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2.2 Two-dimensional meshes TRNOXX

2.2.1 Aim and utilization limits

Preprocessor TRNOXX is used to visualize meshes (the two-dimensional case is described here). In the case of an elasticity problem for which the displacements are known, we can also visualize the deformed mesh with TRNOXX (the displacements, multiplied by a given factor, are added to the nodes in the initial mesh).

Note:

The visualization of deformations are only possible in the following cases:

• the finite elements are of type Lagrange,
• the displacements are the NDIM (2 here) first degrees of freedom of each node,
• where ND is the number of degrees of freedom per node.

For other cases, preprocessor TRMCXX, requiring data structures MAIL and COOR, is used.

2.2.2 Utilization of TRNOXX (2D)

1. Activate preprocessor TRNOXX.

2. Choose the output terminal.

3. Input the name of the file containing the mesh.

4. The general menu is displayed (see further down).

5. Type 0 to obtain an automatic plot.

6. To obtain the values of the visualization parameters, type V.

7. Modify these values, if necessary, by choosing the corresponding key and entering the required information. Once the desired state is obtained, type 0 to display the plot.

8. A graphics menu is displayed on the plot to perform modifications, to exit or to return to the menu mentioned above and described in the coming sections.

2.2.3 Complete description of TRNOXX (2D)

In practice, having input the output terminal and the file containing the mesh, we need to specify the choices made from the different possibilities offered by the module.

The module automatically calculates the extrema corresponding to the mesh treated to define the corners of the box in which the plot is displayed.

The general menu of TRNOPO (module called in this case) is shown below:

 ------------------------------------------------------------
 | 10 | PLOT TYPE                 |         MESH ONLY
 ------------------------------------------------------------
 | 11 | DEVICE NUMBER             |              1
 ------------------------------------------------------------
 | 20 | MESH TO PLOT              |         carre.nopo
 ------------------------------------------------------------
 | 31 | QUESTIONS ABOUT THIS MESH |          NO
 ------------------------------------------------------------
 | 30 | PLOT SIZE                 |         AUTO
 ------------------------------------------------------------
 | 40 | CHARACTER TYPE            |         HARD
 ------------------------------------------------------------
 | 50 | ITEMS TO BE PLOTTED       |         TRIANGULATION
 ------------------------------------------------------------
 | 60 | LEGEND                    |         YES
 ------------------------------------------------------------
 | 70 | NUMBER                    |         NONE
 ------------------------------------------------------------
 | 80 | LINE TYPE                 |         SOLID
 ------------------------------------------------------------

A default value is proposed for each option. The above table lists the automatic, or default, selections. To obtain the plot corresponding to the above status, type 0.

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

Key 10:

the plot type: mesh only (default choice); we can also request to visualize a mesh and its deformation: type 10 after which the program requests the name of the file containing data structure B of displacements. A number of additional lines then appears on the general menu (see below).

Key 11:

the device number.

Key 20:

the name of the file containing the mesh. To change files, we activate this key and input the new file name.

Key 31:

by activating this key, we can make enquiries about the mesh and obtain information regarding its contents.

Key 30:

the plot will be full screen, or else we need to specify its 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:

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

The shrink operation consists of contracting, for 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, ...). By typing 60, we specify that we do not want the general legend.

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
    SUB-DOMAIN         : 4
    REFERENCE (ALL)    : 5
    REFERENCE POINTS   : 6 - NODES : 7
    REFERENCE EDGES    : 8

Key 80:

the line type: SOLID (by default) or, by activating this key, the choice between:

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

Once a plot has been displayed on screen, a graphics menu appears 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) plot;
• Refresh (4) the screen;
• Zoom (5 or M) (designate the zoom zone by clicking, or designate manually), or a zoom - (6);
• Move (7) a vertex (action described below);
• 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).

Moving points, possible in dimension 2, enables us to modify the mesh by displacing certain vertices ( Only the internal vertices are modifiable, in particular, the non-vertex nodes are not acceptable for a P2 mesh.). Place the cursor in the neighborhood of the (internal) point to move and type 7,. The point selected is highlighted (a small star appears near the point). Move the cursor to the desired position and validate it by typing 7. The point moves and the corresponding elements are reformed (on some terminals, the screen needs to be refreshed).

