Topology optimization of deformable bodies with dissimilar interfaces

The topology optimization for practical engineering problems is computationally expensive owing to the complexity of the entire system. Therefore, most of the topology optimization is currently being conducted on simplified decomposed subsystems, which are then assembled in order to reduce the computational cost. Under these circumstances, there is a possibility that an inappropriate design might be obtained from the overall system. To overcome this limitation, an accurate and efficient algorithm for performing the structural topology optimization of deformable bodies containing dissimilar interfaces is introduced. Based on the mortar method, the condensed mortar method is proposed to connect dissimilar interface boundaries and to handle them in a manner similar to that used in conventional structure analysis. In this way, the treatment of such a problem becomes very concise, and the computational cost can be significantly reduced. Furthermore, the topology optimization is implemented using a modified SIMP method to derive the most suitable optimum layout. For alleviating the numerical deficiency at the interfaces, appropriate filtering schemes are adopted. Finally, several numerical examples are presented to verify the validity of the proposed method.