Structural Optimization

Academic advisor: Krister Svanberg

Sponsor: Swedish Research Council (VR)

Structural optimization is a discipline dealing with optimal design of load-carrying mechanical structures. A growing subfield of structural optimization is topology optimization, where a typical problem might be as follows: Given a predefined design domain (in two or three dimensions), some given supports in connection to the design domain, some given external loads, and a given material to be used, the problem consists of designing an optimal structure to carry the given loads. This should be done by finding the optimal subdomain, of the given design domain, to fill with material. The objective might be to minimize the total weight of the structure subject to constraints on displacements and stresses in the structure under the given loads. In order to attack this problem numerically, the design domain is discretized by a finite element model. One thus considers a ``discretized universe'' in which for each individual discrete point, i.e. finite element, it should be decided whether to place material there or not! The aim of our project is to develop mathematical models and efficient numerical optimization methods for large-scale problems of this type.