Explicit Topology Optimization of Three-Dimensional Geometrically Nonlinear Structures

In this work, a three-dimensional explicit geometrically nonlinear topology optimization method is developed. Moving morphable voids (MMVs) are used to describe the optimized structures, which enjoy the advantages of fewer design variables and seamless integration with CAD system. Furthermore, attributing to the decoupling between the description of topology and finite element analysis, redundant degree of freedoms in the void regions are directly removed during mechanical analysis, and this could significantly alleviate the mesh distortion of weak elements and also improve the computational efficiency of finite element analysis in the finite deformation regime. Numerical examples verify the effectiveness of the developed method and reveal that: (1) the finite deformation has a significant influence on the optimal topology of the three-dimensional structures both for single and multiple load cases; (2) the optimized geometrically nonlinear structures may take advantage of large displacements and small strains for achieving a minimized end compliance; (3) the critical load factor should be evaluated to guarantee the validity of the optimized structures.