PLUS POIN
40. RITERE is given as argument only if the density of the points is not known otherwise only the points separated by less than one tenth of the current density will merge Remark Generally speaking one should be cautious when using those two directives It is better to structure the set of data so as to avoid using them as much as possible If for instance two surfaces have a line in common it is preferable to create the line first then the two surfaces from that line rather than create the surfaces and use ELIM between them 100 CASTEM2000 C E A D M T L A M S 3 6 Lesson 10 THE SORTIR AND LIRE DIRECTIVES It is possible by means of the SORTIR directive to write a mesh or a part of a mesh on a logical file defined by the OPTION directive Example construction of the GEO mesh OPTI SORT 15 SORTIR GEO FIN On the other hand it is possible by means of the LIRE directive to read a mesh from a logical file defined by the OPTION directive Example OPTI LIRE 15 LIRE GEO MM MODL GEO MECANIQUE ELASTIQUE COQ2 oT 101 CASTEM2000 C E A D M T L A M S 4 ELASTIC CALCULATION 4 Lesson 11 REPRESENTATION OF FIELDS 4 1 1 Fields by points The first way to represent a field consists in defining it by its values at the nodes of the mesh it is called a CHPOINT type object or field by points Here is the simplest way of creating it Example Cl 0 0 CHP1 MANU CHPO Cl
41. T L A M S The user is free to generate as many fields by points as there are independent loading conditions to be considered in the analysis stage either successively or together Properly selected operators enable a direct specification of concentrated loadings and or regularly distributed surface loadings The mass and or non regularly distributed loadings can easily be generated by means of selected sequences of general operators A few specific cases will be detailed in the following pages of this manual 4 4 1 1 Eigen weights The generic loading vector stemming from the mass forces is expressed as follows 1 f N xbxav V where V stands for the studied region N the matrix of shape functions and b the vector of mass force densities In the case of an eigen weight we have DX y z pg x y z where p stands for the mass density and g the acceleration vector If for convenience the vector g is expressed in relation to its nodal values by way of the shape functions formula 1 can be rewritten as follows f p NT xNxdVxg V where the vector g contains the nodal values of the g acceleration The calculation of the loading vector corresponding to an application of a gravitational loading in direction z can thus be performed in three stages calculation of the mass matrix of the region 46 CASTEM2000 C E A D M T L A M S M px N xNxdV V definition of a vectorial field by point C
42. When displacements are imposed at one point the constraint stiffness generated by the BLOQ operator must be added to the stiffness matrix 107 CASTEM2000 C E A D M T L A M S 4 4 Lesson 14 ELEMENTS REQUIRING ADDITIONAL CHARACTERISTICS They are elements whose geometrical description cannot be entirely done with the MAILLAGE type objects The list of elements of this type and both the compulsory and optional characteristics in italics are given in Table C These characteristics may be added in MATR or in an object CARACTERISTIQUE subtype created by CARB which is combined with the object created by MATR The elastic calculation will take the following form for COQ3 elements Example MO MODL GEO MECANIQUE ELASTIQUE COQ3 MA MATR MO YOUN 2E11 NU 0 3 CA1 CARB MO EPAI 0 2 MA1 MA ET CAI RIl RIGI MO MAI CL1 BLOQ DEPL L1 RI2 RI1 ET CL1 FO FORCE 0 1 P1 DE RESOU RI2 FO SI1 SIGMA MO MAI DE We could have written Example MA MATR MO YOUN 2E11 NU 0 3 EPAI 0 2 For POUT elements the syntax can be the following Example CA1 CARB MO SECT 5 2 INRY 10 4 LNRA 20 TORS 25 SECT INRY INRZ are the section and the different inertias of the beam 108 CASTEM2000 C E A D M T L A M S element characteristic s COQ2 COQ3 COQ4 EPAI shell thickness DKT ALFA plasticity criterion EXCE offset COQ6 COQ8 EPAI shell thickness EXCE offset BARRE SECT cross sectio
43. act that the mass matrix is replaced with the matrix of initial stresses calculated by the KSIGMA operator and multiplied by 1 The result will be Example MA1 MATR MO YOUN 2E11 NU 0 3 RIl RIGI MO MAI FOSFORCE us de CL1I BLOQ 43 RIZ2 RI1 ET CL1 DEl RESOU RI2 FO1 SE1 SIGMA MO MAI DEI KSEl KSIGMA MO SEL FLAM SOISVIBR PROC PROG 4 3 RIZ 1 KSE1 The result is therefore the buckling mode associated with the multiplicator coefficient closer to 4 3 131 CASTEM2000 C E A D M T L A M S 8 LIST OF COMMON ERRORS Use of the name of an object corresponding to the name of an operator Illustration FIN DE FICHIER SUR L UNITE 3 LES DONNEES SONT MAINTENANT LUES SUR LE CLAVIER OPTI DIME 2 ELEM SEG2 OPTI DIME 2 ELEM SEG2 0 0 D1 DROI 2 A B MO MODL D1 MECANIQUE ELASTIQUE COQ2 MO MODL D1 MECANIQUE ELASTIQUE COQ2 MA MATR MO YOUN 2E11 NU 0 3 RHO 7800 EPAI 0 01 MA MATR MO YOUN 2E11 NU 0 3 RHO 7800 EPAI 0 01 RIGI MASSE MO MA RIGI MASSE MO MA RI1 RIGI MO MA RIT1 RIGI MO MA xik ERREUR 11 ee dans l operateur Il y a un resultat de type MMODEL et de nom MO en trop par rapport aux noms a affecter Premiere ligne donnees deuxieme ligne type des donnees RIGI MO M aes MMODEL MCHAML Ge X X X eo xe ESE The syntax analyzer can no longer recognize the name of the operator which the user tried to use From now on RIGI is a RIGIDITE type object Use
44. associated density Object containing the data relative to a stiffness or mass matrix Object containing all the eigen vectors and values associated with a modal analysis 24 CASTEM2000 C E A D M T L A M S STRUCTURE Object connected with the description of a structure and containing the stiffness and mass related to it TABLE Set of objects which can have any type and are characterized by any type of index VECTEUR VECTOR Object relative to the display of a field by points by means of vectors 3 2 Classification of CASTEM2000 main operators Operators are grouped together according to their function operators of general interest operators used for the preparation of the model operators used for solving the problem and postprocessing operators OPERATORS OF GENERAL INTEREST Direct creation of objects general type COPI EXIS MANU fields field by elements and field by points CHPO HOOK MOME VARI ZERO Stiffness AMOR CABL CAPA COND EXCI LUMP MASS PERM RELA RIGI evolution BRUI EVOL FDT FILT LAPL MAPP objects relating to the substructuration CHOC CSLT DEPB DEVE ELST JONC LIAI RELA STRU lists of objects integers real numbers words fields 25 CASTEM2000 C E A D M T L A M S LECT MOTS PROG SUIT other objects modal basis table configuration BASE FORM MOT SUPE TABL TEXT VECT Management of objects and memory AC
45. ature values PRGT PROG 0 200 progression containing the values of YOUNG s modulus PRGY PROG 2 E11 1 E11 function E T YT EVOL MANU PRGT PRGY CHPOINT containing the values of YOUNG s modulus CHPYT TEMPE YT definition of the behavior model and F E MM MODL GEO MECANIQUE ELASTIQUE QUA4 transformation CHPOINT E T into CHAMELEM E T CHAMYT CHAN CHAM CHPYT GEO definition of the material properties PMAT MATR MM YOUN CHAMYT NU 0 3 ALPH 1 E 6 Besides there are special operators for automatically applying complex type boundary conditions SYMT ANTI For structural applications the conditions of displacement and or imposed rotation can be specified by referring to the three usually accepted directions or to any of the directions defined by the user 4 3 Definition of boundary conditions In CASTEM2000 the boundary conditions on the values of the unknown function are processed by the Lagrangian multipliers method 44 CASTEM2000 C E A D M T L A M S In practise the series of boundary conditions is defined as follows Cu q 1 in which C is a matrix of constant coefficients and q the vector of values imposed on the nodal displacements in this case the Lagrangian multipliers method consists in writing the system of linear equilibrium equations as follows Ku C Aa f 2 Cu q where vector A contains unknown multipliers In order to have the resolution system
46. can be joined by means of the ET operator The point and the component which are common to the two fields are taken and their corresponding values are added The names of components are either chosen by the user or arbitrarily determined by the operators that create the objects The name of a component can be modified by means of the NOMC operator if the field by point only contains one component Example CHP8 MANU CHPO C1 1 UZ 10 CHPS NOMC T CHP8 CHPS is overwritten and the name of its component UZ is turned into T It is possible to extract a one component CHPOINT from a multiple component CHPOINT by specifying the name of this new component by means of the EXCO operator Example CHP9 EXCO UX CHPI T 4 1 2 Fields by elements Another way of representing a field consists in defining the field by its values in the different elements of the mesh this is what is called a MCHAML type object former CHAMELEM or field by element In each element the field can lie respectively on the nodes stiffness integration points 103 CASTEM2000 C E A D M T L A M S mass integration points centres of gravity stress calculation points Here is the simplest way of creating it Example CHAM1 MANU CHML GEO G 9 81 TYPE GRAVITE CHAMI is an MCHAML type field by elements with a single component G a GRAVITE subtype pertaining to the GEO mesh In the same way as for the fields by points it i
47. chapter 2 that the whole computer structure of CASTEM2000 was based on the concept of objects 1 e of data or information relating to each process Some special operators enable the direct construction of elementary objects On the other hand others are used for the construction of more complex objects by modifying or associating one or several objects of elementary types All the existing general type operators for the construction of complex objects are detailed further on in this chapter However we suggest giving you now a classification of these objects to specify their potentialities and the rules for using each of them 3 1 Classification of objects The objects available in CASTEM2000 i e liable to be generated handled or processed are ordered according to the type of data they contain and to the meaning they have in the analysis Some of these objects contain data which are defined and memorized solely in relation to the operations to be run in the course of the process cc CASTEM2000 C E A D M T L A M S Here is the list of the main types of objects one can easily obtain the type of each object by listing its contents using the LIST operator Object type Description AFFECTE ATTACHE BASEMODA BLOQSTRU FIELD BY ELEMENTS CHPOINT FIELD BY POINT CHARGEMENT LOADING CONFIGURATION Object relating to the definition of the calculation model and containing the data relating to the discretized
