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3.2 Two-dimensional solutions TRMCXX

3.2.1 Aim and utilization limits

Preprocessor TRMCXX is used to visualize meshes and the corresponding solutions. It enables the user to visualize:

• the displacements in the form of a deformed mesh obtained by adding the displacements, multiplied by a given factor, to the corresponding nodes of the initial mesh.
• the velocities, either as a deformed mesh obtained by adding the velocities, considered as displacements and multiplied by a given factor, to the corresponding nodes of the initial mesh, or by arrows placed at the different nodes.
• the isovalues of the solution on the mesh (the solution is therefore interpreted in terms of P1 triangles, see further down).
• the flux (D.S. B obtained during the solution of a problem with mixed finite elements) on a mesh.

Note:

The visualization of isovalues, ..., and flux is only possible for certain finite elements.

3.2.2 Utilization of TRMCXX

1. Activate preprocessor TRMCXX.

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 and to choose the type of plot desired. In this case, enter the name of the file containing the solution (D.S. B) 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.

3.2.3 Complete description of TRMCXX

In practice, using preprocessor TRMCXX, the user indicates 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 TRMACO (module called in this case) is shown below:

 ------------------------------------------------------------
 | 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 ONE 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 solution 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) deformations
• (2) isovalues
• (3) velocities
• (4) cuts through a displayed solution
• (5) 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 its 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 reader is referred).

Deformations:

Activate key 10 and choose option 1. It is then necessary to enter the name of the file containing D.S. B containing the solutions (displacements or velocities interpreted as displacements). The enlarged menu (additional keys followed by an asterisk) is given below:

 ------------------------------------------------------------
 | 10 | PLOT TYPE                 |         MESH AND DEFORMATION
 ------------------------------------------------------------
 | 11 | DEVICE NUMBER             |              1
 ------------------------------------------------------------
 | 12 | PLOT TITLE                |
 ------------------------------------------------------------
 | 20 | D.S. MAIL TO PLOT         |         carre.mail
 ------------------------------------------------------------
 | 20 | D.S. COOR TO PLOT         |         carre.coor
 ------------------------------------------------------------
 | 21 | S.D. B USED               |         carre.solu2
 ------------------------------------------------------------
 | 24 | LOAD CASE                 |              1
 ------------------------------------------------------------
 | 27 | ARRAY B4 SELECTED         |              1
 ------------------------------------------------------------
 | 22 | DEFORMATION RATIO         |            100.0000
 ------------------------------------------------------------
 | 31 | QUESTIONS ABOUT ONE D.S.  |   NO
 ------------------------------------------------------------
 | 30 | PLOT SIZE                 |  AUTO
 ------------------------------------------------------------
 | 40 | CHARACTER TYPE            |  HARD
 ------------------------------------------------------------
 | 50 | ITEMS TO PLOT             |  NO MESH
 ------------------------------------------------------------
 | 50 | ITEMS TO PLOT (DEFORM)    |  TRIANGULATION
 ------------------------------------------------------------
 | 60 | LEGEND                    |  YES
 ------------------------------------------------------------
 | 70 | NUMBER                    |  NONE
 ------------------------------------------------------------
 | 80 | LINE TYPE (MESH)          |  SOLID
 ------------------------------------------------------------
 | 80 | LINE TYPE (DEFORMED)      |  SOLID
 ------------------------------------------------------------

A default value is proposed for each option. The above table lists the selections made automatically when plotting the deformations. Type 0 to obtain the 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 and deformation (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. B). 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. B.

Key 27*:

array B4 to consider (1 by default). This value must lie between 1 and NBBLOC, the total number B4 arrays present in the D.S.

Key 22*:

the deformation amplification ratio (100. by default), this value can be changed by activating this key.

Key 31:

already seen.

Key 30:

already seen.

Key 40:

already seen.

Key 50:

already seen, we stipulate similarly the manner in which the deformations are plotted.

Key 60:

already seen.

