Maximum Stress Minimization Via Data-Driven Multifidelity Topology Design

Abstract

The maximum stress minimization problem is among the most important topics for structural design. The conventional gradient-based topology optimization methods require transforming the original problem into a pseudo-problem by relaxation techniques. Since their formulation methods and the parameter settings significantly influence optimization, a method is required to accurately solve the original maximum stress minimization problem without using relaxation techniques. This paper focuses on this challenge and compares solutions obtained by gradient-based topology optimization with those obtained by solving the original maximum stress minimization problem without relaxation techniques. We employ data-driven multifidelity topology design (MFTD), a gradient-free topology optimization based on evolutionary algorithms. The basic framework involves generating candidate solutions by solving a low-fidelity optimization problem, evaluating these solutions through high-fidelity forward analysis, and iteratively updating them using a deep generative model without sensitivity analysis. In this study, data-driven MFTD incorporates the optimized designs obtained by solving a gradient-based topology optimization problem with the p-norm stress measure in the initial solutions and solves the original maximum stress minimization problem based on a high-fidelity analysis with a body-fitted mesh. We demonstrate the effectiveness of our proposed approach through the benchmark of L-bracket. As a result of solving the original maximum stress minimization problem with data-driven MFTD, a volume reduction of up to 22.6% was achieved under the same maximum stress value, compared to the initial solution.