48. created lines from points likewise we can create surfaces from lines and volumes from surfaces These automatic meshing processes can be performed with the following operators DALLER REGLE ROTA SURF TRANS and VOLUME The size of the elements created within the contours is limited by the size of the elements of the contour Example OPTI ELEM QUA4 Cl 0 0 3 CAN Ss dv On C3 1 1 C4 0 1 LIl C1 D 1 C2 D 3 C3 D 2 C4D 1 SUL LI1 SURF PLAN As a result the surface SU1 will be meshed with 4 node quadrangles and 3 node triangles and the line LI1 will be meshed with 2 node elements In fact it is not possible to mesh any surface with only quadrangles and conform to an imposed mesh However ELEM TRI3 is specified in the OPTION directive the surface will contain only 3 node triangles Illustration Fin trace Zoon Initial Qualification Noeuds Elements PS Fin trace Zoon Initial Qualification Noeuds Elenents PS 96 CASTEM2000 C E A D M T L A M S It would also have been possible to use 8 node quadrangles or 6 node triangles if ELEM QUAS or ELEM TRI6 had been specified in the OPTION directive The ROTA and TRANS operators make it possible to generate a surface from a line Example OPTI DIME 2 ELEM TRI3 Pl 0 0 Cle T3095 C2 2 0 LI1l Cl D 3 C2 SL LIL ROTA 3 45 P1 oz pl TRANS
49. d end C1 and C2 in relation to the current density Example 0 sous reference s lere ligne numero element 2eme couleur 3eme noeud s BLAN BLAN BLAN BLAN 64 66 6 68 66 67 68 65 94 CASTEM2000 C E A D M T L A M S The DROIT and CERCLE operators will create 2 node lines SEG2 elements or 3 node lines SEG3 elements depending on whether the OPTION directive specified linear or quadratic elements This directive will also be employed to check the types of elements used in the generation of surfaces or volumes Remarks The names of the DROIT and CERCLE operators can respectively be shortened in D and C The DROIT and CERCLE operators create a certain number of points for building the segments These points will have no name and will be accessible to the user at first only through their internal numbers Example OPTI ELEM SEG2 Ol 0 0 2 C2 1 0 Lil C1 DROIT 3 C2 Two intermediate points with no name are created between C1 and C2 The user will be able to name them with the POINT operator N1 POINT 3 LIL N2 POINT 4 LII and list the coordinates according to the x axis for instance of these points with the COOR operator LIST COOR 1 N1 LIST COOR 1 N2 The successive results will be the values 33 and 66 the x coordinates of N1 and N2 95 CASTEM2000 C E A D M T L A M S 3 3 Lesson 7 CREATION OF SURFACES OR VOLUMES We have
50. d the name of an operator it sends the monitoring progress to it Only the first 72 characters of a line are taken into account An instruction may contain brackets In accordance with the rules of algebra the sos CASTEM2000 C E A D M T L A M S instructions found in the inner brackets are executed before those in the outer brackets The brackets are replaced with the result of their contents before the external instructions be interpreted However the user cannot have access to this result since no name has been allocated to it Thesign enables the user to attribute a name to the result of the instruction The name attributed cannot exceed eight characters The program associates a type with each string encountered in a line A MOT type object is a 72 character string at most ranged in apostrophes If the program detects a character string which cannot be interpreted as numerical value it checks whether this string is the name of an object the type of which is already filed If this is the case it gives a type and a pointer to it otherwise it interprets it as a MOT type object Finally last recommandation to users try not to attribute the name of an already existing operator to an object For reasons of clarity and precision an operator once defined again as a new object can no longer have its initial function in the sequence of data 3 Structures data and general operators We have shown in
51. diagonal matrix MANU creation of objects MAILLAGE CHPO SOLUTION RIGIDITE MCHAML CHAMELEM MAPP construction of a Poincarre type chart MASQ construction of a field composed of 0 and 1 from a field by elements or a field by points MASS construction of the mass matrix 70 CASTEM2000 C E A D M T L A M S name description MATE gives the properties of a material CHAMELEM MATR gives the properties of a material MCHAML MAXI normalizes an object with respect to its maximum component MAXI finds again the maximum of a field by points field by elements or LISTMOTS MENA releases memory space MESS message display MINI finds again the minimum of a field by points field by elements or LISTMOTS MODE definition of the material type CHAMELEM MODI mesh interactive modification on screen MODL definition of the material type MCHAML MOIN calculation of the difference between two objects translation of an object MOME creation of a punctual moment MOT attribution of an alias to a key word MOTA calculation of the tangent modulus MOTS creation of a list of MOT type objects MULT comparison between two integers NBEL gives the number of elements of a MAILLAGE type object NBNO gives the number of nodes of a MAILLAGE type object NEG comparison between two objects NNOR normalizes a SOLUTION type object NOEUD identification of the node of a mesh by its number or name NOM
52. e data available in CASTEM2000 objects can be displayed on screen or stored in an appropriate file to be printed later on This can be done by means of the general operator LIST which once judiciously combined with the parameters of the OPTI operator enables the transmission of requested data on the selected unit 7 Procedures CASTEM2000 can be used by anybody following the rules of exploitation of the program that meet as best as possible the requirements of the problem to be solved In fact combining different operators between them makes it possible to define resolution procedures which can be complex and the preparation of which demands basic knowledge of mechanical computation but has been made easier by the programming language both very simple and concise and by the special operators allowing loops and instructions to be executed The precoded procedures prepared according to the method described below are particularly useful for repetitive calculations which can be performed directly once the sequence of basic controls has been developed and checked out This enables the user even if he is not yet familiar with the program to solve complex problems Moreover the user should keep in mind that a procedure does not necessarily cover the whole resolution process for a calculation problem In fact the same data architecture can be used for carrying out a series of analyses and for the definition and prior macro coding of general intere
53. e elements of a mesh VIBR calculation of the eigen modes and frequencies of an object VMIS calculates a stress equivalent to a stress field Von Mises stress in the case of 2D and 3D massives VOLU construction of a volume by translation rotation or automatically from a closed surface WORK calculation of the trace of the contracted tensorial product of a stress field with a gradient field XTMX calculation of the symmetrical bilinear form X M X XTX calculation of the scalar product X X XTY calculation of the scalar product Y X IS CASTEM2000 C E A D M T L A M S name description YTMX calculation of the symmetrical bilinear form Y M X ZERO creation of a field by element the components of which are all null 96 CASTEM2000 C E A D M T L A M S ANNEX C Index of the procedures in alphabetical order Bold names ACIER refer to both the new and the modified procedures description ACIER allows the material properties of the 316L steel to be defined in the system S I procedure called on by ACIER if former chamelems ACIERI ACIER2 ACTI3 procedure called on by ACIER if new chamelems evaluates the displacement incremental field allowing the problem relating to the restriction of the application tangent to the 3D subspace defined by input fields to be solved makes it possible to display the deformed shape of a structure AFFICHE ANIME allows an animation to
54. e logical unit on which the program reads the data 5 keyboard 3 default number attributed to the data file DENS stands for the current density value used in meshing operations for specifying the reference length of a element 90 CASTEM2000 C E A D M T L A M S 2 5 Lesson 4 TYPES OF OBJECTS The various objects used in CASTEM2000 can store several kinds of data integers or floatings words meshes fields etc During the execution of CASTEM2000 the user can read by means of the LIST directive the objects type Example d Re FOO Re Res Re opti dime 2 elem seg2 opti dime 2 elem seg2 a 0 0 a 0 0 b 1 0 b 1 0 d droi 1 a b d droi 1 a b mo modl d mecanique elastique cog2 mo modl d mecanique elastique cog2 list mo list mo POINTEUR SUR L OBJET MAILLAGE 1827 TYPE D ELEMENT FINI CoQ2 FORMULATION MECANIQUE MODELE DE MATERIAU ELASTIQUE ISOTROPE e The list of the different types of existing objects is given in chapter 3 1 of the user s manual Among other things these different types of objects enable an operator to check whether the objects supplied do represent the requested information have a non positional syntax when all the argument objects of an operator have a different type 9 CASTEM2000 C E A D M T L A M S 3 MESH 3 1 Lesson 5 POINT type objects A point can be created in the following way Example OPTI DIME
55. eal number PAR 12 PI 3 14 makes it possible to generate the corresponding ENTIER and FLOTTANT type objects that will be used to perform algebraic operations with other objects multiplication division etc The operations performed on objects lead to the creation of new objects which may have the same type as operands As a result the algebraic type operators such as or the ET operator which combines two or several objects are usually used for the creation of new objects of same type as the initial objects More sophisticated operators on the other hand create objects of a different type The MODL operator for instance uses a MAILLAGE mesh type object and MOT word type objects for the creation of a MMODEL type object containing the references to the geometry the finite element formulation the material behavior of the analyzed structure 2 4 CASTEM2000 potentialities 2 4 Notion of procedure The structure adopted in CASTEM2000 is above all useful for the elaboration of procedures which are as it were upper level operators these procedures call on in turn a series of elementary operators These procedures have been created to meet various requirements first it is possible to use the same data for several operators which allows them to be gathered and found easily by means of a single instruction second in the case of rather complex or repetitive problems the user may find it difficult to exp
56. ed sequence of operations it is possible in the case of a recurring situation characterized by the points a and b of the previous section in which solely the first 5 eigen frequencies smaller than 200 Hz must be determined to define an appropriate procedure which already contains all the precoded selections the parameters of analysis being unlikely to vary This procedure can be constructed as follows SSSS VALPRO DEBP VALPRO GEO MAILLAGE COND RIGIDITE 2 MOD1 MODL GEO MECANIQUE ELASTIQUE COQ3 COQ4 3 MATI MATR MOD1 YOUN 2 1E11 NU 0 3 RHO 7850 EPAI 0 001 4 CARI CARB MOD1 EPAI 0 001 MAT1 MAT1 ET CARI 6 STIF RIGI MOD1 MATI 7 KTOT STIF ET COND 8 MTOT MASSE MOD1 MATI 9 AUTO VIBR INTE 0 200 BASSE 5 KTOT MTOT 10 OPTI SAUV test2 so0rtgqibi 10 SAUV GEO AUTO MODI MATI FINE As shown by the numbers attributed to the instructions the procedure decribed above is capable of running all the stages of the modal analysis except for the geometry 1 and the boundary conditions 5 As a result the user can perform a calculation by merely defining what is needed at the points 1 and 5 before calling on the VALPRO procedure by means of the following command 60 CASTEM2000 C E A D M T L A M S VALPRO name mesh name boundarycond 7 2 3 Precoded procedures In this version of CASTEM2000 there are several precoded procedures A complete list and a brief description
