Abstract: The design domain of lath-shaped structure has a large length-width ratio, so it is difficult to obtain a solution or a clear and periodic topology configuration using the conventional algorithm. The mathematical model for periodic topology optimization is built; in which mean compliance is taken as objective function and relative densities of elements are taken as design variables. A method for periodic topology optimization is presented using variable density method solid isotropic microstructures with penalization (SIMP). An additional constraint condition is taken part in the mathematical model to ensure a topological structure which possesses periodicity. The iterative formula of virtual sub-domain design variables is deduced taking advantage of optimality criteria method and Lagrange multiplier is calculated using volume constraint. A filtering function is imported in order to solve checkerboard and mesh-independent. Results show that periodic holes are appeared in the process of optimization. The numbers of holes do not change as the iterative number increasing, which shows that the proposed method has stronger robustness. Periodic topology configuration which has a good consistency is achieved when the number of sub-domain is different.

Key words: Periodicity, Solid isotropic microstructures with penalization, Topology optimization, Variable density method