Modulef
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3.2 Test 5: Elasticity Problem

3.2.1 Description

Calculate the displacements and stresses of a clamped beam subject to a vertical traction at its extreme.

Figure 3.4: Two-dimensional elasticity problem

The beam problem is a two-dimensional elasticity problem with plane deformation. We consider a homogeneous isotropic material.

Remark: It is favorable that the nodes at corners (20, -2) and (20, 2) on belong to two elements, due to discontinuities. For example, on the boundary

whereas on boundary

3.2.2 The boundary value problem

Find the displacement in and which satisfies:

where

: are the Lamé coefficients, and
: is Young's modulus and the Poisson ratio, respectively.

Assume that

: = 50 000, and
: = 0.25.

The exact solution is not known.

The type of finite element utilized in order to solve this problem: TRIA 2P2D (P2 Lagrange triangle)

Figure 3.5: Suggested mesh

Execute program: D5NOXX

Modules used: APNOPO ... 2D mesh generator [MODULEF User Guide - 3]

CONOPO ... manual mesh generator

MODNOP ... translation

RETRIN ... subdivision of mesh

RECOLC ... 'glue together' of meshes

ADPNOP ... addition of nodes

GIBBS ... renumbering of nodes

Libraries: NOP2, NOPO, UTSD, UTII

Input data file: D5NOPO.D

Output data structure: T5NOPO

Step2: Interpolation [13]

Execute program: D5COXX

Module used: COMACO [13]

Libraries: ELAS, COSD, UTSD, UTII

Element type: TRIA 2P2D

Output data structures: T5MAIL

T5COOR

Step 3: Calculation of the element arrays and description of boundary conditions

Execute program: D5CAXX

Modules used: ELASCT ... calculates element arrays for the constant case [14]

CONDL1 ... construction of numbers of the degrees of freedom associated with each node [20]

COBDC1 ... introduction of boundary conditions [18]

Libraries: COSD, ELAS, ELA2, UTII, UTSD

Output data structures: T5TAE

T5BDCL

Step 4: Solution

Execute program: D5REXX ... solution by a Crout direct method after assembly of the matrix and RHS vector and incorporation of boundary conditions [MODULEF User Guide - 5]

Modules used: PREPAC ... allocation of pointers

ASSMUA ... assembly of matrix in main memory (m.m.)

ASEMBV ... assembly of RHS vector in m.m.

CLIMPC ... introduction of boundary conditions

CROUPC ... factorization by Crout

DRCRPC ... forward and backward substitution

Libraries: RESB, RESO, RESD, UTSD, UTII

Output data structure: T5B

The number of words necessary to store the matrix in main memory is 38 127.

The number of words necessary to store the corresponding right-hand-side (RHS) vector is 1377.

Step 5: Calculation of stresses [90]

Execute program: D5STXX

Modules: STRESS [90]

Output data structure: T5TAES

3.2.4 Memory usage and Execution time

The table below represents the approximate maximum values of memory usage and execution time.

Step Dimension of Execution time

the super array LM (DPS8 Multics)

Mesh 15 000 23.0

Interpolation 8 000 3.5

Element arrays 8 000 12.7

Solution 45 000 25.0

Stresses 6 000 7.0

The super array M is dimensioned to 45 000 words in all the programs.

3.2.5 Results

The output of the D.S. B, containing the displacements at all the nodes in the mesh, is found in the file S5B.D in library TESD. The stress values of the first 45 elements are found in file S5TAES.D in library TESD.

The remainder of this section contains the partial or total printout of the various D.S. created by the different programs. 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  0

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           : BENCHMARK MODULEF NUMBER 5 :PLANE DEFORMATION-STRESS           
 DATE AND USER'S NAME            : 29/10/90  dutoit                  
 DATA STRUCTURE TYPE             : NOPO
 LEVEL AND STATE NUMBER          :      0     0
 NUMBER OF ASSOCIATED TABLES     :      0


 TABLE  N O P 2 
 --------------
 CHARACTERISTICS OF THE MESH : 

