Homogenization method for dynamic problems based on continuous size field

Based on homogenization theory, hexagonal microstructure with isotropic behavior is adopted as description of the macroscopic material. A new topological optimization method of continuum structure for dynamic problems is presented based on continuous size field. The proper character of the microcosmic cell is numerically validated to avoid localized modes. The size of the hexagonal cell for the material point instead of element or node is applied as design variables. Continuity of design variables field is ensured by interpolation of the modified filtering interpolation functions. Checkerboard patterns concerned in most topological optimization methods are avoided naturally. Sensitivities of global stiffness matrix, global mass matrix and so on are derived according to calculation method for partial derivative of compound function. Topological optimization models are established where dynamic structural responses are taken as objective and prescribed volume fraction is referred to as constraint conditions. Numerical examples show that the proposed method is feasible and effective in dynamic topological optimization design of continuum structure.