A discrete-continuous parameterization (DCP) for concurrent optimization of structural topologies and continuous material orientations

Combining topology optimization and continuous orientation design of fiber-reinforced composites is a promising way to pursue lighter and stronger structures. However, the concurrent design problem of structural topologies and continuous orientations is a tough topic due to the issue of local optimum solutions. This paper presents a new parameterization of orthotropic materials with continuous orientations, which is labeled as discrete-continuous parameterization (DCP), to handle this difficulty. The starting point of DCP is that the risk of falling into local optima will be much smaller if the search range of orientation variables can be greatly reduced. To do so, the searching interval of orientation is averagely divided into several subintervals. Then, the original continuous orientation optimization problem is changed to a discrete subinterval selection problem and a continuous orientation optimization problem in a subinterval. Based on this, the new DCP is proposed to model orthotropic materials with continuously varying orientations by combining both discrete and continuous variables. Finally, a new and general concurrent topology optimization method is built based on the proposed DCP and a three-field topology optimization scheme. Verification studies with several benchmark examples are provided to validate the effectiveness of the proposed approach.