14.3.5 Displacement and Stress along Disc Outline

It is instructive to make a graph of the displacements and stresses along the outline of the disc. Therefore we need to know the numbers of the nodes along this outline because these will form the horizontal X -axis of the graph.

Horizontal axis for graph    (cont.fvc)

 
VIEW MESH OUTER
LABEL MESH NODES
CONSTRUCT LINE NODES LIST 1 TO 44
 

The VIEW MESH command displays the mesh as generated for the lines in set OUTER , i.e., the interface elements along the outline of the disc [§14.1.1]. The LABEL MESH NODES command labels each node in this part of the mesh with its number [Fig.14.14].

Figure 14.14: Nodes along disc outline

The labels show that the nodes along the outline have numbers 1 to 44. Now we may specify a polyline in the model along the outline of the disc with the CONSTRUCT LINE NODES command and a LIST of nodes specified via a range from 1 to 44. The X -axis of the graphs that we will produce now starts in node 1 at the `east' point of the disc and runs along the outline of the disc over a distance of 2$\pi$ r = 2$\pi$ x 5 = 31.415 .^14.2The vertical axis of the graph will show the values of the analysis results.

Displacements    (cont.fvc)

 
RESULTS LOADCASE LC1 10
RESULTS NODAL TDTX...G TDTX
RESULTS STACK ADD
RESULTS NODAL TDTX...G TDTY
PRESENT GRAPH LINE OLD
PRESENT OPTIONS GRAPH POINTS SYMBOLS OFF
 

We start with selection of the last load step. Then with the TDTX attribute component we select the total horizontal displacement u_X as result item. With the RESULTS STACK ADD command we save these results on the stack to be able to draw multiple Y -axis graphs, i.e., graphs for various results along the same X -axis. As second result item we select the vertical u_Y displacement with the TDTY attribute component.

Now the PRESENT GRAPH LINE command draws graphs of the two selected results along the outline of the disc: the u_X in blue and the u_Y in red [Fig.14.15a].

Figure 14.15: Graph along disc outline

(a) displacements u_{X, Y}

(b) vertical stress $\sigma_{{YY}}^{}$

The distribution of the horizontal displacements u_X is symmetric at x = 0 and x = $\pi$ x r = 15.78 , i.e., at the east and west point of the circle. The vertical displacements u_Y are skew-symmetric in these points.

Vertical stress    (cont.fvc)

 
RESULTS ELEMENT EL.SXX.G SYY
RESULTS CALCULATE AVERAGE
PRESENT GRAPH LINE OLD
RESULTS STACK CLEAR
DRAWING DISPLAY
 

With the SYY attribute component we select the vertical $\sigma_{{YY}}^{}$ stresses as result item. The PRESENT GRAPH command displays the graph. However, in this case iDIANA draws the graph for $\sigma_{{YY}}^{}$ in the already displayed graphs for the displacements. Therefore we use the CLEAR option to clear the results stack and the DRAWING DISPLAY command to redraw the graph which now shows only the distribution of the vertical stress $\sigma_{{YY}}^{}$ along the disc outline [Fig.14.15b]. Note that the stresses repeat their pattern every $\Delta$x = $\pi$ r = 15.78 .

For comparison we will now make a contour plot of the vertical stress $\sigma_{{YY}}^{}$ via the following commands.

    (cont.fvc)

 
VIEW MESH ALL
DRAWING CONTENTS LEGEND AUTOMATIC
DRAWING CONTENTS MONITOR AUTOMATIC
DRAWING CONTENTS AXES AUTOMATIC
PRESENT CONTOUR LEVELS
 

With the VIEW MESH command we leave the graph display mode and revert to mesh display. Then we restore the decorations that we had removed for the animation display via the DRAWING CONTENTS commands. Due to the AUTOMATIC option the decorations will be displayed at their default positions. Finally the PRESENT CONTOUR LEVELS command draws the contour plot of the currently selected result item $\sigma_{{YY}}^{}$ [Fig.14.16].

Figure 14.16: Vertical stress $\sigma_{{YY}}^{}$

The contour colors along the disc outline show the same distribution as the graph in Figure 14.15b: small positive values along the free edges (orange-red) and sudden large negative values, i.e., pressure, along the contact surface (blue).