Multi-material topology optimization considering both isotropy and anisotropy with fibre orientation optimization

Research on multi-material topology optimization (MMTO) considering both isotropic and anisotropic materials as candidate materials is limited. Previous studies required researchers to preselect the anisotropic material fibre orientations, which are not subject to change during the optimization. As the preselected orientations cannot change, better MMTO solutions may be overlooked. To address this issue, a novel MMTO algorithm incorporating the anisotropic material fibre orientation as a design variable is proposed, eliminating the need to preselect fibre orientations and leading to better MMTO solutions. A numerical approximation method named the carry-through method is also proposed. This allows the compliance sensitivity over anisotropic material fibre orientation to be calculated without the need for the strain–displacement matrix information, simplifying the MMTO method implementation. Comparative studies on three models demonstrate that the proposed MMTO method outperforms the existing MMTO method, achieving improvements of 7%, 10% and 14% on the objectives in these models.