A novel multi-stage concurrent topology optimization for variable-stiffness structures

The concurrent optimization of topology and fibre orientation is a promising approach to pursue higher strength and lighter weight of variable-stiffness structures. This paper suggests a novel discrete-continuous scheme for the concurrent optimization. Considering the global convergence, Discrete Material Optimization is first utilized to select a dominant angle for each element from several predefined candidate angles. However, some regions with multiaxial stress make it difficult to select the definite angles for the elements. Therefore, the Sequential Binary-Phase Topology Optimization is suggested to guarantee the uniqueness of the element to candidate angle mapping. Moreover, to obtain better mechanical properties, Continuous Fibre Angle Optimization with a spatial filter is introduced to optimize fibre continuity. Several classic numerical examples are used to verify the excellent performance of the suggested method in terms of fibre angle convergence and show robustness regarding sensitivity to the initial setting.