57. ed together in the same object to be avoided After ELIM one can use the REGE operator which makes it possible to correct the topologies of the elements by deleting the sides which after ELIM are of null length As a result the elements of the model are regenerated the TRI3 elements are turned into SEG2 the QUAA into TRI3 and so on as shown below TRI3 gt SEG2 QUA4 gt TRIB TRI6 gt SEG3 QUAS gt TRI6 CUB8 gt PRI6 CU20 gt PRIS 4 1 1 Construction of volumes In the same way as lines had been created from points and surfaces from lines volumes are defined from surfaces The user can select between these two possibilities 41 CASTEM2000 C E A D M T L A M S generate the volume by the translation or the rotation of a given surface VOLU operator generate the volume from its external surface PAVE The options offered by the VOLU operator also enable the constuction of a volume from two surfaces top and bottom by means of rectilinear segments The mesh constructed by automatic operators can be composed of both prismatic elements with rectangular basis and tetrahedral elements Each of these elements is available either in the linear displacement version or in the quadratic displacement version by means of the following directive OPTI ELEM geometrical element type 4 2 Definition of the characteristics of the material In CASTEM2000 the stage during which the characteristics of
58. edure called on by G_THETA if former chamelems G THETA2 INCREME JEU procedure called on by G THETA if new chamelems procedure used by NONLIN it allows a solution increment to be calculated for a loading increment in non linear INCREME2 procedure called on by INCREME allows the right hand side corresponding to a play between two solids to be calculated LIREFLOT MONTAGNE in interactive enables the user to read a real number between two boundaries enables the display in 3D of the component of a field by points NEWMARK enables the step by step dynamic calculation of an incremental solution by Newmark centered algorithm allows an incremental non linear calculation to be performed procedure called on by NONLIN if former chamelems procedure called on by NONLIN if new chamelems 78 CASTEM2000 C E A D M T L A M S name description allows the energy restitution rate to be calculated by the crack virtual expansion method makes it possible to retreive the results of a calculation performed using NONLIN for a given time POINTCYL POINTSPH allows a point to be defined by its cylindrical coordinates allows a point to be defined by its spherical coordinates POLYNO PROPAG RESEAU makes it possible to calculate a polynomial reserved for the cracked piping element it enables the user to determine the global moment rotation behavior la
59. egration points scalar at the stress points displacements forces Stresses Strains material characteristics Hooke s matrix internal variables temperature 15 CASTEM2000 C E A D M T L A M S 6 2 Lesson 19 ELEMENTARY AND COMPOSED OBJECTS In CASTEM2000 both elementary objects and objects composed of several elementary objects can be manipulated When for instance a surface is meshed only with triangles the object is an elementary object If on the other hand that surface is meshed with both quadrangles and triangles the object is composed of two elementary objects This breakdown into elementary objects concerns the objects that are directly or implicitely connected with a mesh for instance the MCHAML or RIGIDITE type objects Theses two notions are tied to the use of the ET operator which allows several elementary objects to be merged for the creation of a composed object on the one hand and the REDU operator which allows an elemenatary object to be extracted from a composed object on the other 116 CASTEM2000 C E A D M T L A M S 6 3 Lesson 20 RELATIONS BETWEEN OBJECTS Some objects are closely related The relations depend on the computer structure of objects They are summarized in the following diagram MAILLAGE A CHPOINT type object is connected with the MAILLAGE and POINT type objects which had been used to construct it This notion is i
60. en with illustrates this statement Example Cl 0 0 7 V3 2 2 C2 C1 PLUS V3 The same is true of the TRANS operator which uses a POINT type object standing for a vector Example V3 10 10 LI1 Cl D 2 C2 LI2 TRANS LI1 V3 The user can get the number of points contained in an object with the NBNO operator any time Example NN1 NBNO LI2 93 CASTEM2000 C E A D M T L A M S 3 2 Lesson 6 CREATION OF LINES The MAILLAGE type objects stand for line surface or volume elements The simplest way to create them is to use the MANUEL operator followed by the key word referring to the type of element to be created Example QQ1 MANU SEG2 Cl C2 QQI is a 2 node segment connecting the points C1 and C2 Of course this method does not fit when the user wishes to create complex meshes in this case he will have to resort to automatic meshing operators As for lines the DROIT and CERC operators make it possible to build segments of straight line and arcs of circles Example Lll C1 DROIT 3 C2 CIl C1 CERC 4 C3 C2 LII will be a straight line composed of 3 segments ranged between the points C1 and C2 CII will be an arc of a circle composed of 4 segments of centre C3 ranged between the points C1 and C2 In this example we have explicitely specified the number of segments for the creation of a line This number can be checked by the densities attributed to the nodes of both origin an
61. ent description POI 1 node point SEG2 2 node line TRI3 3 node triangle QUA4 4 node quadrangle TET4 4 node tetrahedron PRI6 6 node prism PYRS5 5 node pyramid CUBS8 8 node cube RAC2 4 node element transitioning some SEG2 LIA3 6 node element transitioning some TRI3 LIA4 8 node element transitioning some QUA4 quadratic elements element description SEG3 3 node line TRI6 6 node triangle QUAS 8 node quadrangle TE10 10 node tetrahedron PR15 15 node prism PY13 13 node pyramid CU20 20 node cube RAC3 6 node element transitioning some SEG3 LIA6 12 node element transitioning some TRI6 LIA8 16 node element transitioning some QUA8 The transition elements make it possible to define double node lines or surfaces These double nodes have the same coordinates but not the same unknowns This category of elements is required when one wishes to transition meshes with formulations where the degrees of freedom are different 99 CASTEM2000 C E A D M T L A M S 3 5 Lesson 9 THE CONFONDRE AND ELIM DIRECTIVES In a meshing process it may occur that two different parts of the mesh be constructed separately but have points in common If the nodes are known by name the CONFONDRE directive should be used Example CONF C1 C2 C1 and C2 are the nodes to be merged Otherwise it is requested to use the ELIM directive Example ELIM SUL SU2 CREITERE SUI and SU2 are the names of two meshes C
62. ents be distributed in a specific way in order that the costs for analysis be profitable as much as possible it is advisable to concentrate the elements in the regions liable to undergo sudden variations in the unknown function and on the contrary to avoid storing them in regions of minor interest Gathering several different mathemetical formulations beams shells solids relating to several parts of the structure i e making them compatible within a same structure or defining particular types of boundary conditions or loadings may sometimes seem extremely difficult Within the framework of an analysis it might thus be interesting to be able to define step by step the most adequate sequence of elementary processes of the different stages by joining them and by supplying the requested data at each new step 2 2 CASTEM2000 distinctive features The CASTEM2000 system has been designed and developed to be more flexible than the conventional codes As a result the user among other things has the GIBIANE macrolanguage at his disposal which enables him to define easily each operation of the different stages of analysis by means of extremely simple instructions 2 The structural stress calculation from displacements can for instance be performed either directly by means of a single instruction u 9 when both the geometrical and material characteristics or the displacements are known or by means of several successive instructio
63. ents in the thin shells GREEN calculation of Green functions associated with beams HOMO construction of a mesh by homothety HOOK calculation of Hooke s matrices 69 CASTEM2000 C E A D M T L A M S name description HOTA calculation of Hooke s tangent matrices in plasticity IFRE calculation of Fresnel integrals INCL extraction of an object located within a contour INDE gives all the indices of a table INDI supplies information about the quality of a mesh planearity criterion only INFO gives an operator instructions INSE insertion of an object into a list of objects INTE construction of a line intersection of two surfaces INTG integration of a field component on a region INVA calculation of the three invariants of a tensor INVE inversion of the direction of a line IPOL linear interpolation ITER interruption of a block running JACO calculation of a jacobian absolute value JONC creation of an ATTACHE type object connection between substructures KP calculation of the pressure matrix KSIG calculation of the initial stress matrix KTAN calculation of the tangent stiffness matrix in elastoplasticity LAPL construction of Laplace transfom LECT creation of a list of integers LIAI creation of connections between substructures LIRE reading of a mesh on a logical file LIST information about objects LOG logarithm LUMP construction of a
64. eral operators with the MODL MODEL and MATR MATER operators described below makes it possible to define a material whose properties vary with time By way of an example we have chosen the characteristic case of a linear material for which Young s modulus linearly depends on temperature It consists in composing in an EVOLUTION type object two definite progressions containing the temperature values T and the corresponding values of Young s modulus in order to obtain the function E T As soon as the connection between E and T is established it is associated with the temperature scalar field by points defined from the analyzed region and constructed above This very field by points is then turned into a field by elements which will in turn be associated with that containing the other properties of the material The sequence of appropriate control is as follows NEW CHAMELEMS YOUNG s modulus 2D model F T T inversely proportional to the square distance from the origin construction of the geometrical model OPTI DIME 2 ELEM QUA4 PO 0 0 Pl 10 0 COTE1l1 D 10 PO P1 n GEO COTE1 TRAN 10 0 10 3 construction of the temperature CHPOINT DISTX COOR 2 GEO DISTY COOR 1 GEO DISTO DISTX DISTX DIES EY DESDY 3 43 CASTEM2000 C E A D M T L A M S TEMP 1 DISTO s TEMPE NOMC YOUN 200 TEMP progression containing the temper
