Modulef
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2.3 Test 2: 2D Elasticity Problem with plane deformation

2.3.1 Description

Calculate the displacements and the distribution of stresses for the lever, shown below in figure 2.8, submitted to a point force.

Figure 2.8: Lever

Constraints:

All the nodes situated on the circle, , of radius have zero displacement in y.
All the nodes situated on the circle, , of radius have zero radial displacement.

2.3.2 The boundary value problem

where

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

if

if

where are the coordinates at point

The type of finite element utilized: QUAD 2Q1D

We consider a unit system where the physical values are defined by:

l = 12.0

= 10.0 = 3.5

= 15.5 = 7.5

= 7.5 = 3.5

= 40.0 = 70.0

and, Young's Modulus E =

Poisson's coefficient = 0.3

Point force P = 100.0

Figure 2.9: Suggested mesh

Call preprocessor: APNOXX

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

QUACOO ... mesh utilizing quadrangles

RECOLC ... 'glue together' meshes

Libraries: CONV, NOPO, NOP2, UTII, UTSD

Specify input data file: D2NOPO.D

Output data structure: T2NOPO

REMARK: The file D2NOPO was generated automatically by EMC²
[4] [MODULEF User Guide - 3].

Step 2: Interpolation [13]

Call preprocessor: COMAXX

Module used: COMACO

Libraries: CONV, COSD, ELAS, ELA2, UTII

Element type: QUAD 2Q1D

Specify input data file: D2COMA.D

Output data structures: T2MAIL

T2COOR

Step 3: Description of data [14]

Call preprocessor: FOMIXX

Modules used: COFORC

COMILI

Specify input data file: D2FOMI.D

Output data structures: T2FORC

T2MILI

Step 4: Calculation of the element arrays (general case) [14]

Call preprocessor: THELXX

Module used: THENEW

Specify input data file: D2TAE.D

Output data structure: T2TAE

Step 5: Description of boundary conditions [18]

Call preprocessor: COBDXX

Module used: COBDC1

Specify input data file: D2BDCL.D

Output data structures: T2BDCL

We consider boundary conditions of the following types:

nodal values at the boundary , and
linear relationships at the boundary .

Step 6: Assembly and solution by an iterative method: conjugate gradient preconditioned by a incomplete Cholesky factorization [MODULEF User Guide - 5]

Call preprocessor: GRADXX

Modules used: PREPGC ... allocation of pointers

ASSAMA ... assembly of compact matrix

ASEMBV ... assembly of RHS vector

CLIMGC ... incorporate boundary conditions

FANIGC ... incomplete factorization

ICHRGC ... solution

Specify input data file: D2B.D

Output data structure: T2B

The number of words necessary to assemble the matrix is 9184.

The number of words necessary to assemble the corresponding right-hand-side (RHS) vector is 785.

Step 7: Calculation of stresses [90]

Call preprocessor: STREXX

Specify input data file: none

Output data structures: T2TAES

An example of responses to the questions of program STREXX can be found in file TEST.HELP in library TESD.

2.3.4 Memory usage and execution time

The table below represents the approximate maxima of the values.

Step Dimension of Execution time

the super array (DPS8 Multics)

Mesh 15 000 58.3

Interpolation 9 000 6.1

Data 1 000 5.0

Element matrices 10 000 12.5

Boundary conditions 6 000 11.0

Solution 30 000 33.5

2.3.5 Results

The output of the D.S. B, containing the value of the displacement at each node in the mesh, is found in the file S2B.D in library TESD. The output of the D.S. TAE, created by STREXX, containing the stress values, is found in file S2TAES.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. MAIL OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 16/11/90  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) :      2
 NUMBER OF TYPES OF ELEMENTS             (NTYELM) :      1
 NUMBER OF REFERENCES                       (NNR) :      7
 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) :     21
 NUMBER OF WORDS OF THE TABLE MAIL        (LMAIL) :   2300
 STORAGE OPTION                           (NOPFI) :      0

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

 NUMBER OF ELEMENTS                          (NE) :    135
 NUMBER OF NODES                            (NOE) :    185
 NUMBER OF POINTS                            (NP) :    185
 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   |        |        |        |        |        |        |QUAD2Q1D|        |
--------------------------------------------------------------------------------



--------------------------------------------------------------------------------
|  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 
 -------------------------------
   DESCRIPTOR OF THE TYPES OF NODES

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

  TYPE  1 :   2

 TYPE OF NODE      1 : 
 --------------------
          DISPLACEMENT IN X (UNKNOWN  :  1) : VN  
          DISPLACEMENT IN Y (UNKNOWN  :  2) : VN  

