# 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

## 3.2.3 Execution of the test

Step 1: 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)

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