Topological Optimization Using the SIMP Method

Abstract

The Volume-to-Point (VP) Heat Conduction Problem is concerned with the optimal distribution of conductive material over a heat generating domain. This thesis begins with an overview of the heat equation and its discretization using the Finite Volume Method. We proceed to give a summary of the topic of mathematical optimization and optimization techniques. After completing this brief presentation of background information we proceed to present the application of the Solid Isotropic Material with Penalization (SIMP) method to the VP heat conduction problem to create designs with optimal conductive material placement which minimize average temperature.