Topological optimization and minimal compliance in linear elasticity

TL;DR

This paper presents a new regularization-based approach for topology optimization in linear elasticity, enabling gradient-based solutions and demonstrating effective numerical results for compliance minimization.

Contribution

A novel regularization technique for fixed domain topology optimization that improves differentiability and applicability across various boundary value problems.

Findings

Effective gradient algorithm for compliance minimization

Numerical experiments show descent in cost values

Demonstrates topological and boundary variations in optimized domains

Abstract

We investigate a fixed domain approach in shape optimization, using a regularization of the Heaviside function both in the cost functional and in the state system. We consider the compliance minimization problem in linear elasticity, a well known application in this area of research. The optimal design problem is approached by an optimal control problem defined in a prescribed domain including all the admissible unknown domains. This approximating optimization problem has good differentiability properties and a gradient algorithm can be applied. Moreover, the paper also includes several numerical experiments that demonstrate the descent of the obtained cost values and show the topological and the boundary variations of the computed domains. The proposed approximation technique is new and can be applied to state systems given by various boundary value problems.