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3.3 Two-dimensional stresses TRSTXX

3.3.1 Aim and utilization limits

Preprocessor TRSTXX is used to visualize meshes and the corresponding stresses for a two-dimensional elasticity problem. The stresses are contained in a TAE data structure obtained by combining the solutions (displacements) with the element stresses computed at the same time as the element matrices and right-hand-sides (see part 1 of this user guide).

The module is used to visualize the stresses as follows:

• by plotting the principal stresses in terms of arrows.
• by plotting (in the form of more or less dense hatching or in color) the module associated with the stresses. The module corresponds to the following criteria:
  • Tresca, which is written as follows in the case of plane stresses:
    

    and in the case of plane deformations:

    

    where for the isotropic case, and for the orthotropic case. The purely anisotropic case is not considered.

  • Von-Mises, which is written as follows in the case of plane stresses:
    

    and in the case of plane deformations:

    

    where is defined above.

The user can also visualize the plastic zones when considering a plastic problem. In this case, the Von-Mises or Drucker-Prager criterion is used to determine the plastic zones.

In addition, the user can also visualize the temperatures and flux obtained when considering a thermal problem with mixed finite elements. The temperatures or flux are contained in a TAE data structure obtained by combining the solutions (flux or temperatures) with the element temperatures or flux computed at the same time as the element matrices and right-hand-sides (see part 1 of this user guide).

3.3.2 Utilization of TRSTXX

1. Activate preprocessor TRSTXX.

2. Choose the output terminal.

3. Enter the names of the files containing the mesh (D.S. MAIL and COOR).

4. The menu appears (see below).

5. An automatic plot ( mesh only) is obtained by typing 0.

6. The values of the visualization parameters are obtained by typing V.

7. Modify, if necessary, these values by choosing the corresponding key and entering the requested information. Once the desired state is obtained, type 0 to display the plot. In particular, key 10 is used to plot the solution associated with the mesh (stresses, temperatures flux or plastic zones) and to choose the type of plot desired. In this case, enter the name of the file containing the solution (D.S. TAE) followed by the type.

8. A graphics menu is available on the plot which enables the user to perform modifications to the plot, to quit, or to return to the menu mentioned above and described in the sections which follow.

3.3.3 Complete description of TRSTXX

In practice, we use preprocessor TRSTXX to indicate to the module the different choices made from the possibilities offered.

The module computes the extrema corresponding to the mesh and solution automatically so that the corners of the box in which the plot will be displayed can be defined.

The menu of TRSTRE (module called to visualize the stresses or plastic zones) is shown below: To visualize the temperatures or flux, module TRFLUX is used (see further down).

 --------------------------------------------------------
 | 10 | PLOT TYPE                 |  MESH ONLY
 --------------------------------------------------------
 | 11 | DEVICE NUMBER             |       1
 --------------------------------------------------------
 | 12 | PLOT TITLE                |
 --------------------------------------------------------
 | 20 | D.S. MAIL TO PLOT         |  carre.mail
 --------------------------------------------------------
 | 20 | D.S. COOR TO PLOT         |  carre.coor
 --------------------------------------------------------
 | 31 | QUESTIONS ABOUT A D.S.    |   NO
 --------------------------------------------------------
 | 30 | PLOT SIZE                 |  AUTO
 --------------------------------------------------------
 | 40 | CHARACTER TYPE            |  HARD
 --------------------------------------------------------
 | 50 | ITEMS TO PLOT             |  TRIANGULATION
 --------------------------------------------------------
 | 60 | LEGEND                    |  YES
 --------------------------------------------------------
 | 70 | NUMBER                    |  NONE
 --------------------------------------------------------
 | 80 | LINE TYPE (MESH)          |  SOLID
 --------------------------------------------------------

A default value is proposed for each option. By default, only the mesh is visualized. To view the stresses, plastic zones, flux or temperatures as well, key 10 must be selected. The above table lists the selections made automatically. Type 0 to obtain a plot.

A key (a number) and a status correspond to each item. To modify the status, it suffices to type the key and enter the values corresponding to the status desired (see the general introduction). The list of keys is given below:

Key 10:

the plot type: mesh only (default value), we can also plot:

• (1) stresses or plastic zones
• (2) temperatures
• (3) flux

Key 11:

the device number.

Key 12:

the title which will appear on the plot in the general legend part (there is no title by default).

