论文标题
快速机械设计的一阶双层拓扑优化
First-Order Bilevel Topology Optimization for Fast Mechanical Design
论文作者
论文摘要
拓扑优化（TO）在材料重量约束下最大化结构鲁棒性，已成为机械零件自动设计的重要步骤。但是，现有的算法使用需要大量计算资源的有限元分析（FEA）。我们为算法提供了一部小说，其迭代成本要低得多。与需要在每次迭代时需要精确反转大型FEA系统矩阵的常规方法不同，我们将问题重新制定为可以使用一阶算法来求解的双层优化，并且仅将系统矩阵倒置大约反转。结果，我们的方法会产生较低的迭代成本，用户可以在快速设计更新方面进行交互预览结果。进行理论收敛分析和数值实验以验证我们的有效性。我们进一步讨论了在图形处理单元（GPU）上使用高性能预处理和细粒并行性的扩展。
Topology Optimization (TO), which maximizes structural robustness under material weight constraints, is becoming an essential step for the automatic design of mechanical parts. However, existing TO algorithms use the Finite Element Analysis (FEA) that requires massive computational resources. We present a novel TO algorithm that incurs a much lower iterative cost. Unlike conventional methods that require exact inversions of large FEA system matrices at every iteration, we reformulate the problem as a bilevel optimization that can be solved using a first-order algorithm and only inverts the system matrix approximately. As a result, our method incurs a low iterative cost, and users can preview the TO results interactively for fast design updates. Theoretical convergence analysis and numerical experiments are conducted to verify our effectiveness. We further discuss extensions to use high-performance preconditioners and fine-grained parallelism on the Graphics Processing Unit (GPU).
