Level-Set-Based Topology Optimization of a Geometrically Nonlinear Structure Considering Thermo-mechanical Coupling Effect

Abstract

This paper presents an improved level set method for topology optimization of geometrically nonlinear structures accounting for the effect of thermo-mechanical couplings. It derives a new expression for element coupling stress resulting from the combination of mechanical and thermal loading, using geometric nonlinear finite element analysis. A topological model is then developed to minimize compliance while meeting displacement and frequency constraints to fulfill design requirements of structural members. Since the conventional Lagrange multiplier search method is unable to handle convergence instability arising from large deformation, a novel Lagrange multiplier search method is proposed. Additionally, the proposed method can be extended to multi-constrained geometrically nonlinear topology optimization, accommodating multiple physical field couplings.