Key 70:

already seen.

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 execute operations (0), (1), (2), (3), (4), (5 or M), (6), (8) and (9) already described.

Example:

A plot of a two-dimensional mesh and its deformation, obtained via TRMCXX is given in figure 3.1. It corresponds to test example 2 of a two-dimensional elasticity problem with plane deformations described in [MODULEF User Guide - 1]. The deformations are amplified by a factor 4., which is displayed in plot window F4.

The plot was obtained by typing the following sequence:

• figure 3.1 : -1 t2mail t2coor 10 1 t2b 22 4. 80 1 2 0 8 2 bw ncadre nlogo x12 y12 ftrmaco1 v

 
Figure 3.1: Example TRMCXX 2D: mesh and deformation 

Isovalues:

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

 -------------------------------------------------------------
 | 10 | PLOT TYPE                 |         MESH AND ISOVALUES
 -------------------------------------------------------------
 | 11 | DEVICE NUMBER             |              1
 -------------------------------------------------------------
 | 12 | PLOT TITLE                |
 -------------------------------------------------------------
 | 20 | D.S. MAIL TO PLOT         |         carre.mail
 -------------------------------------------------------------
 | 20 | D.S. COOR TO PLOT         |         carre.coor
 -------------------------------------------------------------
 | 21 | S.D. B USED               |         carre.solu
 -------------------------------------------------------------
 | 24 | LOAD CASE                 |              1
 -------------------------------------------------------------
 | 27 | ARRAY B4 SELECTED         |              1
 -------------------------------------------------------------
 | 32 | MNEMONIC IN USE           |  VN
 -------------------------------------------------------------
 | 25 | NUMBER OF ISOVALUES       |      20
 -------------------------------------------------------------
 | 26 | CHOICE FOR ISOVALUES      |   MIN < ** < MAX
 -------------------------------------------------------------
 | 72 | ISOVALUES PLOT            |   IN COLOUR
 -------------------------------------------------------------
 | 45 | COLOR SPECTRUM            |   STANDARD : RED -> BLUE
 -------------------------------------------------------------
 | 46 | SPECTRUM DIRECTION        |   DIRECT
 -------------------------------------------------------------
 | 34 | COLOR-VALUE IMPOSED       |   NO
 -------------------------------------------------------------
 | 71 | ISOVALUES ARE POINTED     |   NO
 -------------------------------------------------------------
 | 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 (ISOVALUES)     |  SOLID
 -------------------------------------------------------------

A default value is proposed for each option. The above table lists the selections made automatically when plotting the isovalues. Type 0 to obtain the 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 and isovalues (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. B). 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. B.

Key 27*:

array B4 to consider (1 by default). This value must lie between 1 and NBBLOC, the total number B4 arrays present in the D.S.

Key 32*:

the number of variational unknown to consider (1 by default), this value must lie between 1 and NINCFV (see D.S. MAIL), the number of unknowns, and the mnemonic of the unknown to be considered (VN by default).

Key 25*:

the number of isovalues (25 by default, value used for a black-and-white terminal). Activate this key to change this value.

Key 26*:

the extreme isovalues. By default the minimum and maximum are determined automatically as the minimum and maximum of the values contained in the D.S. To change these values, activate this key and select only the part of the solution which is desired.

Key 72*:

the plot type for the isovalues (by default, in color if the terminal allows it, or black-and-white if not). We have the following choice:

   REPRESENTATION CHOICE:
     -1 : FIXED COLOUR LINE
      0 : COLOUR LINE
      1 : SHADED

Key 45*:

the choice of color spectrum (by default from red to blue). We have the following choice:

   SPECTRUM ON 8 PLANE MONITOR:
   STANDARD  : RED TO BLUE           : 1
   RAINBOW   : RED TO MAGENTA        : 2
   THERMAL   : BLACK-RED-YELLOW-BLACK: 3
   MAXIMUM   : BLACK-COLOUR-WHITE    : 4
   BLACK AND WHITE                   : 5

Key 34*:

to associate a color with a value (specify, for each color, the value to associate with it).

