Topology Optimization of Geometrically Nonlinear Structures Under Thermal–Mechanical Coupling

A geometrically nonlinear topology optimization (GNTO) method with thermal–mechanical coupling is investigated. Firstly, the new expression of element coupling stress due to superimposed mechanical and thermal loading is obtained based on the geometrically nonlinear finite element analysis. The lightweight topology optimization (TO) model under stress constraints is established to satisfy the strength requirement. Secondly, the distortion energy theory is introduced to transform the model into structural strain energy constraints in order to solve the implicit relationship between stress constraints and design variables. Thirdly, the sensitivity analysis of the optimization model is derived, and the model is solved by the method of moving asymptotes (MMA). Numerical examples show that temperature has a significant effect on the optimal configuration, and the TO method considering temperature load is closer to engineering design requirements. The proposed method can be extended to the GNTO design with multiple physical field coupling.