ISBN 978-3-8439-5378-8

978-3-8439-5378-8, Reihe Mathematik

Jonas Holley
Stress-Constrained Topology Optimization with Application to the Design of Electrical Machines

199 Seiten, Dissertation Humboldt-Universität Berlin (2023), Softcover, A5

Zusammenfassung / Abstract

In the process of designing a physical object, the mechanical stability is an essential requirement in nearly every area of application. Stability can be quantified mathematically by suitable criteria based on the stress tensor, aiming at the prevention of damage in each point within the physical object. This thesis deals with the development of a framework for the solution of optimal design problems with pointwise stress constraints.

First, a regularization of the optimal design problem is introduced. This perturbation of the original problem represents a central element for the success of a solution method. After analyzing the perturbed problem with respect to the existence of solutions, a line search type gradient descent scheme is developed based on an implicit design representation via a level set function. The core of the optimization method is provided by the topological gradient, which quantifies the effect of an infinitesimal small topological perturbation of a given design on an objective functional. Since the developed approach is a method in function space, the numerical realization is a crucial step towards its practical application. The discretization of the state and adjoint equation provide the basis for developing a finite-dimensional version of the optimization scheme.

In the last part of the thesis, numerical experiments are conducted in order to assess the performance of the developed algorithm. First, the stress-constrained minimum volume problem for the L-Beam geometry is addressed. An emphasis is put on examining the effect of the proposed regularization. Afterwards, the multiphysical design of an electrical machine is addressed. In addition to the pointwise constraints on the mechanical stress, the maximization of the mean torque is considered in order to improve the electromagnetic performance of the machine. The success of the numerical tests demonstrate the potential of the developed design method in dealing with real industrial problems.