65. erator directive or procedure he can get their instructions from the in line help by executing the following instruction INFO ABCD where ABCD are the first 4 letters of the name of the requested operator if it has at least four letters Example FIN DE FICHIER SUR L UNITE 3 LES DONNEES SONT MAINTENANT LUES SUR LE CLAVIER INFO ABS INFO ABS DATE 30 11 05 Operateur ABS Voir aussi SIGN L operateur ABSOLU calcule la valeur absolue d OBJETI RESU1 ABS OBJETI Commentaire OBJET1 objet dont les types possibles sont ENTIER CHAMELEM MCHAML reruns RESU1 objet de meme type qu OBTET1 ERS CASTEM2000 C E A D M T L A M S 2 3 Lesson 2 A FEW ELEMENTARY OBJECTS AND OPERATORS a ENTIER type objects They can be created with the sign as follows Example 5 Dz7 it is then possible to perform elementary arithmetic operations on these integers such as and Example I3S I1 I2 I4 I1 I2 i Ud ae Ol Ne am It is possible to know the result of these operations by listing the outcoming objects with the LIST directive Example LIST I5 b FLOTTANT type objects They are created in the same way as the previous objects apart from the fact that they must contain a decimal point or be written with powers Example F1 1 5 or F1 215E 1 F2 2 3 F3 F1 F2 LIST Foy c LOGIQUE type objects These objects can be created
66. es non null displacements imposes the right hand side of a relation DEPL displacement of a POINT or MAILLAGE type object DESS plot of EVOLUTION type objects DETR destruction of an object DEVE construction of an ATTACHE type object weir 61 CASTEM2000 C E A D M T L A M S name description DEVO calculation of the solution of a system of matrix equations DFOU calculation of a CHPO or MCHAML or CHAMALEM for a given angle Fourier s analysis DIAG number of negative eigenvalues of a RIGIDITE type object DIFF symmetrical difference between two MAILLAGE type objects DIME dimension of an object DIMN dimension of the kernel of the stiffness matrix DROI construction of a straight line DSPR construction of the power spectrum density curve of a signal DTAN calculation of a tangent matrix DYNE calculation of a dynamic response by explicit algorithm EGA comparison between two objects ELAS calculation of strains from stresses calculation of stresses from strains ELEM extraction of the elements of a MAILLAGE type object ELFE test of the different algorithms on beams or plates ELIM removal of the nodes located between two MAILLAGE type objects ELST construction of an ELEMSTRU type object ENER calculation of the tensorial product of a stress field and a strain field ENLE removes objects from a list of objects ENSE creation of a SOLUTION type object containing all
67. etization field z D CASTEM2000 C E A D M T L A M S DEFORME ELEMSTRU ENTIER INTEGER EVOLUTION FLOTTANT REAL LISTCHPO LISTENTI LISTMOTS LISTREEL LOGIQUE LOGICAL MAILLAGE MESH MODELE MOT WORD POINT RIGIDITE STIFFNESS SOLUTION Object relating to the characterization of a deformed region obtained by superimposing a MAILLAGE type object on a CHPOINT type object field by points Object allowing linkages to be written between substructures it contains the description of an element of a structure with the associated geometry Object composed only of an integer Object defining a graph Object composed only of a real number Object composed of a list of CHPOINT Object composed of a list of integers Object composed of a list of words Object composed of a list of real numbers Object containing a logical variable with a true or false value Object containing the topology of the discretized region Object defining the material type of behavior Since the data of the FIELD BY ELEMENT type objects have been reorganized those of the MODELE type objects have also be revised For the time being there are two types of objects allowing the material behavior type to be described MODELE associated with a CHAMELEM type field by element MMODEL associated with an MCHAML type field by element Object composed of one word Object defining the coordinates of a point and the
68. euxieme ligne type des donnees MODL D1 MECANIQUE ELASTIQUE COQ2 MA1 MATR MO YOUN 0 2000 MOT MAILLAGE MOT MOT MOT MOT MOT MOT MMODEL MOT FLOTTA 0000E 12 NU 0 3 RHO 7800 EPAI 0 10000000E 02 y MOT FLOTTANT MOT ENTIER MOT FLOTTANT The syntax analyzer can no longer perform its decoding properly and the error message printed is that of the operator contained in the next line Rule of hierarchy between operators Illustration I123 5 1 I123 5 1 list It list I1 tier valant 14 I121 3 5 I121 3 5 list It list If ntier valant 10 gt Ev T3 Gt He OI oe xe The rules of hierarchy between arithmetic operators do not follow the usual mathematical rules Operator used with an insufficient number of arguments 133 CASTEM2000 C E A D M T L A M S Illustration MOT MODL MECANIQUE ELASTIQUE COQ MOT MODL MECANIQUE ELASTIQUE COQ voto ERREUR 37 e dans l op rateur MODL On ne trouve pas d objet de type MATLLAGE Premiere ligne donnees deuxieme ligne type des donnees MODL MECANIQUE ELASTIQUE COQ2 MOT MOT MOT In this case there is always a message such as we cannot find any type object Operator used with an excessive number of arguments Illustration OPTI DIME 2 ELEM SEC2 OPTI DIME 2 ELEM SEG2 4 0 0 0 A0 0 0 Merk ERREUR 14 k dans l operateur Tl y aun resultat de type ENTIER et de non en trop par rapport aux nons a affecter Premiere ligne donnees deux
69. for density and Young s modulus are gathered in the following table Length Mass Force Density beats m kg N 7 85 10 210 m 10 kg 10 N 7 85 2 108 cm kg 10 N 7 85 10 2 10 cm 10 kg 10N 7 85 106 2 106 mm kg 10 N 7 85 106 2 105 mm 10 kg N 7 85 10 2 10 cm 10 kg N 7 85 10 2 107 m 10 kg 104 N 7 85 10 210 cm 10 kg 10 N 7 85 10 2 10 mm 107 kg 10 N 7 85 10 13 2 10 m 10 kg 10N 7 85 10 2 1010 cm 10 kg 10N 7 85 10 210 mm 10 kg 10N 7 85 10 2 10 13 CASTEM2000 C E A D M T L A M S References 1 P Verpeaux A Millard Quelques consid rations sur le d veloppement de grands codes de calcul Report DEMT 88 179 2 M F Robeau P Verpeaux Langage de donn es Gibiane 77 Report DEMT 86 80 14 CASTEM2000 C E A D M T L A M S 1 Introduction CASTEM2000 is a computer code for structure analysis by the finite element method FE This code was originally developed by the D partement des Etudes M caniques et Thermiques DEMT Department of Mechanical and Thermal Research of the French Commissariat l Energie Atomique CEA Nuclear Energy Agency equivalent to the British AEA The development of CASTEM2000 is part of a program of research in the field of mechanical engineering it aims at defining an advanced tool to be used as a proper support for the design resistance evaluation and analysis of structu
70. geometry to the behavior model and to the finite element formulation which must be used CAUTION the AFFECTE type objects correspond to the former computer organization and will no longer be used from the 93 Clients version Object containing the description of the linkages between substructures with a view to dynamic analysis Object containing the description of the linkages applying to a structure and the specification of all the modes and static solutions Object containing the description of the linkages between substructures with a view to dynamic analysis Object containing any type of data defined in the elements material characteristics shell thicknesses beam cross sections stresses etc Each finite element can support several types of fields by elements each field is characterized by a given number of components In the current version of CASTEM2000 there are two types of objects enabling the description of a field by element the CHAMELEM type objects that correspond to the former data computer organization and the MCHAML that correspond to the new organization From the 93 Clients version the operators only function with this structure It is possible to move from one type to the other by means of the CHAN operator Object containing any type of data defined at the temperature displacements nodes Object containing the time and space description of a loading Object relating to the description of a discr
71. ieme ligne type des donnees 0 0 a ENTIER ENTIER The message always takes the form there is a type result too many with respect to the names to be allocated The first 4 letters of both the key words and the operators are tested Illustration MOT MOD GEO MECANIQUE ELASTIQUE COQ MOT MOD GEO MECANIQUE ELASTIQUE COQ week ERREUR 11 66 dans l operateur Il y a un resultat de type MAILLAGE et de nom GEO en trop par rapport aux nows a affecter Premiere ligne donnees deuxieme ligne type des donnees MOD GEO MECANIQUE ELASTIQUE COQ2 MOT MAILLAGE MOT MOT MOT MOT MODL GEO MECANIQUE ELASTIQUE COQ MOI MODL GEO MECANIQUE ELASTIQUE COQ2 8 characters of the names of objects are tested 124 CASTEM2000 C E A D M T L A M S Illustration MAUVATSNOM MODL GEO MECANIQUE ELASTIQUE COQ2 MAUVATSNOM MODL GEO MECANIQUE ELASTIQUE COQ2 eee ERREUR 315 dans operateur Une constante ne peut pas etre un now d objet Premiere ligne donnees deuxieme ligne type des donnees MODL GEO MECANIQUE ELASTIQUE COQ2 MOT MAILLAGE MOT MOT MOT 135
72. ional characteristics of the elements MCHAML MAT 1 type object 4 definition of possible additional characteristics of the elements and of the material characteristics CARB CARI type object if they have not already been specified in MATI 5 definition of kinematic type boundary conditions by the construction of a RIGIDITE COND type object 6 definition of conditions of loading and or displacement imposed by the construction of a CHPOINT FORCES type object 7 calculation of the stiffness matrix of the free structure STIF 8 assembly of the stiffnesses stemming from the elements and the stress conditions in a global RIGIDITE KTOT type object 9 resolution of the linear system KTOT DEPL FORCES 10 calculation of stresses SIGMA from the displacement vector DEPL 51 CASTEM2000 C E A D M T L A M S 11 backup of the main objects GEO DEPL SIGMA MODI MAT 1 required for the execution of a later graphical postprocessing After having presented the sequential execution let us now assume the hypothesis of a recurrent application characterized by a theuse of geometrical models requiring the use of shell type elements with 3 and 4 nodes which are of the same thickness e 0 001 b the constant use of some steel with the following characteristics E 2 1 1011 n 0 3 and p 7850 c the sole use of mechanic type loadings corresponding to concentrated forces and mo
73. iven boundaries 120 CASTEM2000 C E A D M T L A M S The procedure is written as follows DEBPROC LIREFLOT UMIN FLOTTANT UMAX FLOTTANT REPETER BLOCL OBTENIR FL FLOTTANT SI gt EG UMIN ET lt EG FL UMAX QUITTER BLOCI FINSI MESSAGE DONNEZ UN NOMBRE COMPRIS ENTRE UMIN ET UMAX FIN BLOC1 FINPROC FL It will be used as follows XX LIREFLOT 0 1 E10 It allows interactive softwares to be easily structured in CASTEM2000 by means of the OBTENIR and MESSAGE operators 21 CASTEM2000 C E A D M T L A M S 6 6 Lesson 23 TABLE TYPE OBJECTS Within the context of the CASTEM2000 objects it is required to assemble a series of objects under the same name index that series of objects allocate a type to these indices FLOTTANT ENTIER MOT The TABLE type object fulfils this function This object is used as follows Example creation of the table MAT1 TABLE the element of index 1 equals 5 MAT1 1 5 the element of index 1 i e 5 is printed LIST MAT1 1 the table may also be indexed using key words Example MAT2 TABLE M1 MOT ESS M2 MOT TYP MAT2 M1 1 8 MAT2 M2 2 3 LIST MAT2 M1 LIST MAT2 M2 Remark Several types of indices may be used at once in a table 122 CASTEM2000 C E A D M T L A M S 6 7 Lesson 24 MANIPULATION OF THE COMPONENTS OF CHPOINT OR MCHAML Complex operati
