GPU-accelerated large-scale topology optimization of 3D continuous fiber-reinforced composites for maximum fundamental eigenfrequency

AbstractTopology optimization of three-dimensional continuous fiber-reinforced composites (CFRCs) for maximum fundamental eigenfrequency is computationally challenging due to the repeated solution of nested generalized eigenvalue problems. To address this, an efficient GPU-accelerated solver is developed. At its core, the successive iteration of analysis and design (SIAD) method is employed to integrate approximate eigenvalue analysis and design variable updates into a single iteration loop, thereby replacing the conventional, computationally expensive double-loop approach. Within each design iteration, the one-step inverse iteration is accelerated by a multigrid-preconditioned conjugate gradient (MGPCG) solver. The computational efficiency of the MGPCG solver is further enhanced by an improved Taylor approximation-based method for computing element stiffness matrices, which is specifically tailored for Cartesian parameterization of fiber orientations to expedite sparse matrix-vector multiplications. Additionally, an efficient scheme for sensitivity analysis is developed, and a decoupled update strategy for density and fiber orientation variables is applied. The accuracy, efficiency, and scalability of the proposed solver are verified through several numerical examples. It is demonstrated that optimized CFRC designs can achieve higher fundamental eigenfrequencies than their aluminum counterparts at a lower mass. Notably, for a problem with 6.3 million elements, the proposed solver requires only approximately 13.1 hours (300 iterations) on a single NVIDIA Tesla V100 GPU.