Concurrent Optimization of Topology and Fiber Orientation in Fiber Reinforced Composites Using the Moving Morphable Components Method

To enhance the structural performance of fiber-reinforced composites, this study proposes a framework for concurrent topology and fiber orientation optimization. This method employs an embedded bar model to represent fibers, thereby establishing a composite unit cell structure. Taking minimum compliance as the objective function, the method defines the relationship between the macro- and micro-scales and derives the sensitivity formulas for the two-dimensional unit structure. Furthermore, it adopts Gaussian quadrature to accurately calculate the stiffness matrix of anisotropic elements. Numerical examples validate the effectiveness of the proposed parallel topology optimization approach. The results of the Michell beam example demonstrate that, compared with the optimized structure using isotropic material, the single-scale optimized structure achieves a 30.48% improvement in stiffness. In addition, compared with the single-scale optimized structure, the multiscale optimized structure yields a further 13.99% improvement in stiffness. Multi-scale optimization fully exploits the properties of fiber materials and mitigates stress concentration. This research provides a reference for the development of topology optimization techniques for fiber-reinforced composites.