Key 20:

the names of the files containing the mesh (D.S. MAIL and COOR). To change files, we activate this key and input the new file names.

Key 31:

by activating this key, we can "inquire" about the D.S. and obtain information regarding their contents.

Key 30:

the plot will be full screen, otherwise the user must specify the size in cm.

Key 40:

the type of characters plotted: hardware (by default), software if not.

Key 50:

the choice of items to plot: the triangulation (by default). By activating this key, we have a choice between:

  -- MESH
     NOTHING                 : 0
     TRIANGULATION           : 1
     GEOMETRIC BOUNDARY      : 2
     REFERENCED BOUNDARY     : 3
     SHRINK                  : 4  ?

The shrink operation consists of contracting, by a given ratio (0.8 by default, value modified via key 23), each element with respect to its barycentre.

Key 60:

the general legend (there is a legend by default) corresponds to the indications appearing to the right of the plot (see examples: title, date, file name, ...).

Key 70:

the numbers to be displayed, none (by default) or, by activating this key, the choice between:

    NO NUMBER          : 0
    ELEMENT : 1 - POINT: 2 - NODE  : 3
    SUBDOMAIN          : 4
    REFERENCE (ALL)    : 5
    REFERENCE POINTS   : 6 - NODES : 7
    REFERENCE EDGES    : 8

Key 80:

the type of plot lines desired: solid (by default) or, by activating this key, the choice between:

    SOLID      : 1  --   DOTTED    : 2
    DASHED     : 3  --   MIXED     : 4 ?

Once a plot is displayed on the screen, a graphics menu appears, as for the other modules, which allows us to:

• Exit (0) from the session,
• Continue (1), i.e., return to the module's main menu;
• Display the next (2) or previous (3) view;
• Refresh (4) the screen;
• Zoom (5 or M) (designate the zoom zone by clicking or designating manually), or a zoom- (6);
• Produce a hardcopy (9) of the screen, or a softcopy (8) on another graphical terminal; having done this, the user is returned to the initial state (of this graphics menu).

We now give some details regarding the choices possible as a function of the type of visualization selected:

Mesh only:

This corresponds to the case described above (identical with respect to the possibilities offered by preprocessor TRNOXX for the two-dimensional case, to which the user is referred).

Stresses:

Activate key 10 and choose option 1. It is then necessary to enter the name of the file containing D.S. TAE containing the stresses. The enlarged menu (additional keys followed by an asterisk) is given below:

 ------------------------------------------------------------
 | 10 | PLOT TYPE                 |  MESH AND STRESSES
 ------------------------------------------------------------
 | 11 | DEVICE NUMBER             |       1
 ------------------------------------------------------------
 | 12 | PLOT TITLE                |
 ------------------------------------------------------------
 | 20 | D.S. MAIL TO PLOT         |  carre.mail1
 ------------------------------------------------------------
 | 20 | D.S. COOR TO PLOT         |  carre.coor1
 ------------------------------------------------------------
 | 21 | D.S. TAE USED             |  carre.taes
 ------------------------------------------------------------
 | 24 | LOAD CASE                 |       1
 ------------------------------------------------------------
 | 33 | CRITERION TO PLOT         |   PRINCIPAL STRESSES
 ------------------------------------------------------------
 | 28 | ARROW ENDS                |      -1
 ------------------------------------------------------------
 | 29 | BIGEST ARROW IN CM.       |     2.000000
 ------------------------------------------------------------
 | 31 | QUESTIONS ABOUT A D.S.    |   NO
 ------------------------------------------------------------
 | 30 | PLOT SIZE                 |  AUTO
 ------------------------------------------------------------
 | 40 | CHARACTER TYPE            |  HARD
 ------------------------------------------------------------
 | 50 | ITEMS TO PLOT             |  TRIANGULATION
 ------------------------------------------------------------
 | 60 | LEGEND                    |  YES
 ------------------------------------------------------------
 | 70 | NUMBER                    |  NONE
 ------------------------------------------------------------
 | 80 | LINE TYPE (MESH)          |  SOLID
 ------------------------------------------------------------
 | 80 | LINE TYPE (STRESSES)      |  SOLID
 ------------------------------------------------------------

A default value is proposed for each option. The above table lists the selections made automatically when plotting the stresses. Type 0 to obtain the plot of the mesh.

