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Contents
This test has been proposed by NAFEMS (National Agency for Finite Element Methods & Standards) [Robinson].
Figure 2.12: Study of the rigid movement of a rectangular plate under bending
The displacement in and
is known as well as the rotation
with respect to y at point A.
Then at each point the displacement w and the rotations with respect to
and
are given by:
and D is defined by:
where
The type of finite element utilized in order to solve this problem: TRIA DKTP of library ELAS.
The physical values are defined as follows:
l | = | 10.0 |
e | = | 0.01 |
c | = | 1 |
E | = | ![]() |
![]() | = | 0.3 |
Step 1: Mesh
Call preprocessor: | APNOXX | |
Modules used: | APNOPO | ... 2D mesh generator [MODULEF User Guide - 3] |
QUACOO | ... mesh generation utilizing quadrangles | |
Specify input data file: | D3NOPO.D | |
Output data structure: | T3NOPO |
Step 2: Interpolation [13]
Call preprocessor: | COMAXX |
Module used: | COMACO |
Finite element library: | ELAS |
Element type: | TRIA DKTP |
Specify input data file: | D3COMA.D |
Output data structures: | T3MAIL |
T3COOR |
Step 3: Description of data [14]
Call preprocessor: | FOMIXX |
Modules used: | COFORC |
COMILI | |
Specify input data file: | D3FOMI.D |
Output data structures: | T3FORC |
T3MILI |
Step 4: Calculation of the element arrays (general case) [14]
Call preprocessor: | THELXX |
Module used: | THENEW |
Specify input data file: | D3TAE.D |
Output data structure: | T3TAE |
Step 5: Description of boundary conditions [18]
Call preprocessor: | COBDXX |
Module used: | COBDC1 |
Specify input data file: | D3BDCL.D |
Output data structure: | T3BDCL |
Step 6: Assembly and solution by a direct Cholesky method
[4][MODULEF User Guide - 5]
Call preprocessor: | CHOLXX | |
Modules used: | PREPAC | ... allocation of pointers |
ASSMUA | ... assembly of matrix in m.m. | |
ASEMBV | ... assembly of RHS vector in main memory | |
CLIMPC | ... incorporate boundary conditions | |
DRCHPC | ... forward and backward substitution | |
Specify input data file: | D3B.D | |
Output data structure: | T3B |
The number of words necessary to assemble the matrix is 2330.
The number of words necessary to assemble the corresponding right-hand-side (RHS) vector is 195.
The table below represents the approximate maxima of the values.
Step | Dimension of | Execution time |
the super array | (DPS8 Multics) | |
Mesh | 6 000 | 9.5 |
Interpolation | 3 000 | 4.9 |
Element matrices | 4 000 | 5.0 |
Boundary conditions | 2 000 | 3.8 |
Solution | 3 000 | 6.4 |
The output of the D.S. B, containing the value of the displacement w at each node in the mesh,
as well as the rotations with respect to the axis and
, is found in file S3B.D
in library TESD.
The remainder of this section contains a partial or total printout of the output D.S. created in each step. These data structures can be viewed by calling preprocessor IMAGXX and specifying the names of the files containing the desired data structures.
