Visualization of Simulation Results

The simulation computes results for the condensed mesh. The results on the condensed mesh nodes can be visualized by glyphs placed on the nodes. Several visualization objects consisting of glyphs can be created, analogous to the rigid body visualization detailed in Section 6.2.3.

The results for the original FE mesh can be recovered using the information generated during the condensation. Data that are recovered to the FE mesh can also be visualized directly on the mesh.

Deformation of bodies

At each simulation time stept, simulation result data contain the global motiong(t)of the body and the local displacement componentdi(t)of each node. The complete motionmi(t)of each node is the sum of the two,mi(t) =g(t) +di(t). The basic approach is to produce an animated visualization of the elastic body’s motion by displacing its nodes bym_i(t)for each time stept.

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(b) (a)

Figure 6.17: (a) One of the main bearings of the engine. Part of the crankshaft is clipped to reduce occlusion. The IDs of the connected nodes are shown. (b) Piston-liner contact. The piston itself is hidden to reveal the connection.

The deformation is generally very small. The displacement of nodes is often smaller than a pixel. The deformation can be made more visible when scaled up by a factorcso the motion of nodes ism_i(t) =g(t) +c·d_i(t). Note that this magnified deformation is not physically correct.

It is merely a geometric magnification to make deformation more visible. The global motion (overall rotation) of rotating bodies (e.g., crankshafts) can be turned off and only the vibration component shown to allow exact comparison of the crankshaft’s deformation at various crank angles.

When deformation of rotating components (e.g., crankshafts) is analyzed, the torsional de-formation is often of special interest. The linear magnification of displacement can create very strange visualizations. Parts of the body are distorted in a very disproportional way, and the torsional deformation, which is often the interesting feature, is very difficult to discern. Some of the problems associated with this approach are shown in Figure 6.18.

The situation can be improved by magnifying the displacements in a cylindrical coordinate system defined by the body’s center of gravity and axis of rotation. Different scaling factors can be used for the radial, angular and axial component of the deformation. If the radial and axial scaling factors are set to zero and the angular scaling factor is not zero, then only the angular component of the deformation is preserved. The resulting visualization, shown in Figure 6.19, better depicts the torsional deformation. We must again note that this is not a physically correct deformation, but merely a method of making torsional deformation more visible. The

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Figure 6.18: Deformation of a crankshaft scaled up 500 times. Note the disproportional distortion of the flywheel and the crank webs.

Compare this to the original shape as shown in Figure 6.16.

Figure 6.19: The same crankshaft as in Fig-ure 6.18 with only the angular component of the deformation scaled up 500 times. Tor-sional vibration is more visible.

fication of the deformation in the cylindrical coordinate system is described by the following algorithm:

for each nodeiin the mesh

p=original local coordinates of nodeiin the mesh q=p+d_i(t)

(r_p, ϕ_p, z_p) =cartesian to cylindrical(p) (rq, ϕq, zq) =cartesian to cylindrical(q) rs=rp+c_radial(rq−rp)

ϕ_s=ϕ_p+c_angular(ϕ_q−ϕ_p) zs=zp+caxial(zq−zp)

s= cylindrical to cartesian(rs, ϕs, zs) f =p+s+g(t)

move nodeito positionf Surfaces and cross-sections

Attributes can be displayed using color mapping on the surface of the FE mesh. For example, in Figure 6.20 the displacement of the surface of the engine block is shown. Parts of the mesh can be hidden by the tools described in Section 6.3.2 so that data pertaining to cells inside the body can be made visible. The global, local, and user-defined color mapping schemes introduced in Section 6.2.2 can be used to support different analysis tasks. When parts of the mesh are hidden, then the color mapping can use the range pertaining to the visible part of the mesh. Analogous to coloring the mesh surface, planar cross-sections of the meshes can be created and colored to display attributes of the cells that the plane intersects. The intersection plane can be rotated and translated in the volume as a probe. The cross-sections can also be used as the reference plane of height fields (shown in red in Figure 6.21). The height field can depict any scalar attribute, including components and magnitudes of vectors.

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Figure 6.20: Displacement of the surface of the engine block shown using color mapping.

Figure 6.21: Stresses on the cross-section of the crankshaft visualized using a height field.

Peaks highlight areas of high stress.

Glyphs

Many of the simulation results’ attributes are vectors. Displacement, velocity, acceleration, and forces can be visualized very intuitively by arrow glyphs, similar to those used for the visualization of rigid multibody systems (Section 6.2). Arrows are positioned at the nodes of the condensed mesh. In Figure 6.22 the arrows show the constraint forces on the crankshaft.

Furthermore, vector attributes can be visualized by drawing arrows at each cell of the surface or the cross-section, similar to the hedgehog visualization [226] used in computational fluid dynamics. Unfortunately, this often leads to a very crowded display when the mesh is of high resolution. In order to reduce the visual clutter and occlusion, the resampling tool proposed by Laramee [145] can be adapted. As an illustration, note that there are fewer arrows than nodes indicated by the wireframe in Figure 6.23. Drawing arrows at each node would only clutter the view.