Shape optimization

In shape optimization or contour optimization, the outer contour of a component is changed locally so that peaks in the decisive target function are reduced and uniformed. To do this, material is either added or removed. The most common target functions in structural mechanics are stresses or safety or rather damage values.

A method for shape optimization was originally developed by Prof. Mattheck at the Karlsruhe Institute of Technology. It is based on the observation that biological, supporting structures show a load-adaptive growth, which means at locations where high stresses occur, more material is added. In the first version of this method, a separate growth layer was also modelled. In the long run, however, this has proved to be too time-consuming during model preperation. Today, growth or shrinkage occurs iteratively directly on the surface in the direction of the surface normal. This type of shape optimization is applied directly to the mesh. It is therefore one of the parameter-free and, due to its reproducibility, exact optimization methods.

Another possibility for shape optimization is morphing. The nodes on the surface are not moved individually, but the position of previously defined morphing points are changed instead. The nodes of the whole structure move according to their individual distances to the surrounding morphing points. This changes the shape while maintaining the basic topology. Since the number of morphing points is considerably less than the number of surface nodes, the number of degrees of freedom is also significantly reduced. This optimization problem can thus be parameterized. Thus, shape optimization can also be treated with classical methods, such as the gradient method or an evolutionary algorithm.

Both approaches for shape optimization are very robust and function almost without exception. By limiting the direction of growth, production restrictions can also be introduced in some cases. The great challenge that results from this is, on the one hand, the return of the geometry obtained to the CAD system and, on the other hand, the manufacturability with the metal-cutting manufacturing processes. Since almost all of the surfaces are freely formed, a clean representation in CAD and production is considerably more complex and therefore more difficult to handle.