Improved discrete-continuous parameterization method for concurrent topology optimization of structures and continuous material orientations

Concurrent topology optimization of structures and material orientations is a hot topic over the past decades. However, how to avoid the local optima of such problems is quite challenging. To handle this issue, a method combining the discrete material optimization method and continuous fiber orientation optimization method is proposed in our previous work, referred to as discrete-continuous parameterization (DCP), which takes advantage of the global search capability of discrete methods and the full design space of continuous methods. However, the DCP method requires too many design variables, resulting in a huge computational burden. Hence, we provide an improved DCP method to reduce the number of design variables and at the same time without sacrificing the convexity of the optimization problem in this work. In the proposed method, an extended multimaterial interpolation is firstly developed, which is capable of reducing the number of design variables greatly. Then, we integrate the proposed interpolation into the DCP method, generating an improved DCP method for the concurrent optimization of structural topology and fiber orientation. Several benchmark optimization examples show that the proposed method can greatly reduce the risk of falling into local optima with much fewer design variables.