Geometrically Nonlinear Optimization of Thin‐Walled 3D Structures Using a Novel Reduced‐Order Method

Due to the computational difficulties in numerical robustness and efficiency caused by geometrical nonlinearities, the design of thin‐walled structures is commonly conducted based on the small‐deformation assumptions. However, the large deflection frequently occurs due to the insufficient out‐of‐plane stiffness and the demands of the lightweight design. In this work, optimizations of thin‐walled structures are carried out considering the geometrically nonlinear effects. A reduced‐order method using hybrid‐stress solid‐shell formulations is presented for large‐deformation analysis in the optimization process. By adopting the two‐field Hellinger–Reissner variational principle, a reduced‐order model with only one degree of freedom is efficiently constructed. The entire geometrically nonlinear response is automatically and accurately traced by a predictor‐corrector phase. Starting from a completed plate, the topology optimization is achieved by digging arbitrary circular holes or varying the thickness distribution. Three categories of optimization objectives are achieved to minimize the deflection deformation, minimize the maximum stress, and approach the target response curve, respectively. Different optimization constraints on the design variables, shapes, and volumes of thin‐walled structures are considered. The favorable optimization design on geometrically nonlinear responses of thin‐walled structures is achieved, which demonstrates the efficiency and robustness of the presented method.