Topology optimization of gradient lattice structure under harmonic load based on multiscale finite element method

This work develops a topological optimization framework for parametric lattice structure design under harmonic load based on the scale-dependent multiscale finite element method (MsFEM). Two different design variables are introduced and optimized simultaneously in the topology optimization, i.e., the control parameters represent the lattice cell’s material consumption and the configuration. To improve analysis accuracy and efficiency, the MsFEM with periodic boundary condition is used for structures with strong periodicity and the MsFEM with six nodes on each edge of the coarse element is used for those with weak periodicity, respectively. Then the scale-dependent lattice cell’s equivalent stiffness and mass matrices can be established. The surrogate model of the relationship between the lattice control parameters and stiffness matrices and mass matrices is built based on the proper orthogonal decomposition and diffusion approximation methods. Therefore, sensitivity analysis of the dynamic responses concerning the control parameters can be performed. Finally, numerical examples and vibration testing results are presented to show the validity of the optimization framework using gradient lattice structures to suppress vibration under frequency band loading and its potential application in engineering practice.