Density-based topology optimization of thin plate structure with geometric nonlinearity using a three-dimensional corotational triangle element formulation

Topology optimization for three-dimensional (3D) thin plate structure is an attractive methodology for versatile industrial and biomedical applications. For this perspective, the topology optimization requires an appropriate treatment of the 3D geometric nonlinearity of thin structures that avoids numerical instabilities, which is a well-known challenge in topology optimization. This paper develops a density-based topology optimization for thin plates and considers geometric nonlinearity using a 3D corotational triangle element formulation. The corotational formulation is an approach for expressing a finite deformation by dividing small strains and finite rotations into local element coordinates. Thus, the mechanical behavior in local coordinates can be assumed to be linearly elastic behavior that follows the small strain theorem. This technique is expected to be effective and stable for topology optimization with geometric nonlinearity. Complementary work minimization with volume constraints was applied for density-based topology optimization of the plate structure by a solid isotropic material with penalization method. Numerical examples of two benchmarks demonstrated consistencies with existing related works. We conducted topology optimization of an ankle-foot orthosis (AFO) as a biomedical application and showed the capabilities of the proposed methodology and the minimum increases of the complementary work with an optimum design with a volume reduction ratio. These achievements highlight the capabilities of the developed topology optimization as an efficient framework and feasibilities for a new orthosis design.