Computational feasibility of simultaneous analysis and design in interior point topology optimization

Abstract

Topology optimization is a class of algorithms designed to optimize a design or structure to accomplish some goal. It is part of a process of computer generated design that allows engineers to design better products faster. One such algorithm that has piqued the imagination of developers is called Simultaneous Analysis and Design (SAND), especially in the context of Interior Point Optimization (IPO). This method is known to generate extremely optimal designs, and is good at avoiding local minima. However, this method is not used in practice, due to its computational cost. This thesis examines the SAND IPO method, and develops an effective algorithm to generate a design using it. I begin by discussing nonlinear optimization algorithms, selecting pieces that work together for this problem, to generate a cohesive algorithm for the whole process. Inside this developed algorithm, as with most nonlinear optimization algorithms, the most ex- pensive part is a linear solve. In my case, it is a linear solve of a block system. I develop and implement a multi-tier preconditioning approach to solve this system in a reasonable amount of time. Finally, I present a large topology optimization problem presented in three dimensions that has been solved using IPO and SAND, demonstrating the usability of the implemented algorithm.