Key 71*:

indicate isovalues (no indications by default). Activate this key in order to display isovalue numbers from place to place; in addition, the isovalues are plotted by changing the line type modulo the number of possibilities.

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: solid (by default) or, by activating this key, the choice between:

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

and for the isovalues (for an unmarked line plot) with the same choice.

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);
• obtain the value of a isovalue designated on screen (7 S F X A Z W);
• 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).

The only new feature is the item to obtain the value of an isovalue. There are several ways of performing this interrogation, described below:

(7):

click on a point in the mesh and validate by typing 7: we obtain (on the console) the value of the closest isovalue plotted and its number, as well as (still on the console) the value of the clicked point (P1 interpolation) and its coordinates.

(S):

click on a point in the mesh and validate by typing S: we obtain (on the console) the value of the closest isovalue plotted and its number, as well as (on the console and on the clicked point in a color which differs from the background) the value of the clicked point (P1 interpolation) and its coordinates (on the console).

(F):

click on a point in the mesh and validate by typing F: we obtain (on the console) the value of the closest isovalue plotted and its number, as well as (on the console and on the clicked point in the background color) the value of the clicked point (P1 interpolation) and its coordinates (on the console).

(X):

the same as (F), but the color in which the value is displayed is not determined.

(A):

delete the last number entered on the screen. After refreshing (4) the screen, all the values present on the plot will be displayed except the last one.

(Z):

delete all the values entered on the screen. After refreshing (4) the screen, all the values present on the plot will be deleted.

(W):

the same as (F), but the the number (and not the value) of the isovalue closest to the designated point will appear on the screen.

Remark:

There could be some differences between the above description and the result actually obtained due to the terminal used (color, black-and-white, ...), the type of visualization selected (lines or shaded) and the precision with which the points are designated.

Example:

The example shown in figures 3.2 to 3.4 corresponds to a plot of the isovalues of the displacements in x-direction of the problem considered in test 2 of [MODULEF User Guide - 1]. The first plot is produced without the isovalue markings, but by clicking (action (S) in the graphics menu) on certain isolines such that the corresponding value appears on the screen. The second plot includes the isovalue markings (note that the line type changes from one line to another). The third plot is done on a color terminal and sent as a softcopy to a black-and-white postscript printer.

The plots were obtained by typing the following sequences:

• figure 3.2 : -1 t2mail t2coor 10 2 t2b 50 2 25 50 0 S S S S S 8 2 bw ncadre nlogo x12 y12 ftrmaco2 v
• figure 3.3 : -1 t2mail t2coor 10 2 t2b 50 2 25 50 71 0 8 2 bw ncadre nlogo x12 y12 ftrmaco2b v
• figure 3.4 : -1 t2mail t2coor 10 2 t2b 50 2 25 50 72 1 0 8 2 ncadre nlogo x12 y12 ftrmaco2c v

 
Figure 3.2: Example TRMCXX 2D: Mesh and isovalues 

 
Figure 3.3: Example TRMCXX 2D: Isovalues indicated 

 
Figure 3.4: Example TRMCXX 2D: Isovalues with shading 

Velocities:

Activate key 10 and choose option 3. It is then necessary to enter the name of the file containing the D.S. B containing the velocities. The enlarged menu is shown below:

 ------------------------------------------------------------
 | 10 | PLOT TYPE                 |         MESH AND VELOCITY
 ------------------------------------------------------------
 | 11 | DEVICE NUMBER             |              1
 ------------------------------------------------------------
 | 12 | PLOT TITLE                |
 ------------------------------------------------------------
 | 20 | D.S. MAIL TO PLOT         |         carre.mail
 ------------------------------------------------------------
 | 20 | D.S. COOR TO PLOT         |         carre.coor
 ------------------------------------------------------------
 | 21 | S.D. B USED               |         carre.solu2
 ------------------------------------------------------------
 | 24 | LOAD CASE                 |              1
 ------------------------------------------------------------
 | 27 | ARRAY B4 SELECTED         |              1
 ------------------------------------------------------------
 | 29 | BIGEST ARROW IN CM.       |            2.000000
 ------------------------------------------------------------
 | 28 | ARROW ENDS                |             -1
 ------------------------------------------------------------
 | 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 (ARRAYS)        |  SOLID
 ------------------------------------------------------------

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

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 velocities (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. B). 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. B.

