Topology optimization of shell–infill structures for maximum stiffness and fundamental frequency

Shell–infill structures, composed of the high strength shell and porous infill, have been used in lightweight design for enhancing the load-bearing and energy absorption capabilities. In this paper, we propose a shell–infill structure modeling method based on the Gaussian function and conducts multi-objective topology optimization for maximum stiffness and fundamental frequency. After two-step density filtering in the density-based topology optimization, the Gaussian function is introduced to map the intermediate densities to extract the shell. The shell thickness is controlled by the parameters of the Gaussian function and the filter radius, and their relationship is also derived. Pseudo modes are often found in eigenvalue optimization problems using the Solid Isotropic Material with Penalization (SIMP). By integrating the design variable into the penalization, we propose the Solid Isotropic Material with Variable Penalization (SIMVP) that can effectively suppress the pseudo modes. The proposed interpolation function is applied to the material model of the shell–infill structure. Numerical examples in both 2D and 3D are presented to verify the effectiveness of the multi-objective topology optimization method for shell–infill structures. Additionally, the effects of weights in the objective function, filter radius, parameters of the Gaussian function, constraints, and material properties on the optimization results are investigated.