Models for Shape Optimization

The basic idea of shape optimization with respect to model requirements is described.

In shape optimization, the boundaries or surfaces of a component are modified. At first, the optimizer calculates the new coordinates of the design nodes on the component surface based on the stress condition and then adjusts the remaining FE mesh accordingly. The calculation of the new coordinates of the nodes is not based on geometrical parameters, but rather on each individual coordinate for the nodes. Generally, every FE model can serve as a basis for shape optimization.

The mesh must be of such quality that the analysis results from the FE mesh remain essentially unaffected. To assure this, most FE preprocessors have checking routines. The user must define an adequate mesh density for a subsequent optimization, that is, high stress gradients should not be present within an element. The mesh density must be set correctly in order to achieve smooth contours. For example, smooth contours cannot be expected when a 90 degree curve is meshed by only three elements. The finer the mesh density, the closer the contour will be to the optimum. Tosca Structure.shape features an integrated efficient smoothing mesh algorithm. It is capable of adjusting the FE mesh to the optimized displacement of the design nodes without remeshing. It is possible that the FE model will collapse when there is a large optimized displacement of the design nodes due to a poor mesh. This can be avoided by setting the mesh to an adequate density.