A novel discrete–continuous material orientation optimization model for stiffness-based concurrent design of fiber composite

The cooperation of tailoring fiber angles and designing its macro layout is an excellent approach to improve the performance of composite structures and achieve lighter weight. This article proposes a novel discrete–continuous optimization model for the concurrent optimization of the macro structural topology and local fiber angle for the fiber-reinforced composite structure. Therein, the novel modeling consists of a two-step strategy, where the normal distribution function is adopted to form the discrete material interpolation scheme firstly and then the continuous angle design on fine angle subintervals is conducted. Because it requires the fixed discrete design variables regardless of the number of angle subintervals and simultaneously achieves the continuous fiber angle design, it can save computational cost and provide an infinite design domain. Furthermore, the subdividing angle interval reduces the risks of falling into the local optimum solution for continuous angle design. Besides, the fiber discontinuity may cause stress concentration and manufacturing problems in the intersection of discontinuous fiber paths. Therefore, a linear density technique is used to achieve fiber continuity. Finally, a concurrent topology optimization model is built based on the proposed novel model. And several numerical examples are well-organized and presented to illustrate the validity of the proposed model.