A key (a number) and a status corresponds to each item. To modify the status, it suffices to type the key and enter the values corresponding to the status desired (see the general introduction). The list of keys is given below:

Key 10:

the plot type: mesh and stresses (default value).

Key 11:

already seen.

Key 12:

already seen.

Key 20:

already seen.

Key 21*:

the name of the file containing the solution (D.S. TAE). To change files, activate this key and enter the name of the new file to be consider.

Key 24*:

the load case to consider (1 by default). This value must lie between 1 and NDSM, the total number of load cases present in D.S. TAE (number equal to to that of D.S. B used to construct this structure.

Key 33*:

the stress visualization mode: principal stresses by default. This choice can be modified by choosing between:

    PRINCIPAL STRESSES            : 1
    TRESCA CRITERION              : 2
    VON MISES CRITERION           : 3
    VON-MISES PLASTIC ZONE        : 4
    DRUCKER-PRAGER PLASTIC ZONE   : 5 ?

Key 29*:

the maximum size of the arrows (2 cm by default). This value can be changed by activating this key.

Key 28*:

the type of arrows. The manner in which the arrowheads are plotted can be specified as follows:

   EXTREMITY OPEN , NORMALISED : -1
   EXTREMITY CLOSED , NORMALISED  :  1
   EXTREMITY OPEN , FIXED      : -2
   EXTREMITY CLOSED , FIXED       :  2

The arrowhead is open (2 lines) or closed (a triangle), and its "length" is calculated as a function of the size of the arrow (which is related to the velocity modulus) or fixed (for all the arrows) to a value specified by the user.

Key 31:

already seen.

Key 30:

already seen.

Key 40:

already seen.

Key 50:

already seen.

Key 60:

already seen.

Key 70:

already seen.

Key 80:

the type of plot lines desired for the mesh and arrows: solid (by default) or, by activating this key, the choice between:

    SOLID      : 1  --   DOTTED    : 2
    DASHED     : 3  --   MIXED     : 4 ?

When visualizing a criterion (via key 33), it is plotted by hatching (defined by key 27 with respect to the density), or in color.

Note:

For a Von-Mises or Tresca criterion in the case of plane deformations, it is necessary to know the Poisson coefficient, , and the nature (isotropic, etc.) of the material, information which is not stored in the D.S. Consequently, this information must be entered here via keys 42 and 43 which will appear in the general menu.

Once a plot is displayed on the screen, we have, as for all the other modules, a graphics menu at our disposal to perform operations (0), (1), (2), (3), (4), (5 or M), (6), (8) and (9) already described.

Example:

Two examples of two-dimensional meshes and the corresponding stresses obtained via TRSTXX are shown in figures 3.7 to 3.9. It corresponds to the example of test 2 in 2D elasticity with plane deformations described in [MODULEF User Guide - 1].

The plots were obtained by typing the following sequences:

• figure 3.7 : -1 t2mail t2coor 10 1 t2taes 80 2 1 0 8 2 bw ncadre nlogo x12 y12 ftrstre1 v
• figure 3.8 : -1 t2mail t2coor 10 1 t2taes 33 2 27 .75 0 8 2 bw ncadre nlogo x12 y12 ftrstre2 v
• figure 3.9 : -1 t2mail t2coor 10 1 t2taes 33 2 0 8 2 ncadre nlogo x12 y12 ftrstre3 v

 
Figure 3.7: Example TRSTXX 2D: mesh and principal stresses 

 
Figure 3.8: Example TRSTXX 2D: mesh and stresses (Tresca's criterion) 

 
Figure 3.9: Example TRSTXX 2D: stresses (Tresca's criterion) with shading 

Plastic zones:

In the case of an elasticity problem, we return to the above case by choosing options 4 or 5 in key 33. The user then needs to indicate, depending on the type of plasticity chosen, the values for the plasticity threshold (4) via key 43, or the frictional angle and cohesion coefficient (5) via key 43.

Temperatures:

Activate key 10 and choose option 2. It is then necessary to enter the name of the file containing D.S. TAE containing the temperatures. The enlarged menu (additional keys indicated with an asterisk) is given below:

Flux:

Activate key 10 and choose option 3. It is then necessary to enter the name of the file containing D.S. TAE containing the flux. The enlarged menu (additional keys indicated with an asterisk) is given below: