A cascadic multilevel optimization framework for the concurrent design of the fiber-reinforced composite structure through the NURBS surface

This paper proposes a novel cascadic multilevel optimization framework for the fiber-reinforced composite structure, inspired by the character of the non-uniform rational basis spline (NURBS) surface, to control the structural topology, fiber angle distribution, and to improve the computational efficiency. The NURBS surface is not only used for the calculation of the structural response and the geometry modeling of the design but also introduced to construct the hierarchy of the parameterization of design variables. The optimization problem is formulated and solved successively from a coarse mesh level to the finest mesh level. The initial design of a fine level is computed using the solution of a coarse level. The number of meshes and design variables is gradually increased, and the design freedom and the resolution of parameterization remain the same to the optimization at the finest mesh level. Because there are fewer design variables and meshes at the coarse level and the finest level is used to find an accurate solution, it efficiently reduces the computational cost of the optimization. Meanwhile, the local support character of the NURBS surface avoids the checkerboard phenomenon and improves the continuity of local fiber angle. Several numerical examples for compliance minimization are presented to verify the effectiveness of the proposed method.