Topology optimization of functionally graded anisotropic composite structures using homogenization design method

This paper proposes a topology optimization method that is capable of simultaneous design for structural topology, stiff material (i.e. fiber) layout, and its orientations in functionally graded anisotropic composite structures. Functionally graded composites are inhomogeneous materials with continuously varying spatial composition. The spatial variation in material properties might enable better performance than an isotropic multi-material structure or fiber-reinforced composite structure with fixed fiber volume fraction. In order to enable the simultaneous design of composite topology, spatially varying fiber material layout and orientation, a homogenization design method (HDM) is applied together with a solid isotropic material with penalization (SIMP) method taking into account the advantage of each method. The SIMP method is efficient in determining discrete material states while avoiding intermediate states. Thus, it is applied to determine whether a material is void or a composite state. The HDM allows intermediate material states because it considers true anisotropic composite materials. Taking this advantage, the HDM method is applied to optimize spatially varying anisotropic fiber material layout and orientation. The optimization result of the fiber material is visualized using the projection method proposed for periodic composite structures. To validate the effectiveness of the proposed method, numerical examples for compliance minimization problems are provided.