A polygonal topology optimization method based on the alternating active-phase algorithm

We propose a polygonal topology optimization method combined with the alternating active-phase algorithm to address the multi-material problems. During the process of topology optimization, the polygonal elements generated by signed distance functions are utilized to discretize the structural design domain. The volume fraction of each material is considered as a design variable and mapped to its corresponding element variable through a filtering matrix. This method is used to solve a multi-material structural topology optimization problem of minimizing compliance, in which a descriptive model is established by using the alternating active-phase algorithm and the solid isotropic microstructure with penalty theory. This method can accomplish the topology optimization of multi-material structures with complex curve boundaries, eliminate the phenomena of checkerboard patterns and a one-node connection, and avoid sensitivity filtering. In addition, this method possesses fine numerical stability and high calculation accuracy compared to the topology optimization methods that use quadrilateral elements or triangle elements. The effectiveness and feasibility of this method are demonstrated through several commonly used and representative numerical examples.