A strictly feasible sequential convex programming method [Elektronische Ressource] / Sonja Lehmann. Betreuer: Klaus Schittkowski

A Strictly Feasible Sequential ConvexProgramming MethodVon der Universitat Bayreuthzur Erlangung des akademischen Grades einesDoktors der Naturwissenschaften (Dr. rer. nat.)genehmigte Abhandlungvorgelegt vonSonja Lehmanngeboren in Erlangen1. Gutachter: Prof. Dr. Klaus Schittkowski2. Gutachter: Prof. Dr. Michael StinglTag der Einreichung: 9. Juni 2011Tag des Kolloquiums: 18. November 2011Fakultat fur Mathematik, Physik und InformatikAngewandte Informatik VIIAbstractIn free material optimization (FMO), one tries to nd the best mechanical structureby minimizing the weight or by maximizing the sti ness with respect to given loadcases. Design variables are the material properties represented by elasticity tensorsor elementary material matrices, respectively, based on a given nite element dis-cretization. Material properties are as general as possible, i.e., anisotropic, leading topositive de nite elasticity tensors, which may be arbitrarily small in case of vanishingmaterial. To guarantee a positive de nite global sti ness matrix for computing designconstraints, it is required that all iterates of an optimization algorithm retain positivede nite tensors. Otherwise, some constraints, e.g., the compliance, cannot be evalu-ated and the algorithm fails.FMO problems are generalizations of topology optimization problems. The goal oftopology optimization is to nd the sti est structure subject to given loads and alimited amount of material.