Topology optimization of 3D continuous fiber-reinforced composites using Cartesian parametrization of fiber orientations

Fiber orientation parametrization is a fundamental issue in topology optimization of continuous fiber-reinforced composites. The conventional Euler angles-based parametrization often encounters singular points, which can be problematic. To address this challenge, the Cartesian representation-based parametrization is revisited. By leveraging the transversal isotropy property of fiber-reinforced composites, a direct mapping between the Cartesian representation of the 3D fiber orientation and the rotated stiffness matrix is established. Thus, the transformations between Euler angles and Cartesian representation have become unnecessary, simplifying implementation and avoiding associated numerical issues. Building upon the proposed Cartesian parametrization, the classical minimum compliance design problem for 3D continuous fiber-reinforced composites is formulated. Then, efficient sensitivity analysis and decoupled design variable updating strategies are developed. The effectiveness of the proposed parametrization is demonstrated through three large-scale topology optimization examples. These case studies showcase the capability of the approach to solve practical problems and achieve improved optimization outcomes.