74. l forces equivalent to a distributed pressure PRHC conversion of a field by elements into a field by points PRIN calculation of the principal stresses PROG creation of a list of real numbers PROI calculation of the projection of an object onto a new geometry PROJ projection of an object according to a given direction PSCA scalar product of two vectors or two fields 72 CASTEM2000 C E A D M T L A M S name description PSMO calculation of the contribution of the modes which were not taken into account in a modal basis PVEC vectorial product QUEL construction of a broken line QUIT block running interrupted QULX extraction of the Lagrangian multipliers of a CHPO type object RACC transition between two objects RCHO calculation of impact forces and projection onto the modes contained in the modal basis REAC calculation of the reactions at constraint points RECO recombination of the modes and static solutions REDU reduction of a field by points or field by elements to a given support REGE regeneration of a mesh containing degenerated elements REGL construction of a ruled surface RELA creation of linear relations between degrees of freedom REMP replaces an object in a list of objects REPE specifies how many times a loop is repeated RESO resolution of the linear system Ku f RESP restitution of the results calculated in a procedure REST restoration back to memory of
75. licitly define standardized operations every time finally people who are not familiar with the finite element method but use it all the same should like to go back to the program black box running This would amount to hiding elementary procedures as a whole by means of a single procedure The procedures have the following characteristics they can be used in the same way as elementary operators a procedure can call on other procedures and can call on itself a procedure can be composed of other procedures 19 CASTEM2000 C E A D M T L A M S the sequence of elementary operators contained in a procedure is always visible All these characteristics enable the user to program by himself the processes required for solving his own problems In addition he can write and test new algorithms fastly without having to face the difficulties tied to the programming itself 2 4 2 Development of new operators CASTEM2000 special structure not only enables the user to elaborate procedures capable of solving new types of problems but also to define operators different from those in existence in exceptional cases The new operators can actually be developed tuned up and checked apart from the others One just needs to know the structure of the data contained in the objects handled by the new operator and in the objects common to the whole program This is especially useful when the analysis demands specific adaptations
76. ments and or to uniform pressures In this case it is very useful to define an appropriate procedure with a view to recurrent applications it already contains all the precoded selections and all the parameters of analysis that are unlikely to vary This procedure can be called CALINE CAlcul LINeaire Elastique i e Elastic LINear Calculation and can be defined as follows CALINE DEBP CALINE GEO MAILLAGE COND RIGIDITE FORCES CHPOINT 2 MOD1 MODL GEO MECANIQUE ELASTIQUE COQ3 CO4 3 MATI MATR MOD1 YOUN 2 1E11 NU 0 3 RHO 7850 EPAI 0 001 4 CARI CARB MOD1 EPAI 0 001 MATI MATI ET CARI 7 STIF RIGI MOD1 MATI 8 KTOT STIF ET COND 9 DEPL RESO KTOT FORCES 10 SIGMA SIGM MOD1 MAT1 DEPL 11 OPTI SAUV FORMAT essai sortgibi SRE CASTEM2000 C E A D M T L A M S 11 SAUV FORMAT GEO DEPL SIGMA MODI MATI FINP As shown by the numbers attributed to the instructions the procedure decribed above is capable of running all the stages of static linear elastic analysis except for the geometry 1 and the boundary conditions 5 and 6 Stage 4 is optional and is required only when the additional characteristics are not mentioned in stage 3 As a result the user can perform a calculation by merely defining what is needed at points 1 3 and 4 before calling on the CALINE procedure by means of the following instruction CALINE name mesh name boundarycond name fo
77. mesh 3D only ARGU reading of arguments within a procedure ATG arctangent BARY barycentre of a geometry BASE creation of a BASE MODALE type object BIOT constructs an induction field 3D only 65 CASTEM2000 C E A D M T L A M S name description BLOQ boundary conditions with respect to the principal axes BRUI creation of white noise BSIGM calculation of equivalent forces CABLE construction of the stiffness of a cable CALP calculation of a stress field shells and beams CAPA creates a thermal capacity matrix CAPI calculates a Piola Kirchoff stress field from a Cauchy field CARACTERISTIQUE elements geometrical characteristics CARA former chamelems CARACTERISTIQUE elements geometrical characteristics CARB new chamelems CER3 construction of an arc of a circle CERC construction of an arc of a circle CHAM turns a CHPOINT into a CHAMELEM CHAN turns the type of element of a mesh into another type turns an MCHAML or a CHAMELEM into a CHPOINT turns a CHAMELEM into an MCHAML modifies the subtype of an MCHAML creates a CHAMELEM from an MCHAML creates a MMODEL from an AFFECTE turns a CHPOINT into an MCHAML CHAR construction of a loading CHOC construction of an impact link CHOL decomposition of a matrix according to the CROUT method CHPO creation of a field by point CHSP modifies the type of a spectrum CLST creation of a st
78. mportant when one wishes to handle objects removal modification backup If MMODEL type object is saved the MAILLAGE and POINT type objects connected with it will also be saved Illustration sauv mol sauv mol LA PILE DES POINTS CONTIENT 10 POINTS IL YA 2 OBJETS NOMME S B 2 1 LA FILE NUMERO 1 CONTIENT 5 OBJET S MAILLAGE ILVA 2 OBJET S NOMME S SUR 1 M 2 L FILE NUMERO 38 CONTIENT 1 OBJET S MMODEL ILYA 1 OBJET S NOMME S 1 Mot FIN NORMALE DE LA SAUVEGARDE 117 CASTEM2000 C E A D M T L A M S 6 4 Lesson21 REPETITIVE AND ALTERNATE EXECUTIONS 6 4 1 Repetitive executions It merely consists in using loops in the GIBIANE language Example REPETER BOUCI 10 FIN BOUCI Some natural applications stemming from these two instructions concern of course the non linear algorithms in mechanical analysis In order to calculate Euler approximation you would write for instance Example NN 0 EXP 1 REPETER BOUC1 50 NN NN 41 RE 1 FLOTTANT NN EXP EXP RE FIN BOUCI EULER EXP LOG NN 4 2 Alternate executions The directives SI SINON FINSI are used for tests The REPETER and FIN instructions can be used simultaneously with the SI FINSI and QUITTER instructions Let us assume that in the loop there is a LOGIQUE BOL type object checking the output from the loop The loop will be written as follows Example REPETER BOUC2 10 l
79. n POUTRE SECT cross section INRY inertia with respect to the local axis Oy INRZ inertia with respect to the local axis Oz TORS twisting inertia SECY reduced section with shear stress SECZ reduced section with shear stress VECT vector of local axis DX DY DZ distances for the calculation of stresses from moments in plasticity TUYAU EPAI thickness RAYO external radius RACO radius of curvature VECT vector of local axis PRES internal pressure HOMOGENEISE SCEL enlarged elementary cell SFLU fluid area in enlarged cell EPS pas tubulaire of the medium NOFI norm modal tube norm pressure NOF2 ratio between the scalar product of the modal deformed shape and the modal deformed shape of pressure and the square of the norm of pressure LINESPRING EPAI shell thickness FISS notch depth VX VY VZ components of the vector normal to the plane of the shell 109 CASTEM2000 C E A D M T L A M S element characteristic s TUYAU FISSURE EPAI thickness RAYO pipe external radius ANGL crack total opening in degrees VX VY VZ component of the pipe vector axis VXFE VYF VZF orientation of the crack RACCORD For fluid structure transition elements it is required to know the position of the fluid with respect to the transition element For this reason the geometrical object will be given after the LIQU key word Table C 110 CASTEM2000 C E A D M T L A M S 5 USE OF RESULTS 5
80. n two dimensions 2 FLOTTANT type objects will be created in three dimensions 3 FLOTTANT type objects Example OPTI DIME 2 C120 1 F1 F2 COOR Cl OPTI DIME 3 C2405 Us ds F1 F2 ESSCOOR C2 88 CASTEM2000 C E A D M T L A M S 2 4 Lesson 3 NOTION of NAMED object a Objects arising from an operator are named by the user b Some resulting objects may not be named In a chain calculation there is no point naming intermediate results For instance there are two ways to calculate 5x 2 3 I 2 3 g 5 1ls or J 5 2 3 In the second case the user performs his calculation in one instruction but he will not be able to use this intermediate result 2 3 for other operators For this reason the program automatically attributed a name to the intermediate result which is a priori not accessible to the user c Some data are automatically generated even before CASTEM2000 first instruction to be executed They are the control parameters values created by the OPTION directive The most important are DIME stands for the dimension of the space used for the mesh and calculation operators 1 2 or 3 MODE stands for the calculation mode 2 plane stresses 1 plane strains 0 axisymmetrical l Fourier series analysis 2 three dimensional 89 CASTEM2000 C E A D M T L A M S ECHO equals 1 or 0 depending on whether the last instruction echo is done or not DONN number of th
81. nodes identical or when you will have the displacements and the rotations compatible with a junction between shell and massive elements An interesting option of the RELA operator is the key word CORI it makes it possible to impose a stiff body motion to a set of nodes Besides the RELA and BLOQUE operators allow unilateral conditions of type Ux gt var to be input U gt var 128 CASTEM2000 C E A D M T L A M S 7 2 Lesson 27 THERMAL LOADINGS Calculations with thermal loadings can be easily performed as follows We assume that the temperature field was first determined in the form of a TEMPERAT subtype MCHAML let TX1 be this field Therefore it is possible to create the corresponding stress field by means of the THETA operator SIl THETA MODLI MATI TX1 Followed by the equivalent force field with the BSIGMA operator FOI BSIGMA MODL1 SII Therefore it is possible to calculate the outcoming displacement field with RESOU RII RIGI MODL1 MAT GIL BLOQUE LI1 DEPL DEI RESOU RII EI CLhl FOI and the corresponding total stresses SI2 SIGMA MODL1 MATI DEl Finally it is required to substract the stresses of thermal origin to obtain the true stresses SIV SI2 SIl 129 CASTEM2000 C E A D M T L A M S 7 3 Lesson 28 EIGEN FREQUENCIES AND MODES Eigen frequencies and modes can be calculated by means of the RIGI MASSE and VIBRATION operators Example MA1
