Topology optimization for continuous and discrete orientation design of functionally graded fiber-reinforced composite structures

This paper presents a topology optimization method for the sequential design of material layout and fiber orientation in functionally graded fiber-reinforced composite structures. Specifically, the proposed method can find the optimal structural layout of matrix and fiber materials together with optimal discrete fiber orientations. In this method, an orientation design variable in the Cartesian coordinate system is employed with a conventional density design variable. The orientation design variable controls not only the fiber orientation, but also fiber volume fraction. The fiber volume fraction control can be used to relax the orientation design problem and simultaneously design a functionally graded structural layout of fiber material. To avoid intermediate fiber orientations and achieve discrete fiber orientation design, a penalization scheme is applied to the orientation design variable. For solving the optimization problem which involves multiple design variables such as the density variable, fiber orientation variable, and target discrete orientation set, a three-step sequential optimization procedure is proposed. In this procedure, the result for each step provides the isotropic design, continuous fiber orientation design, and functionally graded discrete orientation design, respectively. To validate the effectiveness of the proposed approach, numerical examples for structural compliance minimization and compliant mechanism design are provided.