 TABLES    M A I B  TO   M A I K 
 -------------------------------
   DESCRIPTOR OF THE TYPES OF ELEMENTS

  ELEMENT OF TYPE   1   : 
  -------------------
  NAME OF THE ELEMENT          : ELASQUAD2Q1D
  CODE OF THE ELEMENT          : 200006
  THE ELEMENT IS A             : QUADRANGLE  
  NUMBER OF NODES              :      4
  NUMBER OF POINTS             :      4
  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 |    1.000000       1.000000    
 |     4 |     1 |   0.0000000       1.000000    
 -------------------------------------------------------------------------------
 -------------------------------------------------------------------------------
 | POINT | TYPE  |    COORDINATES ON THE UNIT ELEMENT                          |
 -------------------------------------------------------------------------------
 |     1 |     1 |   0.0000000      0.0000000    
 |     2 |     1 |    1.000000      0.0000000    
 |     3 |     1 |    1.000000       1.000000    
 |     4 |     1 |   0.0000000       1.000000    
 -------------------------------------------------------------------------------
  TABLE        1 ( TYPE ENTIER   ) :   1  MAX VALUE OF INDEX(ES) :     9

 TABLE  M A I L 
 --------------
 DESCRIPTOR OF ELEMENTS IF NOPTFI = 0

-------------------------------------------------------------------
| ELEMENT | TYPE | NBER OF WORDS| S-D | TABLES   | NBER OF NODES  | 
-------------------------------------------------------------------
|     1   |  1   |     9        |   1 |     1    |     4          |
 LIST OF NODES   :     1     6     7     2
 REFERENCE (EDGES VERTICES) :      4     0     0     0     0     4
                 0     0
-------------------------------------------------------------------
|     2   |  1   |     0        |   1 |     0    |     4          |
 LIST OF NODES   :     2     7     8     3
-------------------------------------------------------------------
|     3   |  1   |     0        |   1 |     0    |     4          |
 LIST OF NODES   :     3     8     9     4
-------------------------------------------------------------------
|     4   |  1   |     9        |   1 |     1    |     4          |
 LIST OF NODES   :     4     9    10     5
 REFERENCE (EDGES VERTICES) :      0     0     2     0     0     0
                 2     2


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

     PRINT OUT OF D.S. COOR OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 16/11/90  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) :   185
 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 :    185   PAGE 

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


 TABLE C O O 4 
 -------------
 -------------------------------------------------------------------------------
 | POINT |     X        |     Y       |   | POINT |     X        |     Y       |  
 -------------------------------------------------------------------------------
 |     1 |   12.5491    |  9.09783    |   |     2 |   18.6212    |  6.00000    |
 |     3 |   23.7429    |  6.00000    |   |     4 |   28.8645    |  6.00000    |
 |     5 |   33.6368    |  7.71429    |   |     6 |   14.7438    |  4.78222    |
 |     7 |   19.3138    |  3.28685    |   |     8 |   23.3069    |  3.32708    |
 |     9 |   27.2999    |  3.36731    |   |    10 |   30.9548    |  4.26429    |
 --------------------------------------- ---------------------------------------


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

     PRINT OUT OF D.S. FORC OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 16/11/90  dutoit                  
 DATA STRUCTURE TYPE             : FORC
 LEVEL AND STATE NUMBER          :      1     0
 NUMBER OF ASSOCIATED TABLES     :      1


 TABLE  F O R 2
 --------------
  INFORMATION ( NUMBER OF SETS ) OR NOT ( 0 )

               --------------------------------------------------
               |            |                 |                 |
               |            |   SUB-DOMAINS   |     ELEMENTS    |
               |            |                 |                 |
               --------------------------------------------------
               |  VOLUMES   |          0      |          0      |
               |  SURFACES  |          0      |          0      |
               |  LINES     |          0      |          0      |
               |  POINTS    |          1      |          0      |
               --------------------------------------------------

 TABLE  F O R 6
 --------------
  DESCRIPTION OF REFERENCES FOR POINTS


 REFERENCE  ( OR SUB-DOMAIN ) NUMBER :      7
 TYPE OF THE ELEMENT ( > 0 : ISOTROPIC, < 0 : ANISOTROPIC ) :      2
 USE OF A  TABLE              
 NAME OF THE TABLE : :PON
 ADRESS IN IT :      1


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

     PRINT OUT OF D.S. MILI OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 16/11/90  dutoit                  
 DATA STRUCTURE TYPE             : MILI
 LEVEL AND STATE NUMBER          :      1     0
 NUMBER OF ASSOCIATED TABLES     :      1