Key 27*:

array B4 to consider (1 by default). This value must lie between 1 and NBBLOC, the total number B4 arrays present in the D.S.

Key 29*:

the maximum arrow size (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 ?

Once a plot is displayed on the screen, a graphics menu appears, as for the other modules, which allows us to execute operations (0), (1), (2), (3), (4), (5 or M), (6), (7 X A Z), (8) and (9) already described.

The only new feature is the item to obtain the value of a velocity. There are several ways of performing this interrogation, described below:

(7):

click on a point in the mesh and validate by typing 7: we obtain (on the console) the value of the velocity at the clicked point (P1 interpolation) and its coordinates.

(X):

the same as (F), but an arrow representing the calculated velocity is displayed in the screen.

(A):

delete the last arrow added to the plot. After refreshing (4) the screen, all the arrows present on the plot will be displayed except the last one.

(Z):

delete all the arrows added to the plot. After refreshing (4) the screen, all the arrows present on the plot will be deleted.

Remark:

There could be some differences between the above description and the result actually obtained due to the terminal used (color, black-and-white, ...), the type of visualization selected (lines or shaded) and the precision with which the points are designated.

Example:

Figure 3.5 is nothing other than the representation of the displacements of the problem considered in test 2 in [MODULEF User Guide - 1], using the deformation option in terms of the velocities.

The plots were obtained by typing the following sequences:

• figure 3.5 : -1 t2mail t2coor 10 3 t2b 80 2 1 28 1 5 5 0 8 2 bw ncadre nlogo x12 y12 ftrmaco3 v

 
Figure 3.5: Example TRMCXX 2D: mesh (zoom) and velocities 

Cuts:

Activate key 10 and choose option 4. It is then necessary to enter the name of the file containing the D.S. B containing the solution. The enlarged menu is shown below:

 ------------------------------------------------------------
 | 10 | PLOT TYPE                 |  MESH AND CUT OF A D.S. B
 ------------------------------------------------------------
 | 11 | DEVICE NUMBER             |              1
 ------------------------------------------------------------
 | 12 | PLOT TITLE                |
 ------------------------------------------------------------
 | 20 | D.S. MAIL TO PLOT         |         carre.mail
 ------------------------------------------------------------
 | 20 | D.S. COOR TO PLOT         |         carre.coor
 ------------------------------------------------------------
 | 21 | S.D. B USED               |         carre.solu
 ------------------------------------------------------------
 | 24 | LOAD CASE                 |              1
 ------------------------------------------------------------
 | 27 | ARRAY B4 SELECTED         |              1
 ------------------------------------------------------------
 | 37 | CUT SELECTION             |         AUTO
 ------------------------------------------------------------
 | 38 | UNKNOWN CHOSEN            |          1
 ------------------------------------------------------------
 | 38 | MNEMO CHOSEN              |         VN
 ------------------------------------------------------------
 | 39 | TYPE OF FUNCTION(S)       |         VC
 ------------------------------------------------------------
 | 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. The above table lists the selections made automatically when plotting the cuts. Type 0 to obtain the plot of the mesh on which we can define a cut via item (7) of the graphics menu or via key 37.

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 cuts (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. B). 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. B.

Key 27*:

array B4 to consider (1 by default). This value must lie between 1 and NBBLOC, the total number B4 arrays present in the D.S.

