Enhancing Level Set-Based Topology Optimization of Geometrically Nonlinear Structures with Consideration of Thermal-Mechanical Coupling Effects

Abstract

Abstract This paper presents an innovative approach to topology optimization of geometrically nonlinear structures considering the effects of thermal-mechanical couplings. Through geometric nonlinear finite element analysis, an expression for element coupling stress is derived, capturing the combined influence of mechanical and thermal loading. A topological model is then developed, aiming to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements. To overcome convergence instability caused by large deformations, a novel Lagrange multiplier search method is proposed. Additionally, the method is extended to handle multi-constrained geometrically nonlinear topology optimization designs incorporating multiple physical field couplings. The proposed approach enhances the field of topology optimization by providing an effective solution for geometrically nonlinear behavior and thermal-mechanical couplings.