The validity of the repositioning of the points is checked. It is clear that we cannot move a point in an arbitrary fashion; the program checks automatically that the mesh remains correct by calculating the surfaces of the modified elements to ensure that they remain positive.

If the point only belongs to triangles, it suffices to consider their surfaces. If the point belongs to one or several quadrilaterals, the check consists of examining the surfaces of the triangles which could be formed from the 4 vertices of each modified quadrilateral.

 
Figure 2.1: Checking the displacement of a point 

At each modification, the coordinates of the initial and final point positions are displayed. Thus, the move option can be used craftily to establish a vertex position. Place the cursor close to the desired point, validate by typing 7 and then move the point to an obviously impossible position (and validate by 7): the displacement is refused and the position of the desired point is displayed!

Mesh and deformation:

The module (see limits of utilization) enables us to visualize a mesh and its deformed state. The deformed mesh is obtained by adding (with an amplification factor) the displacements to the nodal coordinates.

For those cases possible, selecting key 10 results in the following general menu:

 ---------------------------------------------------------------
 | 10 | PLOT TYPE                 |         MESH AND DEFORMATION
 ---------------------------------------------------------------
 ...
 ---------------------------------------------------------------
 | 20 | MESH TO PLOT              |         carre.nopo
 ---------------------------------------------------------------
 | 21 | S.D. B USED               |         carre.b
 ---------------------------------------------------------------
 | 22 | DEFORMATION RATIO         |            100.0000
 ---------------------------------------------------------------
 | 24 | LOAD CASE                 |              1
 ---------------------------------------------------------------
 ...
 ---------------------------------------------------------------
 | 50 | ITEMS TO BE PLOTTED       |         MESH
 ---------------------------------------------------------------
 | 50 | ITEMS PLOTTED (DEFORM)    |         NO MESH
 ---------------------------------------------------------------
 ...
 ---------------------------------------------------------------
 | 80 | LINE TYPE                 |         SOLID
 ---------------------------------------------------------------

A key (number) and a status corresponds to each item (see, in particular, the new keys marked with an asterisk). To modify the status, type the key and enter (see general introduction) the values corresponding to the desired status.

Key 10:

The plot type: mesh and its deformation; we can also visualize the mesh only by typing 10.

Key 21 *:

The name of the file containing the displacements. To change the file, activate this key and enter the desired file name.

Key 22 *:

Amplification ration for the displacements (100. by default). By activating this key, we can modify this value.

Key 24 *:

The load case to be considered (by default 1, this value must lie between 1 and NDSM, the total number of load cases contained in D.S. B).

Key 50:

The items to plot, for the initial mesh as well as for the deformed configuration. The choice is the same as for the standard case (see key 50 above): we can plot the contour (choice 2) of the initial mesh and the elements of its deformation (choice 1).

Key 80:

The line type of the plot, for the initial mesh as well as for the deformed configuration. The choices are identical to the standard case.

Once the plot is displayed on the screen, the graphics menu described above is at our disposal (except the move option).

Examples:

Some examples of plots of two-dimensional meshes obtained via TRNOXX are given in figures 2.2 to 2.5. Note that the graphics menu is not displayed as the figures correspond to a softcopy done on a laser printer, and as such a terminal does not have any input possibilities.

The plots were obtained by typing the following sequence:

• figure 2.2: -1 naca.nopo 0 8 2 bw ncadre nlogo x12 y12 fnaca v
• figure 2.3: -1 f5508.nopo 0 8 2 bw ncadre nlogo x12 y12 froue v
• figure 2.4: (starting with the above) 5 5 1 70 5 0 0 8 2 bw ncadre nlogo x12 y12 froue1 v
• figure 2.5: -1 cooler.nopo 60 0 8 2 bw ncadre nlogo x12 y12 fcooler v

 
Figure 2.2: Example TRNOXX 2D: automatic mode 

 
Figure 2.3: Example TRNOXX 2D: automatic mode 

 
Figure 2.4: Example TRNOXX 2D: zoom, shrink and reference numbers 

 
Figure 2.5: Example TRNOXX 2D: automatic mode without legend