82. ns enabling the computation of the strain vector at first B u followed by that of the D elasticity matrix and finally by the product o D e These operations are performed on objects which will stand for the complete structure to be studied or each of its elementary components when necessary All this is now possible with the uncommon data base management system which has been created in the program From now on the data of the problem whether mechanical properties of the material or geometrical characteristics of the created mesh or else force fields or stresses etc can be handled easily by referring to the names chosen and attributed by the user himself sy CASTEM2000 C E A D M T L A M S A piece of information or a set of information makes up what is called an OBJECT in the program Besides the fact that they are named by the user which enables him to find them all the objects have a specific type which enables him to find the structure of data associated with them Some objects can be of ENTIER integer or FLOTTANT real type and are characterized by a very simple structure others such as those of MMODEL type will be more complex they contain the reference to the structure geometry the formulation of the relative finite elements or the material behavior What matters most to the user is the name the type is above all a computer requirement which allows however the syntax of data to be checked 2 3 CASTEM2000
83. of the name of an object corresponding to the key word of an operator Illustration DEPL 10 10 DEPL 10 10 CL1 BLOQ DEPL A CLT BLOQ DEPL week ERREUR 37 eee dans l operateur BLOQ On ne trouve pas d objet de type MOT Premiere ligne donnees deuxieme ligne type des donnees BLOQ DEPL MOT POINT POINT E In this example the name DEPL is not compatible with the key word DEPL allowing all the translation d o f to be constrained Remark In order to remedy to these two common errors it is advisable to attribute names containing for instance one digit to the objects because the names of operators do not contain any Confusion between points and substraction 132 CASTEM2000 C E A D M T L A M S Illustration 1 P P1 2 252 e xe list P1 list P1 Entier valant 1 P121 2 p1z1 2 list Pt list P1 Point dont le numero est actuellement 5 poemes 1 0000 2 0000 Densite 0 The first instruction generates an integer the second generates a POINT type object Use of an instruction without hyphen at the end Illustration MOT MODL D1 MECANIQUE ELASTIQUE C002 MOT MODL D1 MECANIQUE ELASTIQUE COQ2 MAT MATR MO YOUN 2E11 NU 0 3 RHO 7800 EPAI 0 001 MAT MATR MO YOUN 2E11 NU 0 3 RHO 7800 EPAI 0 001 ak ERREUR 11 ee dans l operateur Il y a un resultat de type MOT et de nom M l en trop par rapport aux noms a affecter Premiere ligne donnees d
84. of the procedures are given in annex C 61 CASTEM2000 C E A D M T L A M S ANNEXES 62 CASTEM2000 C E A D M T L A M S ANNEX A This section gives the different types of elements available in CASTEM2000 as well as the corresponding geometrical support and the nature of the possible calculations with the following conventions cont plane plane stresses defo plane plane strains axis l axisymmetrical four Fourier s analysis trid three dimensional ELEMENT GEOMETRICAL SUPPORT NATURE OF CALCULATION MASSIVE ELEMENTS TRIS TRIS cont plane defo plane axis four TRI6 TRI6 QUA4 QUA4 QUA8 QUA8 CUB8 CUB8 trid CU20 CU20 TET4 TET4 TE10 TE10 PRI6 PRI6 PR15 PR15 PYR5 PYR5 PY13 PY13 THIN SHELL ELEMENTS COQ3 TRI3 trid DKT TRI3 trid COQ2 SEG2 cont plane def plane axis four THICK SHELL ELEMENTS COQ8 QUA8 trid COQ6 TRI6 COQ4 QUA4 DST TRI3 BEAMS AND PIPES POUT SEG2 trid 63 CASTEM2000 C E A D M T L A M S ELEMENT GEOMETRICAL SUPPORT NATURE OF CALCULATION TUYA SEG2 s BARS BARR SEG2 cont plane def plane axis trid ELEMENTS OF RUPTURE MECHANICS LISP RAC2 trid LISM RAC2 7 TUFI SEG2 u LIQUID ELEMENTS FOR ACOUSTICS LTR3 TRI3 cont plane def plane LQUA4 QUA4 LCU8 CUB8 trid LPR6 PRI6 a LPY5 PYR5 LTE4 TET4 LIQUID MASSIVE TRANSITION ELEMENTS RAC2 RAC2 cont plane def
85. ons may be performed on MCHAML or CHPOINT type objects by characterizing the components of these objects It is possible for instance to calculate the divergence of a displacement field DEPI in the following way Example EPS1 EPSI MODL1 DEP EP10 EXCO EPS1 EPXX EP20 EXCO EPS1 EPYY EP30 EXCO EPS1 EPZZ TR1 EP10 EP20 EP30 The corresponding tensorial product may also be calculated from a stress field SII and a gradient field GRD1 First the components of the 2 fields will be retreived Example SIXX EXCO SIl SMXX SIXYeEXCO SIL SMYY SIXY EXCO SIL SMXY GRXX EXCO GRD1 UX X GRXY EXCO GRD1 UX Y GRYX EXCO GRD1 UY X GRYY EXCO GRD1 UY Y Then the products required for obtaining the components of the tensorial product will be carried out T1 SIXX GRXX SIXY GRYX T2 SIXY GRXX SIYY GRYX T3 SIXX GRXY SIXY GRYY T4 SIXY GRXY SIYY GRYY 123 CASTEM2000 C E A D M T L A M S 6 8 Lesson 25 HOW TO USE THE GEMAT 9 3 release The user can specify the memory space required for his calculation or the translation parameters if he is a developer For this he must alter different parameters contained in a file which is called as soon as CASTEM2000 is executed 6 8 1 The Parameter file Usually it is an ASCII data file EBCDIC on IBM which can be created by an edit program According to the operating system the parameter file is a fortran file number 99
86. ons will be divided KJ w f and then Kej uj Kai uj fj Kij uj Kij uj fj where w u jr ujt P fjT fjr Besides all the connections with the adjacent substructures u j may contain the degrees of freedom of other nodes The stresses on the internal degrees of freedom must be clearly imposed in this stage It is at that point that the static condensing is performed The second system is solved in relation to u the equivalent loadings and stiffnesses can be obtained by replacing the result outcoming in the first system fj fj Key Kiel i Kj K j K j Kij 1 Kj 2 Solution obtained if the degrees of freedom are retained The matrices obtained in stage 1 are gathered together to generate the resolution system of equations K u f At this stage other boundary conditions can be imposed on the degrees of freedom which are stored and the resulting equations can be solved in relation to Us 3 Retreival of internal degrees of freedom 5 CASTEM2000 C E A D M T L A M S So the displacements u j of the external nodes of the qu substructure have been deduced from the displacement of the external nodes of the complete structure ui One then returns to the displacements of the internal nodes ujj by means of the second equation of the system 1 uj Kij 1 fj Kij K j 1 ug so as to be able to proceed with a postprocessing The SUPER operator of CASTEM2000 can perform by itself all the operation
87. oop internal instructions 118 CASTEM2000 C E A D M T L A M S SI BOLI QUITTER BOUC2 FINSI next instructions FIN BOUC2 19 CASTEM2000 C E A D M T L A M S 6 5 Lesson 22 PROCEDURES The fact that CASTEM2000 is provided with numerous operators sometimes entails a drawback the sets of data may be long and complex one will soon realize that some sequences of instructions are used several times in the same set of data or by several users Hence the idea of gathering these instructions together into a specific structure the procedure It takes the following form in the declarative form DEBPROC NOM ARG1 TY1 ARG2 TYPE2 ARG3 TYP3 ARG4 TYP4 series of instructions FINEBOC SORT SOREZ SORTS 404 When adjusting this procedure make sure that this pack of instructions is located before the place where it is wished to be used in calling order RESU1 RESU2 RESU3 NOM DONNI DONN2 DONN3 DONNA Afterwards this procedure will be used as an operator The following example shows how to operate a simple procedure turning coordinates into polar coordinates Example DEBPROC POLAIRE X1 FLOTTANT X2 FLOTTANT RR X1 X1 X2 X2 0 5 7 THE ATG X1 X2 FINPROC RR THE This procedure will then be used as follows RO TET POLAIRE A B Another simple example is given by the LIREFLOT procedure which makes it possible to read in interactive mode a floating number ranged between two g
88. plane axis four LIA3 LIA3 trid LIA4 LIA4 LIQUID SHELL TRANSITION ELEMENTS RACO RAC2 cont plane def plane axis four LICO LIA3 trid FREE SURFACE ELEMENTS LSU2 SEG2 cont plane def plane axis four LSU3 TRI3 trid LSU4 QUA4 trid POROUS ELEMENTS TRIP TRI6 cont plane def plane axis QUAP QUA8 s CUBP CU20 trid TETP TE10 i PRIP PR15 HOMOGENEIZED ELEMENTS TRIH TRIS cont plane def plane axis 64 CASTEM2000 C E A D M T L A M S ANNEX B This section briefly describes all the operators and directives available in CASTEM2000 92 Clients Version The names in italics AFFE refer to the operators that are to disappear Bold names BIOT refer to both the new and the modified operators name description division multiplication addition lt EG less or equal substraction Xx exponentiation gt EG greater or equal lt less gt greater ABS absolute value ACT3 convergence acceleration ACTI convergence acceleration AFCO color allocated to a mesh AFFE finite element allocated to a mesh AFFI construction of a mesh by affinity AMOR constructs a diagonal damping matrix ANTI imposes antisymmetrical boundary conditions on the displacement and or rotation d o f APPU constructs a stiffness associated with linear supports springs applied to d o f ARETE construction of a mesh representing the edges of another
89. r as it favours data exchanges between user and program In spite of the program large flexibility the user still needs to learn to formulate his calculation problems according to the method adopted by the code As a result it is important for him to understand how a finite element analysis is structured and organized so as to be able to establish a direct connection between the mathematical or logical operation to be formulated and the operators to be used 2 1 Organization of the F E calculation process Any generic analysis carried out by the finite element method can be divided into 3 15 CASTEM2000 C E A D M T L A M S successive stages Likewise each stage can be subdivided into a series of elementary processes 1 The stages in question can be described as follows e STAGE 1 DEFINITION OF THE MATHEMATICAL MODEL geometrical discretization of the studied region definition of data featuring the model They include the type of analysis plane strains or stresses axisymmetry etc the type of element beam shell etc the material properties the geometrical characteristics that cannot be infered from the meshes and the boundary conditions e STAGE 2 RESOLUTION OF THE DISCRETIZED PROBLEM calculation of mass and stiffness matrices for each finite element assembly of the stiffness and mass matrices of the complete structure application of external loadings application of boundary conditions