Key 37*:

the cut selection mode. By default automatic, i.e. the cut is chosen by clicking on the screen. By activating this key, we can input the coordinates of the 2 extremities of the cut explicitly.

Key 38*:

the number of the variational unknown to consider (1 by default), this value must lie between 1 and NINCFV (see D.S. MAIL), the total number of unknowns, and the mnemonic of the unknown under consideration (VN by default).

Key 39*:

the solution function to plot on the cut. The user has the choice between:

 1 -- FIELD OF VALUES      : VC
 2 -- DERIVATIVE IN X      : DX
 3 -- DERIVATIVE IN Y      : DY
 4 -- GRADIENT MODULUS     : GR
 5 -- ALPHA * DX           : ADX
 6 -- ALPHA * DY           : ADY
 7 -- ALPHA * GRADIENT     : AGR

The user enters the number of functions to be considered, and for each its type (between 1 (default choice) and 7 ( must be input if the choice is 5, 6 or 7)). As many curves will be plotted as functions input.

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 cuts: solid (by default) or, by activating this key, the choice between:

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

Once a plot (mesh only) is displayed on the screen, a graphics menu appears, as for the other modules, which allows us to execute operations (0), (1), (2), (3), (4), (5 or M), (6), (8) and (9) already described. Option (7) is used to define the cut line:

• Cut (7): to define the cut line. place the cursor on a point on the screen and validate by typing 7 to enter the first extremity of the cut line. Perform the same operations to enter the second extremity.

A question then appears on the screen:

   VOULEZ VOUS PRECISER LES AXES (OUI-NON)

A negative response results in a automatic plot of the cut.

A positive response results in the following sub-menu:

 ------------------------------------------------------------
 | 22 | ECHELLE EN X              |   LINEAIRE
 ------------------------------------------------------------
 | 22 | ECHELLE EN Y              |   LINEAIRE
 ------------------------------------------------------------
 | 61 | LEGENDE SUR LES AXES      |   NON
 ------------------------------------------------------------
 | 62 | DEFINITION DES AXES       |   AUTO
 ------------------------------------------------------------
 | 63 | COURBE(S) AVEC LEGENDE    |   NON
 ------------------------------------------------------------

This menu is analogous to that of TRACXX which enables the user to define the axis of the cut (it corresponds therefore to plotting a curve, which is explained in detail in TRACXX).

Once the plot of the cut has been obtained, the following graphics menu appears:

• End of cuts (0) and return to the module's main menu,
• Continue (1), re-plot the mesh,
• Refresh (4) the screen,
• Exit (5) from session,
• Produce a softcopy (8) or hardcopy (9) of the cut on another graphics terminal; having done this, the user is returned to the initial state (of this graphics menu).

Example:

Figure 3.6 is nothing other that cut through the displacements in the x-direction of test 2. The cut line is vertical and passes through the center of the circles (consult the geometry of the figures shown earlier) which explains the presence of two holes in the cut.

The plot was obtained by typing the following sequence:

• figure 3.6 : -1 t2mail t2coor 10 4 t2b 0 7 7 OUI 61 'cut line' 'displacement in X, VN' 0 8 2 bw ncadre nlogo x12 y12 ftrmaco4 v

 
Figure 3.6: Example TRMCXX 2D: cut 

Flux:

This option enables the user to visualize the flux for mixed finite elements only. The flux is represented by arrows, as in the case of velocities, and we can consequently consult the operating instructions corresponding to plotting velocities. The only difference is that of key 56 in the main menu.

 ------------------------------------------------------------
 | 56 | VISUALISATION OF FLUX     |          EVERYWHERE
 ------------------------------------------------------------

This choice (by default) can be modified by activating key 56:

    ON ALL THE REFERENCES      : 0
    EVERYWHERE                 : 1
    ON SOME REFERENCES         : 2

Case 2 consists of specifying only those reference numbers which we desire.