&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. NOPO OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : BENCHMARK MODULEF NUMERO 3 : PLAQUE DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : NOPO LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 0 TABLE N O P 2 -------------- CHARACTERISTICS OF THE MESH : SPACE DIMENSION (NDIM ) : 2 MAXIMUM NUMBER OF REFERENCES (NDSR ) : 1 MAXIMUM NUMBER OF SUB-DOMAINS (NDSD ) : 1 NODES AND POINTS COINCIDE (NCOPNP) : 1 NUMBER OF ELEMENTS (NE ) : 32 NUMBER OF TRIANGLES (NTRI ) : 32 NUMBER OF BOUNDARY ELEMENTS (NEF ) : 24 NUMBER OF NODES (NOE ) : 25 NUMBER OF NODES BY SEGMENT (NO EXTREMITIES) : 0 TYPE OF COORDINATE VALUES (NTYCOO) : REEL1MOT MAX DIFFERENCE +1 BETWEEN 2 NODES OF AN ELEMENT : 7 NUMBER OF COARSE ELEMENTS (NBEGM ) : 0 NUMBER OF WORDS FOR TABLE NOP5 (LNOP5 ) : 368 REFERENCE AXIS X,Y,Z (NTACOO) : 1 TABLE N O P 4 ---------------- COORDINATES OF POINTS ------------------------------------------------------------------------------- | POINT | X | Y | | POINT | X | Y | ------------------------------------------------------------------------------- | 1 | 0.000000 | -1.00000 | | 2 | 0.000000 | -.500000 | | 3 | 0.000000 | 0.000000 | | 4 | 0.000000 | 0.500000 | | 5 | 0.000000 | 1.00000 | | 6 | 0.250000 | -1.00000 | | 7 | 0.250000 | -.500000 | | 8 | 0.250000 | 0.000000 | | 9 | 0.250000 | 0.500000 | | 10 | 0.250000 | 1.00000 | | 11 | 0.500000 | -1.00000 | | 12 | 0.500000 | -.500000 | | 13 | 0.500000 | 0.000000 | | 14 | 0.500000 | 0.500000 | | 15 | 0.500000 | 1.00000 | | 16 | 0.750000 | -1.00000 | | 17 | 0.750000 | -.500000 | | 18 | 0.750000 | 0.000000 | | 19 | 0.750000 | 0.500000 | | 20 | 0.750000 | 1.00000 | | 21 | 1.00000 | -1.00000 | | 22 | 1.00000 | -.500000 | | 23 | 1.00000 | 0.000000 | | 24 | 1.00000 | 0.500000 | | 25 | 1.00000 | 1.00000 | | --------------------------------------- --------------------------------------- TABLE N O P 5 ---------------- DESCRIPTION OF ELEMENTS | ELEMENT : 1 | TRIANGLE | S-D : 1 | NUMBER OF STORED WORDS : 7 NUMBER OF NODES : 3 : 1 6 7 EDGE REFERENCE : 1 0 0 VERTEX REFERENCE : 1 1 0 | ELEMENT : 2 | TRIANGLE | S-D : 1 | NUMBER OF STORED WORDS : 7 NUMBER OF NODES : 3 : 1 7 2 EDGE REFERENCE : 0 0 1 VERTEX REFERENCE : 1 0 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. MAIL OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : MAIL LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 0 TABLE M A I 2 -------------- SPACE DIMENSION (NDIM) : 2 NUMBER OF UNKNOWNS OF THE VARIATIONAL FORMULATION (NINCFV) : 1 NUMBER OF TYPES OF ELEMENTS (NTYELM) : 1 NUMBER OF REFERENCES (NNR) : 1 NUMBER OF TYPES OF NODES (NTYNOE) : 1 NUMBER OF TYPES OF POINTS (NTYPOI) : 1 NUMBER OF WORDS OF TABLE MAI3 (LMAI3) : 36 POINTS ARE ONLY DEFINED BY COORDINATES NODES AND POINTS ARE IDENTICAL (NCOPNP) : 1 MAX NUMBER OF WORDS FOR AN ELEMENT (NMMAEL) : 18 NUMBER OF WORDS OF THE TABLE MAIL (LMAIL) : 432 STORAGE OPTION (NOPFI) : 0 TABLE M A I 3 -------------- NUMBER OF ELEMENTS (NE) : 32 NUMBER OF NODES (NOE) : 25 NUMBER OF POINTS (NP) : 25 NUMBER OF SUB-DOMAINS (NDSD) : 1 *** TABLE OF THE TYPES OF ELEMENTS *** -------------------------------------------------------------------------------- | S-D | NODE | SEGMENT | TRIANGLE | QUADRANGLE | -------------------------------------------------------------------------------- | | STRAIGHT CURVED | STRAIGHT CURVED | STRAIGHT CURVED | STRAIGHT CURVED | -------------------------------------------------------------------------------- | 1 | | | | |TRIADKTP| | | | -------------------------------------------------------------------------------- -------------------------------------------------------------------------------- | S-D | TETRAEDRON | PENTAEDRON | HEXAEDRON | SUPER-ELEMENT | -------------------------------------------------------------------------------- | | STRAIGHT CURVED | STRAIGHT CURVED | STRAIGHT CURVED | STRAIGHT CURVED | -------------------------------------------------------------------------------- | 1 | | | | | | | | | -------------------------------------------------------------------------------- TABLES M A I 5 TO M A I 8 ------------------------------- DESCRIPTION OF THE TYPES OF NODES NUMBER OF VARIATIONAL UNKNOWNS OF EACH TYPE OF NODE ----------------------------------------------------- TYPE 1 : 1 TYPE OF NODE 1 : -------------------- DISPLAC. NORMAL. (UNKNOWN : 1) : VN DISPLAC. NORMAL. (UNKNOWN : 1) : ROTX DISPLAC. NORMAL. (UNKNOWN : 1) : ROTY TABLES M A I B TO M A I K ------------------------------- DESCRIPTOR OF THE TYPES OF ELEMENTS ELEMENT OF TYPE 1 : ------------------- NAME OF THE ELEMENT : ELASTRIADKTP CODE OF THE ELEMENT : 200050 THE ELEMENT IS A : TRIANGLE NUMBER OF NODES : 3 NUMBER OF POINTS : 3 NUMBER OF ASSOCIATED TABLES : 1 ------------------------------------------------------------------------------- | NODE | TYPE | COORDINATES ON THE UNITY ELEMENT | ------------------------------------------------------------------------------- | 1 | 1 | 0.0000000 0.0000000 | 2 | 1 | 1.000000 0.0000000 | 3 | 1 | 0.0000000 1.000000 ------------------------------------------------------------------------------- ------------------------------------------------------------------------------- | POINT | TYPE | COORDINATES ON THE UNITY ELEMENT | ------------------------------------------------------------------------------- | 1 | 1 | 0.0000000 0.0000000 | 2 | 1 | 1.000000 0.0000000 | 3 | 1 | 0.0000000 1.000000 ------------------------------------------------------------------------------- TABLE 1 ( TYPE ENTIER ) : 1 MAX VALUE OF INDEX(ES) : 7 TABLE M A I L -------------- DESCRIPTOR OF ELEMENTS IF NOPTFI = 0 ------------------------------------------------------------------- | ELEMENT | TYPE | NBER OF WORDS| S-D | TABLES | NBER OF NODES | ------------------------------------------------------------------- | 1 | 1 | 7 | 1 | 1 | 3 | LIST OF NODES : 1 6 7 REFERENCE (EDGES VERTICES) : 1 0 0 1 1 0 ------------------------------------------------------------------- | 2 | 1 | 7 | 1 | 1 | 3 | LIST OF NODES : 1 7 2 REFERENCE (EDGES VERTICES) : 0 0 1 1 0 1 ------------------------------------------------------------------- &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. COOR OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : COOR LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 0 TABLE C O O 2 ------------- TYPE OF THE TABLE COO4 (NTYT) : 2 NUMBER OF ITS INDEX (NINDI) : 2 SPACE DIMENSION (NDIM) : 2 MAX VALUE OF THE SECOND INDEX (M2) : 25 SEGMENTATION CODE (NCODS) : 1 NUMBER OF BLOCS (NBLOC) : 1 TYPE OF THE COORDINATE AXIS (NTACOO) : 