 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 ) :      2
 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            : 16/11/90  dutoit                  
 DATA STRUCTURE TYPE             : TAE 
 LEVEL AND STATE NUMBER          :      1     0
 NUMBER OF ASSOCIATED TABLES     :      1


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

 NUMBER OF ELEMENTS                                (NE) :   135
 NUMBER OF NODES                                  (NOE) :   185
 NUMBER OF ARRAYS CORRESPONDING TO EACH ELEMENT (NTACE) :     3
 MAX NUMBER OF NODES PER ELEMENT               (NNOMAX) :     4
 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) :     4

 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                      :     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        :     4
 NUMBER OF D.O.F. AT EACH NODE             :     2     2     2     2

 TABLE  T A E 4
 --------------
 ASSOCIATED ARRAY NUMBER               ------------  :     1
 MAX NUMBER OF WORDS NECESSARY FOR STORAGE  (NMMAST) :    72
 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) :    16
 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) :    60
 TYPE OF THE ARRAY                           (NTYTA) :     5
 NUMBER OF INDICES                           (NINDI) :     1
 STORAGE OPTION                              (NSTOC) :    -1
 END OF MODULE THELAS 
 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&


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

     PRINT OUT OF D.S. BDCL OF LEVEL  1

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 16/11/90  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) :     14
 NUMBER OF LINEAR RELATIONS BETWEEN CONSTRAINTS  (NCLRL) :     18
 STORAGE OPTION                          (NOPTFI) :      0
 NUMBER OF WORDS OF TABLE BDC3           (NMMAT3) :     42
 NUMBER OF WORDS OF TABLE BDC4           (NMMAT4) :     28
 NUMBER OF WORDS OF TABLE BDC5           (NMMAT5) :     90
 NUMBER OF WORDS OF TABLE BDC6           (NMMAT6) :    108

 TABLE       B D C 3  B D C 4
 -----------------------------
   CLAMPING TYPE :  1 : NODE :    26 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    27 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    28 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    29 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    30 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    31 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    32 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    33 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    57 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00
   CLAMPING TYPE :  1 : NODE :    58 , D.O.F. :  2
         AT VALUE    :   0.00000000000000000E+00

 TABLE       B D C 5  B D C 6
 -----------------------------
 NUMBER OF TERMS  :     2
 TERM      1 NODE    63 D.O.F.  1 COEFFICIENT  -0.75000000000000010E+01
 TERM      2 NODE    63 D.O.F.  2 COEFFICIENT  -0.24438100000000000E-05
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    64 D.O.F.  1 COEFFICIENT  -0.70476900000000010E+01
 TERM      2 NODE    64 D.O.F.  2 COEFFICIENT  -0.25651500000000000E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    65 D.O.F.  1 COEFFICIENT  -0.57453299999999980E+01
 TERM      2 NODE    65 D.O.F.  2 COEFFICIENT  -0.48209100000000000E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    66 D.O.F.  1 COEFFICIENT  -0.37500000000000000E+01
 TERM      2 NODE    66 D.O.F.  2 COEFFICIENT  -0.64951900000000010E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    67 D.O.F.  1 COEFFICIENT  -0.13023600000000000E+01
 TERM      2 NODE    67 D.O.F.  2 COEFFICIENT  -0.73860600000000010E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    68 D.O.F.  1 COEFFICIENT   0.13023600000000000E+01
 TERM      2 NODE    68 D.O.F.  2 COEFFICIENT  -0.73860600000000010E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    69 D.O.F.  1 COEFFICIENT   0.37500000000000000E+01
 TERM      2 NODE    69 D.O.F.  2 COEFFICIENT  -0.64951900000000010E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    70 D.O.F.  1 COEFFICIENT   0.57453299999999980E+01
 TERM      2 NODE    70 D.O.F.  2 COEFFICIENT  -0.48209100000000000E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    71 D.O.F.  1 COEFFICIENT   0.70476900000000010E+01
 TERM      2 NODE    71 D.O.F.  2 COEFFICIENT  -0.25651500000000000E+01
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00
 NUMBER OF TERMS  :     2
 TERM      1 NODE    72 D.O.F.  1 COEFFICIENT   0.75000000000000010E+01
 TERM      2 NODE    72 D.O.F.  2 COEFFICIENT  -0.22737400000000000E-12
   RIGHT HAND SIDE OF THE COMBINATION :  0.00000000000000000E+00


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

     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     1
 NUMBER OF ASSOCIATED TABLES     :      0


 TABLE  B 2
 ----------
 TYPE OF THE TABLE                           (NTYT) :      5
 NUMBER OF INDICES AND THEIR MAX VALUES    (NIND..) :      2     1   370
 OPTION (1: PAGES OF SAME SIZE , 0: IF NOT)  (NCOD) :      1
 NUMBER OF PAGES OF THE TABLE B4            (NBLOC) :      1
 NUMBER OF NODES                              (NOE) :    185
 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) :    370
 STORAGE OPTION FOR B4                     (NCODSB) :     -1

