The problem of optimal material distribution for the topology optimization of structures is considered. Instead of introducing any specific microstructure to get the relationship between the elastic moduli and the density of the material, an artificial material based on the Hashin-Shtrikman lower bound is suggested in order to reduce the number of design variables and to make the optimization algorithm simple and effective. An efficient algorithm is introduced to suppress the checker-board patterns. In the optimization process, density is updated according to the optimality criteria and then re-distributed. Some examples are presented to show the performance of the new artificial material and the density re-distribution algorithm.
