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

Eigenfrequency Topology Optimization of 3D Shell-infill Structures Based on Large-scale Parallel Computing

发展一种大规模并行拓扑优化框架,以最大化三维薄壁填充结构特征频率。通过两步滤波法描述薄壁区与填充区,建立以特征频率为目标、质量分数为约束的薄壁填充结构拓扑优化模型。基于PETSc和SLEPc软件包实现滤波方程和广义特征值方程的高效并行求解。推导特征频率和结构质量关于设计变量的灵敏度,并提交移动渐进线法(Methodofmoving asymptotes,MMA)求解器更新设计变量,直至算法收敛。在拓扑优化中,结合基于模态置信准则(Modal assurance criterion,MAC)的模态追踪方法以解决模态切换问题。研究具有不同质量分数约束的数值算例,以验证算法的有效性。最后,实现具有70万自由度的三维薄壁填充结构拓扑优化设计,分析CPU核数对算法性能的影响:与12核相比,使用28核的计算时间减少了43.7%。扩展薄壁填充结构拓扑优化方法以适用于特征频率最大化和大规模并行计算,为复杂装备结构轻量化设计提供有效的思路。

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.