A Gradient-Based Approach to Optimize the Topological Distribution of Material in Thin-Walled Structures Subject to Geometrical Nonlinearities

Abstract

Thin-walled structures are applied in engineering due to their favorable weight-to-performance ratio for supporting service loads. Topology optimization allows for determining the optimal material distribution in these structures to fulfill mechanical tasks in the context of small or large deformations. Sensitivity analysis is frequently addressed analytically, considering the continuous optimization of a regular and differentiable distribution of artificial densities that define the material arrangement. This work focuses on the topology optimization of a thin-walled structure to minimize ’compliance’, using MITC4 elements adapted for large deformations with a St. Venant–Kirchhoff constitutive law. The material arrangement is interpolated using the Solid Isotropic Material with Penalization (SIMP) technique, and the sensitivity analysis is performed using the adjoint method to enhance computational efficiency.