 SPACE DIMENSION                        (NDIM ) :      2
 MAXIMUM NUMBER OF REFERENCES           (NDSR ) :      3
 MAXIMUM NUMBER OF SUB-DOMAINS          (NDSD ) :      1
 NODES AND POINTS DO NOT COINCIDE      (NCOPNP) :      0
 NUMBER OF ELEMENTS                     (NE   ) :    144
 NUMBER OF TRIANGLES                    (NTRI ) :    144
 NUMBER OF BOUNDARY ELEMENTS            (NEF  ) :     88
 NUMBER OF NODES                        (NOE  ) :    333
 NUMBER OF NODES BY SEGMENT (NO EXTREMITIES)    :      1
 NUMBER OF POINTS                        (NP  ) :     95
 TYPE OF COORDINATE VALUES             (NTYCOO) : REEL1MOT
 MAX DIFFERENCE +1 BETWEEN 2 NODES OF AN ELEMENT :    26
 NUMBER OF COARSE ELEMENTS             (NBEGM ) :      0
 NUMBER OF WORDS FOR TABLE NOP5        (LNOP5 ) :   2468
 REFERENCE AXIS    X,Y,Z               (NTACOO) :      1

  TABLE  N O P 4
 ----------------
  COORDINATES OF POINTS


 -------------------------------------------------------------------------------
 | POINT |     X        |     Y       |   | POINT |     X        |     Y       |  
 -------------------------------------------------------------------------------
 |     1 |   8.88888    | 0.000000    |   |     2 |   10.0000    | 0.000000    |
 |     3 |   8.88888    |  1.00000    |   |     4 |   10.0000    |  1.00000    |
 |     5 |   8.88888    |  2.00000    |   |     6 |   10.0000    |  2.00000    |
 |     7 |   4.44440    | 0.000000    |   |     8 |   6.66662    | 0.000000    |
 |     9 |   4.44440    |  2.00000    |   |    10 |   6.66662    |  2.00000    |
 --------------------------------------- ---------------------------------------



  TABLE  N O P 5
 ----------------
  DESCRIPTION OF ELEMENTS


 | ELEMENT :      1 | TRIANGLE     | S-D :   1 | NUMBER OF STORED WORDS  :  0

 NUMBER OF  NODES  :  6 :      152      176      154      163      164      153
                            
 NUMBER OF  POINTS :  3 :        1        2        3   

 | ELEMENT :      2 | TRIANGLE     | S-D :   1 | NUMBER OF STORED WORDS  :  0

 NUMBER OF  NODES  :  6 :      176      178      154      177      166      164
                            
 NUMBER OF  POINTS :  3 :        2        4        3   
 


 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

     PRINT OUT OF D.S. MAIL OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 13/09/90  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) :      2
 NUMBER OF TYPES OF ELEMENTS             (NTYELM) :      1
 NUMBER OF REFERENCES                       (NNR) :      3
 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 THEIR COORDINATES
 NODES AND POINTS DO NOT COINCIDE        (NCOPNP) :      0
 MAX NUMBER OF WORDS FOR AN ELEMENT      (NMMAEL) :     25
 NUMBER OF WORDS OF THE TABLE MAIL        (LMAIL) :   2756
 STORAGE OPTION                           (NOPFI) :      0

 TABLE  M A I 3 
 --------------

 NUMBER OF ELEMENTS                          (NE) :    144
 NUMBER OF NODES                            (NOE) :    333
 NUMBER OF POINTS                            (NP) :     95
 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   |        |        |        |        |TRIA2P2D|        |        |        |
--------------------------------------------------------------------------------



--------------------------------------------------------------------------------
|  S-D |   TETRAHEDRON   |   PENTAHEDRON   |   HEXAHEDRON    |   SUPER-ELEMENT |     
--------------------------------------------------------------------------------
|      | STRAIGHT CURVED | STRAIGHT CURVED | STRAIGHT CURVED | STRAIGHT CURVED |
--------------------------------------------------------------------------------
|  1   |        |        |        |        |        |        |        |        |
--------------------------------------------------------------------------------




 TABLES   M A I 5   TO   M A I 8 
 -------------------------------
   DESCRIPTION OF NODE TYPES

 NUMBER OF VARIATIONAL UNKNOWNS FOR EACH NODE TYPE 
 -----------------------------------------------------

  TYPE  1 :   2

 NODE TYPE         1 : 
 --------------------
          DEPLACEMENT EN X (UNKNOWN  :  1) : VN  
          DEPLACEMENT EN Y (UNKNOWN  :  2) : VN  

