Multi-resolution nonlinear topology optimization with enhanced computational efficiency and convergence

Huge calculation burden and difficulty in convergence are the two central conundrums of nonlinear topology optimization (NTO). To this end, a multi-resolution nonlinear topology optimization (MR-NTO) method is proposed based on the multi-resolution design strategy (MRDS) and the additive hyperelasticity technique (AHT), taking into account the geometric nonlinearity and material nonlinearity. The MR-NTO strategy is established in the framework of the solid isotropic material with penalization (SIMP) method, while the Neo-Hookean hyperelastic material model characterizes the material nonlinearity. The coarse analysis grid is employed for finite element (FE) calculation, and the fine material grid is applied to describe the material configuration. To alleviate the convergence problem and reduce sensitivity calculation complexity, the software ANSYS coupled with AHT is utilized to perform the nonlinear FE calculation. A strategy for redistributing strain energy is proposed during the sensitivity analysis, i.e., transforming the strain energy of the analysis element into that of the material element, including Neo-Hooken and second-order Yeoh material. Numerical examples highlight three distinct advantages of the proposed method, i.e., it can (1) significantly improve the computational efficiency, (2) make up for the shortcoming that NTO based on AHT may have difficulty in convergence when solving the NTO problem, especially for 3D problems, (3) successfully cope with high-resolution 3D complex NTO problems on a personal computer.