基于大规模并行计算的三维薄壁填充结构特征频率拓扑优化设计

A large-scale parallel topology optimization framework is developed to maximize the eigenfrequency of 3D shell-infill structures. The shell and infill are described through the two-step filtering approach, then the topology optimization model of the shell-infill structure with eigenfrequency objective and mass fraction constraint is built. The parallel solution of filtering equations and generalized eigenvalue equations is based on two software libraries called PETSc and SLEPc. Sensitivities of eigenfrequency and mass with respect to the design variables are derived, which are submitted to the solver of the method of moving asymptotes(MMA) for design variable updating until convergence. During the topology optimization, the modal-assurance-criterion-based(MAC) mode-tracking strategy is employed to handle the mode switching problem. Numerical examples with different mass fraction constraints are investigated to demonstrate the algorithm validity. Finally, the topology optimization design of 3D shell-infill structures with 700, 000 degrees of freedom is realized and the influence of the number of CPU cores on the performance of the algorithm is analyzed, which reduces the computing time by 43.7% with 28 cores compared with 12 cores. The topology optimization method of shell-infill structures is extended to be applicable to eigenfrequency maximization and large-scale parallel computing, which provides an effective idea for lightweight design of complex equipment structures.