 TABLES    M A I B  TO   M A I K 
 -------------------------------
   DESCRIPTION OF ELEMENT TYPES

  ELEMENT TYPE      1     : 
  -------------------
  ELEMENT NAME                 : ELASTRIA2P2D
  ELEMENT CODE                 : 200002
  THE ELEMENT IS A             : TRIANGLE    
  NUMBER OF NODES              :      6
  NUMBER OF POINTS             :      3
  NUMBER OF ASSOCIATED TABLES  :      1
 -------------------------------------------------------------------------------
 | NODE  | TYPE  |    COORDINATES ON THE UNIT ELEMENT                          |
 -------------------------------------------------------------------------------
 |     1 |     1 |   0.0000000      0.0000000    
 |     2 |     1 |    1.000000      0.0000000    
 |     3 |     1 |   0.0000000       1.000000    
 |     4 |     1 |   0.5000000      0.0000000    
 |     5 |     1 |   0.5000000      0.5000000    
 |     6 |     1 |   0.0000000      0.5000000    
 -------------------------------------------------------------------------------
 -------------------------------------------------------------------------------
 | POINT | TYPE  |    COORDINATES ON THE UNIT 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 
 --------------
 DESCRIPTION OF ELEMENTS IF NOPTFI = 0

-------------------------------------------------------------------
| ELEMENT | TYPE | NBER OF WORDS| S-D | TABLES   | NBER OF NODES  | 
-------------------------------------------------------------------
|     1   |  1   |     0        |   1 |     0    |     6          |
 NODE NUMBERS   :   152   176   154   163   164   153
 NUMBER OF POINTS   3 :      1     2     3
-------------------------------------------------------------------
|     2   |  1   |     0        |   1 |     0    |     6          |
 NODE NUMBERS   :   176   178   154   177   166   164
 NUMBER OF POINTS   3 :      2     4     3
-------------------------------------------------------------------
|     3   |  1   |     4        |   1 |     1    |     6          |
 NODE NUMBERS   :   154   178   158   166   167   157
 NUMBER OF POINTS   3 :      3     4     5
 REFERENCE (VERTICES) :      0     0     2
-------------------------------------------------------------------

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

     PRINT OUT OF D.S. COOR OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 13/09/90  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) :    95
 SEGMENTATION CODE                   (NCODS) :     1
 NUMBER OF BLOCKS                    (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 :     95   PAGE 

 ----------------------------------------------


 TABLE C O O 4 
 -------------
 -------------------------------------------------------------------------------
 | POINT |     X        |     Y       |   | POINT |     X        |     Y       |  
 -------------------------------------------------------------------------------
 |     1 |   8.88888    | 0.000000    |   |     2 |   10.0000    | 0.000000    |
 |     3 |   8.88888    |  1.00000    |   |     4 |   10.0000    |  1.00000    |
 |     5 |   8.88888    |  2.00000    |   |     6 |   10.0000    |  2.00000    |
 |     7 |   4.44440    | 0.000000    |   |     8 |   6.66662    | 0.000000    |
 |     9 |   4.44440    |  2.00000    |   |    10 |   6.66662    |  2.00000    |
 --------------------------------------- ---------------------------------------

 
 
 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

     PRINT OUT OF D.S. TAE  OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 13/09/90  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) :   144
 NUMBER OF NODES                                  (NOE) :   333
 NUMBER OF ARRAYS CORRESPONDING TO EACH ELEMENT (NTACE) :     3
 MAX NUMBER OF NODES PER ELEMENT               (NNOMAX) :     6
 CONSTANT NUMBER OF D.O.F. PER NODE ( 0 IF NOT )   (ND) :     2
 MAXIMUM NUMBER OF D.O.F. PER NODE             (NDLMAX) :     2
 NUMBER OF TYPES OF ELEMENTS                   (NTYELM) :     1
 SUM OF THE NUMBER OF NODES OF THESE ELEMENT TYPES  (LNOET) :     6

 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        :     6
 NUMBER OF D.O.F. AT EACH NODE             :     2     2     2     2     2     2

 TABLE  T A E 4
 --------------
 ASSOCIATED ARRAY NUMBER               ------------  :     1
 MAX NUMBER OF WORDS NECESSARY FOR STORAGE  (NMMAST) :   156
 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) :    24
 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) :    84
 TYPE OF THE ARRAY                           (NTYTA) :     5
 NUMBER OF INDICES                           (NINDI) :     1
 STORAGE OPTION                              (NSTOC) :    -1

 ------------------------------------------------------------------------------
 ELEMENT :      1 TYPE :      1 NUMBER OF NODES  :      6
 THEIR NUMBERS   :   152   176   154   163   164   153