3.2.4 P1 interpolation of solutions

When plotting the isovalues of a solution it is necessary to define exactly what we want to plot. The finite elements used (described in D.S. MAIL) can be more, or less, rich (as a function of the degree of interpolation chosen).

The plot program is purely P1 and applies to the case of a triangular type element. Using the solution values at the three vertices of the triangle, the isovalues present in the triangle are calculated.

Consequently, each finite element must be decomposed into the most judicious set of triangles such that the quality of the interpolation is preserved: it does not correspond to making beautiful plots but plots conforming to known information. The decomposition must thus satisfy this concern. It corresponds thus to interpreting each element in terms of P1 triangles.

The choices made for the usual element are given below:

• a P1 triangle (TRIA 2P1D, TRIA AP1D) is considered as such,
• a P2 triangle (TRIA 2P2D or TRIA 2P2C and TRIA AP2C) is decomposed into 4 P1 sub-triangles,
• a Q1 quadrilateral (QUAD 2Q1D, QUAD AQ1C)is decomposed into 4 P1 sub-triangles by creating its barycentre,
• a Q2 quadrilateral (QUAD 2Q2D or QUAD 2Q2C and QUAD AQ2C) is decomposed into 16 P1 sub-triangles in the following manner:
  • we decompose the initial quadrilateral into 4 sud-quadrilaterals by creating its barycentre, and then decompose all these elements into 4 P1 sub-triangles.
• etc.

Only certain elements are actually known and thus considered by the plot module. If an element is not known, the module will stop and indicate that it does not know this type of element. The user must then add it by decomposing it in a consistent manner with the corresponding interpolation.

The decomposition is the object of subroutine RANGPQ in library UTIL. This subroutine has the following form:

      SUBROUTINE RANGPQ(NOM1,NOM2,NCGE,NNO,NONO,NPO,NOPOI,COORP,
     +                  SOLU,XX,YY,SOL,NTRIP1)
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  AIM : DECOMPOSE THE ELEMENT INTO P1 TRIANGLES ONLY
C  ---
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  INPUT PARAMETERS :
C  ------------------
C  NOM1, NOM2 : ELEMENT NAMES
C  NCGE,NNO,NONO(*),NPO,NOPOI(*) : USUAL NOTATION
C  COORP   : POINT COORDINATES
C  SOLU    : SOLUTION ARRAY = B4(NDSMT,NDT,1:NOE)
C            WITH NDSMT : RIGHT-HAND-SIDE CONSIDERED ( BETWEEN 1 AND NDSM )
C                 NDT   : THE D.O.F. CONSIDERED ( BETWEEN 1 AND ND )
C                 B4    : ARRAY B4 CONSIDERED
C            REMARK     : SUBROUTINE CHARB4 CREATES SOLU FROM THE GLOBAL B4
C  OUTPUT PARAMETERS :
C  -------------------
C  XX(*),YY(*) : COORDINATES OF POINTS P1
C  SOL     : CORRESPONDING SOLUTIONS
C  NTRIP1  : NUMBER OF P1 ELEMENTS IN THE DECOMPOSITION OF THE ELEMENT
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C
C  SUBROUTINE TO BE COMPLETED FOR ALL NEW ELEMENTS INTERPRETED INTO P1.
C
C  +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
C  PROGRAMMEUR  : PL GEORGE  INRIA  1987
C  ....................................................................
      DIMENSION NONO(*),NOPOI(*),COORP(2,*),SOLU(*),XX(*),YY(*),
     +          SOL(*),SOLP1(3),SOLP2(6),SOLQ1(4),SOLQ2(9),INDIC(4),
     +          SOLQ5(5)
      CHARACTER*4 NOM1,NOM2
  200 FORMAT(' %% ERREUR RANGPQ : ELEMENT ',A4,A4,' NON CONNU'///
     +       ' VOIR LE SP RANGPQ ET AJOUTER CET ELEMENT'///)
C
      IMPRIM = IINFO('I')
C     -------------------------------------------------------
C     ------------         THE TRIANGLES         ------------
C     -------------------------------------------------------
      IF ( NOM1 .EQ. 'TRIA'  ) THEN
C        -------------   TRIANGLE :  NOM COMMENCANT PAR TRIA
         IF( NOM2 .EQ. '2P1D' ) THEN
C        ------   TRIA 2P1D   ------
             NTRIP1 = 1
             NUMER  = 0
             DO 301 J=1,NNO
                SOLP1(J) = SOLU(NONO(J))
                INDIC(J) = J
  301        CONTINUE
             CALL RANGP1(NUMER,COORP,INDIC,SOLP1,XX,YY,SOL)
         ELSE IF( NOM2 .EQ. 'AP1D' ) THEN
C        ------   TRIA AP1D   ------
             NTRIP1 = 1
             NUMER  = 0
             DO 339 J=1,NNO
                SOLP1(J) = SOLU(NONO(J))
                INDIC(J) = J
  339        CONTINUE
             CALL RANGP1(NUMER,COORP,INDIC,SOLP1,XX,YY,SOL)
         ELSE .....
              .....
              .....               elements unknown
         ELSE
             WRITE (IMPRIM,200) NOM1,NOM2
             CALL TILT                           elements unknown
         END IF
C     -------------------------------------------------------
C     ------------         THE QUADRILATERALS    ------------
C     -------------------------------------------------------
      ELSE IF ( NOM1 .EQ. 'QUAD' ) THEN
         IF ( NOM2 .EQ. '2Q1D' ) THEN
C        ------   QUAD 2Q1D   ------
             NTRIP1 = 4
             DO 406 J=1,NNO
               SOLQ1(J) = SOLU(NONO(J))
               INDIC(J) = J
  406        CONTINUE
             NUMER = 0
             CALL RANGQ1(NUMER,COORP,INDIC,SOLQ1,XX,YY,SOL)
         ELSE .....
              .....
              .....               elements unknown
         ELSE
             WRITE (IMPRIM,200) NOM1,NOM2
             CALL TILT
         END IF                               elements unknown
      ELSE
         WRITE (IMPRIM,200) NOM1,NOM2
         CALL TILT                      elements unknown
      END IF
      END