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


     1           0     2         370

 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  |   -0.993942E-01
          |   2 |        2  |    0.140176    
 |      2 |   1 |        3  |   -0.366348E-01
          |   2 |        4  |    0.146115    
 |      3 |   1 |        5  |    0.367940E-02
          |   2 |        6  |    0.126644    
 |      4 |   1 |        7  |    0.238493E-01
          |   2 |        8  |    0.833960E-01
 |      5 |   1 |        9  |    0.381753E-01
          |   2 |       10  |    0.334481E-01

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

     PRINT OUT OF D.S. TAE  OF LEVEL  2

 &&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&&
 TITLE                           :                                                                                 
 DATE AND USER'S NAME            : 16/11/90  dutoit                  
 DATA STRUCTURE TYPE             : TAE 
 LEVEL AND STATE NUMBER          :      2   0
 NUMBER OF ASSOCIATED TABLES     :      0


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

 NUMBER OF ELEMENTS                                (NE) :   135
 NUMBER OF NODES                                  (NOE) :   185
 NUMBER OF ARRAYS CORRESPONDING TO EACH ELEMENT (NTACE) :     1
 MAX NUMBER OF NODES PER ELEMENT               (NNOMAX) :     4
 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) :     4

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


 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        :     4
 NUMBER OF D.O.F. AT EACH NODE             :     2     2     2     2

 TABLE  T A E 4
 --------------
 ASSOCIATED ARRAY NUMBER               ------------  :     1
 MAX NUMBER OF WORDS NECESSARY FOR STORAGE  (NMMAST) :    60
 TYPE OF THE ARRAY                           (NTYTA) :     5
 NUMBER OF INDICES                           (NINDI) :     1
 STORAGE OPTION                              (NSTOC) :    -1

2.3.6 Post-processing

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

Call preprocessor: TRNOXX

Specify input data structures: T12NOPO

T2B

Figure 2.10: The deformation ( TRNOXX)

A plot of the stresses is generated by the preprocessor TRSTXX
[4] [MODULEF User Guide - 6] as follows:

Call preprocessor: TRSTXX

Specify input data structures: T2MAIL

T2COOR

T2TAES

Figure 2.11: The stresses according to Tresca's criterion ( TRSTXX)

Next: 2.4 Test 3: Plate problem Up: 2 Conversational tests Prev: 2.2 Test 1: Thermal Problem Contents

and,	Young's Modulus	E	=
	Poisson's coefficient		=	0.3
	Point force	P	=	100.0

Call preprocessor:	APNOXX

Modules used:	APNOPO	... 2D mesh generator [MODULEF User Guide - 3]
	QUACOO	... mesh utilizing quadrangles
	RECOLC	... 'glue together' meshes
Libraries:	CONV, NOPO, NOP2, UTII, UTSD

Specify input data file:	D2NOPO.D
Output data structure:	T2NOPO

Call preprocessor:	COMAXX

Module used:	COMACO
Libraries:	CONV, COSD, ELAS, ELA2, UTII
Element type:	QUAD 2Q1D

Specify input data file:	D2COMA.D
Output data structures:	T2MAIL
	T2COOR

Call preprocessor:	FOMIXX

Modules used:	COFORC
	COMILI

Specify input data file:	D2FOMI.D
Output data structures:	T2FORC
	T2MILI

Call preprocessor:	THELXX

Module used:	THENEW

Specify input data file:	D2TAE.D
Output data structure:	T2TAE

Call preprocessor:	COBDXX

Module used:	COBDC1

Specify input data file:	D2BDCL.D
Output data structures:	T2BDCL

Call preprocessor:	GRADXX

Modules used:	PREPGC	... allocation of pointers
	ASSAMA	... assembly of compact matrix
	ASEMBV	... assembly of RHS vector
	CLIMGC	... incorporate boundary conditions
	FANIGC	... incomplete factorization
	ICHRGC	... solution

Specify input data file:	D2B.D
Output data structure:	T2B

Call preprocessor:	STREXX

Specify input data file:	none
Output data structures:	T2TAES

Step	Dimension of	Execution time
	the super array	(DPS8 Multics)
Mesh	15 000	58.3
Interpolation	9 000	6.1
Data	1 000	5.0
Element matrices	10 000	12.5
Boundary conditions	6 000	11.0
Solution	30 000	33.5

Call preprocessor:	TRNOXX

Specify input data structures:	T12NOPO
	T2B