 ELEMENT :      1  , ASSOCIATED ARRAY NUMBER :     1


    1   0.381110E+05    2   0.200000E+05    3   0.423335E+05    4   0.899993E+04 
    7   0.333333E+04    8   0.299998E+04    9   0.000000E+00   10   0.899993E+04 
   13   0.000000E+00   14  -0.333333E+04   15   0.111112E+05   16   0.333333E+04 
   19   0.000000E+00   20   0.000000E+00   21   0.333336E+05   22  -0.359997E+05 
   25  -0.133333E+05   26   0.000000E+00   27   0.000000E+00   28   0.101629E+06 
   31  -0.133333E+05   32  -0.119999E+05   33   0.000000E+00   34   0.000000E+00 
   37   0.000000E+00   38   0.000000E+00   39   0.000000E+00   40   0.133333E+05 
   43  -0.296299E+05   44  -0.266667E+05   45   0.101629E+06   46   0.000000E+00 
   49   0.000000E+00   50   0.133333E+05   51   0.000000E+00   52  -0.266667E+05 
   55   0.112889E+06   56  -0.148149E+05   57  -0.133333E+05   58   0.000000E+00 
   61  -0.133333E+05   62   0.000000E+00   63   0.266667E+05   64  -0.719994E+05 
   67  -0.133333E+05   68  -0.444448E+05   69   0.000000E+00   70   0.000000E+00 
   73   0.266667E+05   74   0.000000E+00   75  -0.266667E+05   76  -0.239998E+05 

 ELEMENT :      1  , ASSOCIATED ARRAY NUMBER :     2


    1   0.000000E+00    2   0.000000E+00    3   0.000000E+00    4   0.000000E+00 
    7   0.000000E+00    8   0.000000E+00    9   0.000000E+00   10   0.000000E+00 



 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

     PRINT OUT OF D.S. BDCL OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 13/09/90  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) :     18
 NUMBER OF LINEAR RELATIONS BETWEEN CONSTRAINTS  (NCLRL) :      0
 STORAGE OPTION                          (NOPTFI) :      0
 NUMBER OF WORDS OF TABLE BDC3           (NMMAT3) :     54
 NUMBER OF WORDS OF TABLE BDC4           (NMMAT4) :     36
 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    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     1 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     2 , D.O.F. :  1
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     2 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     5 , D.O.F. :  1
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     5 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     6 , D.O.F. :  1
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     6 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     8 , D.O.F. :  1
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :     8 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00



 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

     PRINT OUT OF D.S. B    OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 13/09/90  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   666
 OPTION (1: PAGES OF SAME SIZE , 0: IF NOT)  (NCOD) :      1
 NUMBER OF PAGES OF THE TABLE B4            (NBLOC) :      1
 NUMBER OF NODES                              (NOE) :    333
 NUMBER OF TABLES B4 IN THIS D.S.          (NBBLOC) :      1
 CONSTANT NUMBER OF D.O.F. AT EACH NODE OR 0   (ND) :      2
 NUMBER OF D.O.F. OR LENGHT OF A B4 PAGE     (NTDL) :    666
 STORAGE OPTION FOR B4                     (NCODSB) :     -1

 TABLE  B 3 
 ----------
  POINTER ON THE LAST ROW OF EACH PAGE OF B4


     1           0     2         666

 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  |    0.000000    
          |   2 |        2  |    0.000000    
 |      2 |   1 |        3  |    0.000000    
          |   2 |        4  |    0.000000    
 |      3 |   1 |        5  |   -0.161109E-18
          |   2 |        6  |   -0.347244E-05
 |      4 |   1 |        7  |    0.649441E-05
          |   2 |        8  |   -0.399245E-05
 |      5 |   1 |        9  |    0.000000    
          |   2 |       10  |    0.000000    


 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&

     PRINT OUT OF D.S. TAE  OF LEVEL  2

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 13/09/90  dutoit                  
 DATA STRUCTURE TYPE             : TAE       
 LEVEL AND STATE NUMBER          :      2     -1
 NUMBER OF ASSOCIATED TABLES     :      0


 TABLE  T A E 2 
 --------------

 NUMBER OF ELEMENTS                                (NE) :   144
 NUMBER OF NODES                                  (NOE) :   333
 NUMBER OF ARRAYS CORRESPONDING TO EACH ELEMENT (NTACE) :     1
 MAX NUMBER OF NODES PER ELEMENT               (NNOMAX) :     6
 CONSTANT NUMBER OF D.O.F. PER NODE ( 0 IF NOT )   (ND) :     2
 MAXIMUM NUMBER OF D.O.F. PER NODE             (NDLMAX) :     2
 NUMBER OF TYPES OF ELEMENTS                   (NTYELM) :     1
 SUM OF THE NUMBER OF NODES OF THESE ELEMENT TYPES  (LNOET) :     6