Subroutine RANGPQ uses a certain number of element subroutines (RANGP1, RANGP2, RANGQ1, RANGQ2 ...). To add a finite element corresponds to adding the appropriate branch and using the appropriate element subroutine or writing a new one (each one very simple). To govern the computation, we have at our disposal, NOM1 and NOM2, the two parts of the element name, its geometric code, its number of points and nodes and the arrays containing its points and nodes (it seems that with this information we are able to recognize all the elements without ambiguity).

Remark:

The label used for an element recalls its geometry and number. For example, a 2P1D triangle has a geometric code NCGE = 3 and number 1 (100001 or 200001). The label of this element is thus set to 301.

Decomposition example using the subroutine names:

RANGPQ
if	TRIA 2P1D :	RANGP1 1 P1 1 P1
	TRIA AP1D :	the same
if	TRIA 2P2D :	RANGP2 1 P2 4 P1
		- calculate the middle coordinates
		- and store RANGP1 the solution
if	TRIA 2P2C :	RANGP2 1 P 2 4 P1
		- store RANGP1 the solution
	TRIA AP2C :	the same
if	QUAD 2Q1D :	RANGQ1 1 Q1 4 P1
		- calculate the barycentre and the solution
		- and store RANGP1 this solution
	QUAD AQ1C :	the same
if	QUAD 2Q2D :	RANGQ2 1 Q2 16 P1
		- calculate the middle coordinates
		- calculate the barycentre and the solution
		and store RANGQ1 (RANGP1) this solution
if	QUAD 2Q2C :	RANGQ2 1 Q2 16 P1
		- calculate the barycentre and the solution
		- and store RANGQ1 (RANGP1) this solution
	QUAD AQ2C :	the same
	...... etc