An efficient computational approach to stress-constrained topology optimization is presented. Using a multigrid-preconditioned Krylov solver for the state and adjoint problems, the number of Krylov iterations is reduced significantly by enforcing early termination of the iterative solves. The criterion for early termination is based on the convergence of the design sensitivities with respect to Krylov iterations. Consequently, the progress of optimization is not affected by the inexact resolution of the state and adjoint problems. The proposed approach is demonstrated on several design problems that possess different characteristics of the maximum stress. Optimization results obtained with early termination show very good agreement with those obtained with an accurate direct solver—in terms of objective value, constrained maximum stress and overall number of design cycles. Savings of 80% in the number of Krylov iterations are achieved, compared to the number of iterations required to satisfy the force residual convergence criterion to a common tolerance. The approach is directly applicable to high-resolution problems that are solved on parallel computational environments. A MATLAB code for reproducing the results is freely available at https://github.com/odedamir/topopt-stress-inexact-sensitivities

中文翻译：

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使用不精确的设计灵敏度进行有效的应力约束拓扑优化

提出了一种有效的应力约束拓扑优化计算方法。对状态和伴随问题使用多重网格预处理 Krylov 求解器，通过强制提前终止迭代求解，显着减少了 Krylov 迭代次数。提前终止的标准是基于 Krylov 迭代设计敏感性的收敛。因此，优化的进程不受状态和伴随问题的不精确解决的影响。所提出的方法在具有最大应力不同特征的几个设计问题上得到了证明。使用提前终止获得的优化结果与使用精确直接求解器获得的优化结果非常一致——就目标值而言，限制最大应力和设计周期总数。与满足力残差收敛准则到共同容差所需的迭代次数相比，Krylov 迭代次数节省了 80%。该方法直接适用于在并行计算环境中解决的高分辨率问题。用于重现结果的 MATLAB 代码可在 https://github.com/odedamir/topopt-stress-inexact-sensivities 免费获得