 PROBLEM  : 1 THERMAL, 2 ELASTIC, 3 OTHER       (NPROV) :     2
 REQUESTED OPTION                              (NOPTNT) :     0


 NUMBER OF THE ASSOCIATED ARRAY CONTAINING :
 THE MASS MATRIX                           :     0
 THE STIFFNESS MATRIX                      :     0
 THE FIRST LINEAR COMBINATION              :     0
 THE LAST ONE                              :     0
 THE RIGHT HAND SIDE(S)                    :     0
 THE STRESSES OR THE FLUX                  :     1


 TABLE  T A E 3 
 --------------

 NUMBER OF NODES BY TYPE OF ELEMENT        :     6
 NUMBER OF D.O.F. AT EACH NODE             :     2     2     2     2     2     2

 TABLE  T A E 4
 --------------
 ASSOCIATED ARRAY NUMBER               ------------  :     1
 MAX NUMBER OF WORDS NECESSARY FOR STORAGE  (NMMAST) :    84
 TYPE OF THE ARRAY                           (NTYTA) :     5
 NUMBER OF INDICES                           (NINDI) :     1
 STORAGE OPTION                              (NSTOC) :    -1

 ------------------------------------------------------------------------------
 ELEMENT :      1 NDSD :      1

 ELEMENT :      1  , ASSOCIATED ARRAY NUMBER :     1

   -1   10   12    2    2    1    5    1    3    0

    1    9.25925        2   0.333333    

    1   0.270955E+00    2  -0.689490E-03    3  -0.142846E+00

 ------------------------------------------------------------------------------

3.2.6 Post-processing

A plot of the deformation is generated by the preprocessor TRNOXX as follows:

Call preprocessor: TRNOXX

Specify input data structures: T5NOPO

T5B

Figure 3.6: The deformation ( TRNOXX)

The plots of the principal stresses, and stresses according to Tresca's criterion [MODULEF User Guide - 6], are generated by the preprocessor TRSTXX as follows:

Call preprocessor: TRSTXX

Specify input data structures: T5MAIL

T5COOR

T5TAES

Figure 3.7: Principal stresses ( TRSTXX)

Figure 3.8: Stresses according to Tresca's criterion ( TRSTXX)

Next: 3.3 Test 6: Fluid Mechanics Problem Up: 3 Batch tests Prev: 3.1 Test 4: Thermal Problem Contents

Execute program:	D5NOXX

Modules used:	APNOPO	... 2D mesh generator [MODULEF User Guide - 3]
	CONOPO	... manual mesh generator
	MODNOP	... translation
	RETRIN	... subdivision of mesh
	RECOLC	... 'glue together' of meshes
	ADPNOP	... addition of nodes
	GIBBS	... renumbering of nodes
Libraries:	NOP2, NOPO, UTSD, UTII

Input data file:	D5NOPO.D
Output data structure:	T5NOPO

Execute program:	D5COXX

Module used:	COMACO [13]
Libraries:	ELAS, COSD, UTSD, UTII
Element type:	TRIA 2P2D

Output data structures:	T5MAIL
	T5COOR

Execute program:	D5CAXX

Modules used:	ELASCT	... calculates element arrays for the constant case [14]
	CONDL1	... construction of numbers of the degrees of freedom associated with each node [20]
	COBDC1	... introduction of boundary conditions [18]
Libraries:	COSD, ELAS, ELA2, UTII, UTSD

Output data structures:	T5TAE
	T5BDCL

Execute program:	D5REXX	... solution by a Crout direct method after assembly of the matrix and RHS vector and incorporation of boundary conditions [MODULEF User Guide - 5]

Modules used:	PREPAC	... allocation of pointers
	ASSMUA	... assembly of matrix in main memory (m.m.)
	ASEMBV	... assembly of RHS vector in m.m.
	CLIMPC	... introduction of boundary conditions
	CROUPC	... factorization by Crout
	DRCRPC	... forward and backward substitution
Libraries:	RESB, RESO, RESD, UTSD, UTII

Output data structure:	T5B

Execute program:	D5STXX

Modules:	STRESS [90]

Output data structure:	T5TAES

Step	Dimension of	Execution time
	the super array LM	(DPS8 Multics)
Mesh	15 000	23.0
Interpolation	8 000	3.5
Element arrays	8 000	12.7
Solution	45 000	25.0
Stresses	6 000	7.0

Call preprocessor:	TRNOXX

Specify input data structures:	T5NOPO
	T5B