90. ram execution Parameters read in PARAM Illustration ee CASTEM2000 eeee VERSION CLIENT 30 JANVIER 1992 0002Z7ES0PE 1000000 NTRK 2000 LTRK 2048 Q GEMAT 9 3 AVR 90 ESOPE 1000000 MOTS BUF NTRK 2000 LTRK 2048 MOTS ee eee ee eee INFORMATIONS GIBI ee ae as a ee a a a MOTS DATE 92 03 13 Pour obtenir la notice de GIBI gt faire NOTICE Pour obtenir la notice de CASTEM2000 faire NOTICE CASTEM2000 Debutants gt faire INFO DEBU Parameters used in execution Des options existent dans les operateurs POINT et ELEM pour remplacer les operateurs COMA et COMI qui ont ete supprines Il est desormais possible d utiliser les nouveaux CHAMELEMs dans l ensemble des operateurs et des procedures manipulant des champs 6 8 1 2 Translation parameters Specific to the ESOPE translator 126 CASTEM2000 C E A D M T L A M S FORT Makes it possible to generate a fortran language adapted to a selected computer by specifying FORT z xxx xxx can be one of the following values IBM VAX CRAY SUN CONVEX PRIME FPS UNIVAC SEL HP9000 NOSVE NORSK VERCALL Makes it possible to generate a fortran language containing or not the characteristics for checking at the time of the execution whether an Esope subprogram containing SEGxxx instructions has been called by CALL with a variable pertaining to a segment in argument VERCALL OUI yes default Checking of the CA
91. rces 7 2 2 Procedure reserved for modal analysis CASTEM2000 makes it possible to carry out the analysis relating to the extraction of the eigen frequencies and modes of a structure in several stages See Modal analysis section 5 2 1 interactive definition of a MAILLAGE GEO type object or retreival of this object on a stack file 2 definition of the elastic linear behavior model of the material in a MMODEL MODI type object containing also geometric type data and data on the finite element formulation 3 definition of the characteristics of the material and of possible additional characteristics of the elements MCHAML MAT 1 type object 4 definition of possible additional characteristics of the elements and of the characteristics of the material CARB CAR type object if they have not already been specified in MATI 5 definition of kinematic type boundary conditions by the construction a RIGIDITE COND type object 6 calculation of the stiffness matrix of the free structure STIF 7 assembly of the stiffnesses stemming from the elements and the boundary conditions in a global RIGIDITE KTOT type object 59 CASTEM2000 C E A D M T L A M S 8 calculation of the structure mass matrix MTOT 9 calculation of the first eigen modes and frequencies of the structure AUTO 10 backup of the main objects GEO required for a further graphic postprocessing Besides the aforemention
92. res and components in both the nuclear and any other industrial areas From this point of view CASTEM2000 offers a complete system not only does it integrate computer functions proper but also functions for the model construction preprocessor and result processing postprocessor In the current version of CASTEM2000 the manual covers only the part of it that deals with problems of linear elasticity in static and dynamic areas extraction of eigenvalues CASTEM2000 also enables the user to deal with thermal problems non linear problems elasto visco plasticity step by step dynamic problems etc 2 General remarks concerning CASTEM2000 This computer code has the following distinctive feature it enables the user to personalize and complete the available system so as to adapt it to his own requirements moreover the program total flexibility facilitates the resolution of problems Unlike other systems designed to solve specific problems to which the user must submit CASTEM2000 is a program that the user can adapt to his own needs In practise the program is composed of a series of operators each operator can only execute one operation The user only has to call on any operator by means of the appropriate instruction to have it executed as a result the user can define or adapt the sequence of resolution to any problem The language used to define the processing functional instructions is advanced GIBIANE is especially useful insofa
93. ructure constraint CMOY calculation of a mean impact COLI weighted linear combination of fields COMB linear combination of fields by points COMM comments COMP construction of a line between two points 66 CASTEM2000 C E A D M T L A M S name description COMT calculation of the number of impacts in an impact recording CONC joins two objects COND construction of a conductivity matrix CONF merges two points CONG construction of a hollow curvature CONT construction of the contour of an object CONV imposes a forced convection COOR finds again the coordinates of a point mesh CHPO MCHAML or CHAMELEM COPI duplication of an object COS cosine of an object COTE construction of the side of an object COUL color attributed to an object COUR construction of a polynomial curve COUT construction of a surface by connecting two lines CREC creation of a constant CHAMELEM CRIT calculation of the criterion of a plastic model CUBP construction of an arc of a cubic CUBT construction of an arc of a cubic DALL construction of a surface within a contour DEBI calculation of the forces stemming from an imposed flow DEBP beginning of a procedure DEDU construction of a mesh from two other meshes TRI3 and QUAA only DEFO construction of a DEFORME type object DENS density of a mesh DEPB construction of an ATTACHE type object imposed displacements DEPI impos
94. s for condensing and retreiving the internal degrees of freedom for both the stiffness matrix and the vector of nodal loadings For further information report to the handbook For the time being we would suggest you to study a simple example of analysis by substructures The structure studied and the substructures from which it is made are shown in the following figure GEO GEO1 figure 3 The substructure matrices are reduced with respect to the sole degrees of freedom of the interface nodes line I1 is composed of the nodes P1 P2 and P4 by GEO2 and line I3 is composed of the nodes P3 P2 and P4 by GEO3 52 CASTEM2000 C E A D M T L A M S IN 5 2 Modal analysis Locating a structure eigen frequencies and modes amounts to solving the following homogeneous system o M C K u 0 where M stands for the mass matrix C the damping matrix K the stiffness matrix the eigen pulsation W 27f and u the vector accounting for the extent of nodal displacements Since CASTEM2000 does not take into account the damping values the problem relative to eigen vibrations amounts to AM K u 0 where A This system assumes two solutions different from zero for u only for certain values of which precisely correspond to the structure eigen pulsations An eigen vector u of the same eigen mode corresponds to each A If K is real symmetrical and non singular the number of eigenvalues different from zero
95. s of creation of elementary objects points lines surfaces solids As for the process of manipulation of these operators by means of operators specific to the stage of modelization report to the description of these operators see following paragraphs Chapter 3 describes the general operators liable to be also used in the stage of modelization 4 1 1 Creation of points A point is the object of the simplest mesh Once the dimensions of the problem have been defined by means of the following directive OPTION DIME n see 4 6 1 36 CASTEM2000 C E A D M T L A M S a point is constructed by the association of the following coordinates with its name P X Y in2D n 2 BE E P X 1 Y 1 i Zi in 3D n 3 A real number d standing for density i e for the dimensions of the elements converging on that point is also created the corresponding directive is then as follows DENS d see 4 6 1 If during the construction of the geometrical model it proves necessary to modify the dimensions of the problem a null coordinate will be added to the points already created or the third coordinate will be removed depending on whether one moves from 2D to 3D or from 3D to 2D The program numbers the points as they are created in ascending order Once known this number can be obtained by interactive query or by listing the corresponding object the NOEU operator enables the user to attribute a name to
96. s of loadings and or fluxes applied inside or 28 CASTEM2000 C E A D M T L A M S outside the region examined the type of formulation and the characteristics of the finite elements which are to be used Further down this writing you will find a brief description of each data block In annex B all the operators involved in the preparation of the calculation model are arranged in alphabetical order Before proceeding it is important to understand the logical stream of data and information used in CASTEM2000 One should not forget that in order to reach the resolution stage of the calculation one needs the following data and information all the data relating to geometry material behavior and characterization of the finite element formulation grouped together in an AFFECTE or MMODEL type object all the data relating to the boundary conditions grouped together in a CHPOINT type object as for the loadings and a RIGIDITE type object as for the constaints These data are organized rationally in the CASTEM2000 sense in the following synoptic table The two diagrams respectively correspond to the use of former and new fields by elements 29 CASTEM2000 C E A D M T L A M S FORMER CHAMELEMS GENERAL PARAMETERS MATERIAL MODEL MODE GEOMETRY ALLOCATE AFFE CHARACTERISTICS OF ELEMENTS MATERIAL DATA MATE CARA BOUNDARY LOADINGS CONDITIONS
97. s possible to apply the usual operations of algebraic calculation to these fields t T gt E TUS The ET operator makes it possible to merge fields by elements of the same subtype 104 CASTEM2000 C E A D M T L A M S 4 2 Lesson 12 ELASTIC CALCULATION In order to perform an elastic calculation assuming that the mesh object GEO exists one must conform to the following stages a definition of the type of calculation and finite element formulation Example MO MODL GEOL MECANIQUE ELASTIQUE TRI3 The MODL operator makes it possible to define the type of formulation in this instance MECANIQUE mechanic the type of linear behavior in this instance ELASTIQUE elastic and ISOTROPE isotropic by default the type of non linear behavior if necessary for the calculation the type of finite element s to be used TRI3 MO is a MCHAMIL type object or new chamelem MODL groups together in one stage the former data preparation MODELE and AFFE b creation of the material field Example MA1 MATR MO YOUN 2E11 NU 0 3 The MATR operator former MATE constructs the material field This field must contain the additional characteristics of the elements when necessary They can be added into MA1 by means of MATR or using the CARB operator see lesson 14 Example MA1 MATR MO YOUN 2E11 NU 0 3 EPAI 0 001 Or CA1 CARB MO EPAI 0 001 MA1 MAl ET CA1 105 CASTEM2000 C E A
98. st Each macro control thus defined plays the same part as an operator but it develops a complex function Several standard elementary operators of CASTEM2000 participate in its execution which is transparent to the user In conclusion it can be said that defining the precoded procedures as offered by CASTEM2000 is particularly well suited when integrated in the problem to be solved this is true of any application of the program 7 1 Definition of a procedure 54 CASTEM2000 C E A D M T L A M S 7 1 1 During the execution Setting up any resolution procedure or control macro amounts to inserting all the controls for activating and processing the operators requested between an initial control DEBP and a final control FINP as shown below DEBP name procedure objects type objects type requested operations FINP A procedure or control macro can be defined at the start of the execution data sets by merely inserting the DEBP control followed by the name of the procedure and the list of available objects Moreover any object must be followed by its type format type when it is required for the procedure to progress smoothly or format type when it is optional and corresponds to a special application The objects required for running the procedure can also be supplied directly during this very procedure in interactive mode by means of the OBTE and MESS operators At the end of the procedure just