1 TABLE C O O 3 ------------- TABLE OF THE LAST COLUMN NUMBER OF EACH PAGE ---------------------------------------------- PAGE 1 : 25 PAGE ---------------------------------------------- TABLE C O O 4 ------------- ------------------------------------------------------------------------------- | POINT | X | Y | | POINT | X | Y | ------------------------------------------------------------------------------- | 1 | 0.000000 | -1.00000 | | 2 | 0.000000 | -.500000 | | 3 | 0.000000 | 0.000000 | | 4 | 0.000000 | 0.500000 | | 5 | 0.000000 | 1.00000 | | 6 | 0.250000 | -1.00000 | | 7 | 0.250000 | -.500000 | | 8 | 0.250000 | 0.000000 | | 9 | 0.250000 | 0.500000 | | 10 | 0.250000 | 1.00000 | --------------------------------------- --------------------------------------- &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. FORC OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : FORC LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 1 TABLE 1 : FOR OF TYPE REEL2MOT , IT HAS 6 WORDS CONTENTS OF THIS TABLE : SECOND MEMBRE NAME : FOR TYPE : 5 VALUES : 0.00000000000000000E+00 0.00000000000000000E+00 0.00000000000000000E+00 TABLE F O R 2 -------------- INFORMATION ( NUMBER OF SETS ) OR NOT ( 0 ) -------------------------------------------------- | | | | | | SUB-DOMAINS | ELEMENTS | | | | | -------------------------------------------------- | VOLUMES | 0 | 0 | | SURFACES | 1 | 0 | | LINES | 0 | 0 | | POINTS | 0 | 0 | -------------------------------------------------- TABLE F O R 4 -------------- DESCRIPTION OF REFERENCES FOR SURFACES REFERENCE ( OR SUB-DOMAIN ) NUMBER : 1 TYPE OF THE ELEMENT ( > 0 : ISOTROPIC, < 0 : ANISOTROPIC ) : 1 USE OF A TABLE NAME OF THE TABLE : FOR ADRESS IN IT : 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. MILI OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : MILI LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 1 TABLE 1 : MIL OF TYPE REEL2MOT , IT HAS 6 WORDS CONTENTS OF THIS TABLE : YOUNG_POISSON_EPAISSEUR NAME : MIL TYPE : 5 VALUES : 0.10000000000000000E+06 0.30000000000000000E+00 0.10000000000000000E-01 TABLE M I L 2 -------------- INFORMATION ( NUMBER OF SETS ) OR NOT ( 0 ) -------------------------------------------------- | | | | | | SUB-DOMAINS | ELEMENTS | | | | | -------------------------------------------------- | VOLUMES | 0 | 0 | | SURFACES | 1 | 0 | | LINES | 0 | 0 | | POINTS | 0 | 0 | -------------------------------------------------- TABLE M I L 4 -------------- DESCRIPTION OF REFERENCES FOR SURFACES REFERENCE ( OR SUB-DOMAIN ) NUMBER : 1 TYPE OF THE ELEMENT ( > 0 : ISOTROPIC, < 0 : ANISOTROPIC ) : 1 USE OF A TABLE NAME OF THE TABLE : MIL ADRESS IN IT : 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. TAE OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : TAE LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 0 TABLE T A E 2 -------------- NUMBER OF ELEMENTS (NE) : 32 NUMBER OF NODES (NOE) : 25 NUMBER OF ARRAYS CORRESPONDING TO EACH ELEMENT (NTACE) : 3 MAX NUMBER OF NODES PER ELEMENT (NNOMAX) : 3 CONSTANT NUMBER OF D.O.F. PER NODE ( 0 IF NOT ) (ND) : 3 MAXIMUM NUMBER OF D.O.F. PER NODE (NDLMAX) : 3 NUMBER OF TYPES OF ELEMENTS (NTYELM) : 1 SUM OF THE NUMBER OF NODES OF THESE ELEMENT TYPES (LNOET) : 3 PROBLEM : 1 THERMAL, 2 ELASTIC, 3 OTHER (NPROV) : 2 REQUESTED OPTION (NOPTNT) : 111 NUMBER OF THE ASSOCIATED ARRAY CONTAINING : THE MASS MATRIX : 0 THE STIFFNESS MATRIX : 1 THE FIRST LINEAR COMBINATION : 0 THE LAST ONE : 0 THE RIGHT HAND SIDE(S) : 2 THE STRESSES OR THE FLUX : 3 TABLE T A E 3 -------------- NUMBER OF NODES BY TYPE OF ELEMENT : 3 NUMBER OF D.O.F. AT EACH NODE : 3 3 3 TABLE T A E 4 -------------- ASSOCIATED ARRAY NUMBER ------------ : 1 MAX NUMBER OF WORDS NECESSARY FOR STORAGE (NMMAST) : 90 TYPE OF THE ARRAY (NTYTA) : 5 NUMBER OF INDICES (NINDI) : 1 STORAGE OPTION (NSTOC) : 1 TABLE T A E 4 -------------- ASSOCIATED ARRAY NUMBER ------------ : 2 MAX NUMBER OF WORDS NECESSARY FOR STORAGE (NMMAST) : 18 TYPE OF THE ARRAY (NTYTA) : 5 NUMBER OF INDICES (NINDI) : 2 STORAGE OPTION (NSTOC) : -1 TABLE T A E 4 -------------- ASSOCIATED ARRAY NUMBER ------------ : 3 MAX NUMBER OF WORDS NECESSARY FOR STORAGE (NMMAST) : 66 TYPE OF THE ARRAY (NTYTA) : 5 NUMBER OF INDICES (NINDI) : 1 STORAGE OPTION (NSTOC) : -1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. BDCL OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : BDCL LEVEL AND STATE NUMBER : 1 0 NUMBER OF ASSOCIATED TABLES : 0 TABLE B D C 2 -------------- TYPE OF CONSTRAINED VALUES (NTYB) : 5 NUMBER OF CARDS DESCRIBING CONSTRAINTS (NCART) : 48 NUMBER OF LINEAR RELATIONS BETWEEN CONSTRAINTS (NCLRL) : 0 STORAGE OPTION (NOPTFI) : 0 NUMBER OF WORDS OF TABLE BDC3 (NMMAT3) : 144 NUMBER OF WORDS OF TABLE BDC4 (NMMAT4) : 96 NUMBER OF WORDS OF TABLE BDC5 (NMMAT5) : 0 NUMBER OF WORDS OF TABLE BDC6 (NMMAT6) : 0 TABLE B D C 3 B D C 4 ----------------------------- CLAMPING TYPE : 1 : NODE : 1 , D.O.F. : 1 AT VALUE : 0.10000000000000000E+01 CLAMPING TYPE : 1 : NODE : 1 , D.O.F. : 2 AT VALUE : 0.50000000000000000E+00 CLAMPING TYPE : 1 : NODE : 1 , D.O.F. : 3 AT VALUE : 0.31400001049041750E+01 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& PRINT OUT OF D.S. B OF LEVEL 1 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&& TITLE : DATE AND USER'S NAME : 19/11/90 dutoit DATA STRUCTURE TYPE : B LEVEL AND STATE NUMBER : 1 2 NUMBER OF ASSOCIATED TABLES : 0 TABLE B 2 ---------- TYPE OF THE TABLE (NTYT) : 5 NUMBER OF INDICES AND THEIR MAX VALUES (NIND..) : 2 1 75 OPTION (1: PAGES OF SAME SIZE , 0: IF NOT) (NCOD) : 1 NUMBER OF PAGES OF THE TABLE B4 (NBLOC) : 1 NUMBER OF NODES (NOE) : 25 NUMBER OF TABLES B4 IN THIS D.S. (NBBLOC) : 1 CONSTANT NUMBER OF D.O.F. AT EACH NODE OR 0 (ND) : 3 NUMBER OF D.O.F. OR LENGHT OF A B4 PAGE (NTDL) : 75 STORAGE OPTION FOR B4 (NCODSB) : -1 TABLE B 3 ---------- POINTER ON THE LAST ROW OF EACH PAGE OF B4 1 0 2 75 TABLE B4(NDSM,NTDL) NUMBER : 1 ----------------------------------- TABLE B4(NDSM,NTDL) PAGINATED IN 1 OR MORE PAGES ------------------------------------------------ PAGE 1 ---------- ------------------------------------------------------ | NODE | DOF | GLOBAL DOF| LOAD CASE(S) | ------------------------------------------------------ | 1 | 1 | 1 | 1.00000 | 2 | 2 | 0.500000 | 3 | 3 | 3.14000 | 2 | 1 | 4 | 1.25000 | 2 | 5 | 0.500000 | 3 | 6 | 3.14000 | 3 | 1 | 7 | 1.50000 | 2 | 8 | 0.500000 | 3 | 9 | 3.14000
A plot of the displacements is generated by the preprocessor VIS3XX as follows:
Call preprocessor: | VIS3XX |
Specify input data structures: | T3NOPO |
T3B |
Figure 2.14: The displacements ( VIS3XX)