99. stance the method used for showing the difference between the structure with loading and that without loading For this tvo DEFORMEE type objects must be created using the DEFO operator the one with a null amplification coefficient the other with a non null amplification coefficient Then the union of these two objects is plotted Illustration CISISPSISISIN KMS ALME SIT 1 65E 02 0 EN A J USS LPS PN A fa A TE TZ SSF fo WN cd TER A 5 7 SN PE Ze A put eM Lk EAS NZ E A plot of isovalues for a CHPOINT or MCHAML type object It is requested to extract a field with one component that which is to be plotted by means of the EXCO operator then TRACE will be used plot of an MCHAML type object from a deformed object It consists in combining the two previous types 12 CASTEM2000 C E A D M T L A M S Illustration Fin trace Zoom Initial PS VAL 150 8 1 17E 03 RHPLITUDE DEFORMEE FEH 1 690402 plot of a VECTEUR type object Small arrows may be associated with a CHPOINT by means of the VECT operator This allows for instance a displacement field to be displayed Illustration Fin trace Zoom Initial PS EIT PS Ds 23 EX ae 5 E 4 17 COMPOSANT VECTEURS UX UY
100. symmetrical boundary conditions SYNT calculation of the modes of a structure from those of the substructures TABLE creation of a table type object TAGR calculation of the transposed matrix of a gradient matrix TASS reorders the numbering of a MAILLAGE type object TEMP gives the time since the last occurence TEXT construction of a text from objects TFR construction of a signal fast Fourier transform TFRI construction of a signal inverse Fourier transform A CASTEM2000 C E A D M T L A M S name description THETA calculation of the stresses associated with a temperature field TIRE extraction of an object stemming from a solution type object extraction of a CHPO type object stemming from a CHARGEMENT type object TITR definition of a title TOTE calculation of the sum of the intervals on which one of the abscissas of a function exceeds a limit TOUR construction of an object stemming from the rotation of another object TRAC graphic output for MAILLAGE CHPO MCHAML CHAMELEM type objects TRAN construction of a surface generated by the translation of a line TRESCA calculation of Tresca equivalent stress TYPE gives the object type VALE finds again the values of the general calculation operations VALP calculation of the eigenvalues of a tridiagonal matrix VARI construction of a variable field VECT creation of a vector type object VERS checks the direction of th
101. teractive mode for the postprocessing It is actually a matter of performing several successive inputs and transmitting at each new stage the data resulting from the previous one For this purpose there are objects for the management of operators which save both simply and fastly the data on a file see user s manual for using the SORT and SAUV operators or retreive them for the next runnings refer to manual concerning the LIRE and REST operators For interactive mode runnings the user can also call on an on line help which supplies some information about the operators The directive is called INFO and is used as follows INFO name of the operator This directive makes it possible to generate instructions relating to all the operators and procedures of CASTEM2000 2 6 General syntactic rules List of the main syntactic rules to follow when using the GIBIANE language The blank comma equal and colon characters are separating characters The semi colon ends an instruction An instruction must not exceed 9 lines but a single line may contain several instructions The GIBIANE interpreter does not take into account any line beginning by an asterisk in first column as a result the user can annotate his sets of data Both the operators and the directives are defined by the first four characters the next ones are not taken into account An instruction is interpreted from left to right Once the program has detecte
102. the modes of a structure ENTI conversion of a floating into an integer ENVE creation of the envelope of a volume creation of the envelope spectrum of a series of spectra EPSI calculation of the strain field 68 CASTEM2000 C E A D M T L A M S name description ERREUR processing of errors calculation of an error field ET fusion of two objects of same type EVOL creation of an evolution type object EXCE research for the minimum of a function EXCI determination of active constraints in case of unilateral constraints EXCO extraction of the component from an MCHAML or CHAMELEM or CHPO type object EXIS test to check whether an object exists EXP exponential EXTR extraction of an object value or component FACE finds again the side of a volumic mesh FDT creation of a function EVOLUTION type object from a time step FILT calculation of filters FIN program or block stop FINP end of procedure FINSI end of a block SI SINON FLOT conversion of an integer into a floating FLUX imposes a flow on a part of the contour of a structure FOFI calculation of a nodal force field FONC calculation of Bessel or Fresnel functions FORCE creation of a force field FORME manipulation of CONFIGURATION type objects discretization fields GENE construction of a surface generated by a generatrix GRAD calculation of the gradient of a displacement field GRAF calculation of the flexural gradi
103. the points even to those created by automatic procedures see creation of lines in 4 1 2 As for the POIN operator it can either give a name to any point defined by its number like NOEU or identify the points located at the intersection of a MAILLAGE type object and a given line or surface Given any MAILLAGE type object the BARY operator makes it possible to determine the barycentre of that object be it a line surface or volume by attributing the name defined by the user to it 4 1 2 Creation of lines A line is always constructed from its two extreme points according to the rule enabling the computation of the coordinates of internal points Depending on the rule it is therefore possible to generate different types of lines using various operators as shown in table A and Figure 2 As soon as the lines have been created they are automatically subdivided into a certain number of segments This number depends on the density at the extreme points of the line the length of the segments actually stands for a geometrical progression between the values of the densities at the ends It is also possible to directly specify the number of segments of a line in this case all the segments will be the same length 37 CASTEM2000 C E A D M T L A M S The created lines can be composed of two node SEG2 elements or three node SEG3 elements segments depending on whether the following directive is used OPTI ELEM SEG 2 see
104. tized region the magnitudes specific to the type of problem to be solved elementary stiffnesses material density conductivity 49 CASTEM2000 C E A D M T L A M S The problem can be solved using the operators or sequences of appropriate operators as soon as the matrices have been constructed 5 1 Static linear elastic analysis Solving a problem in the static area as for structures amounts to searching for the discretized displacement field for a finite number of nodal points stemming from the application on the studied region of a set of boundary conditions As already mentioned these boundary conditions can be external forces temperature fields initial deformation stress fields imposed displacements fields giving rise to the nodal equivalent loadings In fact solving a problem amounts to solving a system of linear equations Ku f where K stiffness matrix contains all the data relating to the geometrical characteristics dimensions the physical characteristics material properties and the constrained degrees of freedom of the structure f stands for the nodal equivalent loadings and u the set of unknown nodal displacements 5 1 1 Substructures The substructure method is very efficient for analyzing complex structures by subdividing them into smaller components which can therefore be handled more easily Each part or substructure is modeled independently of the others and its degrees of freedom are
105. unning Between those two directives it is possible to use any operator or directive The user should keep in mind that an operator creates one or several objects whereas a directive does not An operator takes the following form OB1 OPERATEUR OB2 OB3 OBI is the object resulting from the OPERATEUR operator work OB2 OB3 are the arguments objects the number of arguments may be arbitrary In order to call on an operator only the first four letters of its name are necessary Example MAT1 MATR MO YOUN 2E11 NU 0 3 A directive takes the following form 84 CASTEM2000 C E A D M T L A M S DIRECTIVE OB4 OBS OB4 and OBS are the argument objects the number of arguments may be arbitrary Example TRAC OEIL1 GEOI If the objects supplied are not compatible with the operator or directive an error message will be displayed warning the user that he did not manage to get the result he expected there will be also an indication about the kind of error Example FIN DE FICHIER SUR L UNITE 3 LES DONNEES SONT MAINTENANT LUES SUR LE CLAVIER OPTI DIME 3 ELEM SEG2 OPTI DIME 3 ELEM SEG2 amp 1 23 3 1 23 3 wt ERREUR 37 ee dans l operateur Troisieme coordonnee Premiere ligne donnees deuxieme ligne type des donnees 1 FLOTTANT FLOTTANT FIN FIN NODE ARRET DU PROGRAMME GIBI NIVEAU D ERREUR 2 MY In interactive mode if the user does not understand the syntax of an op
106. w of the element including the propagation procedure called on by the TRACTUFI procedure RESO ASY SIGNDERI procedure called on by the RESO operator SIGNCORR procedure called on by SIGNSYNT adds a straight line to a signal EVOLUTION type object SIGNENVE procedure called on by SIGNSYNT SIGNSYNT allows synthetic signals to be created by the recombination of random phase sinusoids SISSI SISSI2 enables an interactive input of the data required for a calculation with SISSI2 enables the calculation of the maximum response of a structure with seismic excitation THERMIC TRAC3D allows thermal problems to be solved whether permanent or transient linear or not allows the results of an axisymmetrical analysis to be displayed in 3D TRACTUFI makes it possible to determine the global behavior law of the cracked piping elements TRADUIRE allows a TABLE type object to be created from a SOLUTION type object in modal analysis TRANSFER allows the transfert function of a structure to be calculated response to a localized force or to an overall acceleration 19 CASTEM2000 C E A D M T L A M S name description procedure called THERMIC procedure procedure called THERMIC procedure procedure called THERMIC procedure procedure called THERMIC procedure UNILATER cannot be called on by the user it is used for calculations with unilateral supports

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