Structural topology optimization under uncertain loading

结构拓扑优化是一种灵活的工具，已被证明在概念和初步设计阶段特别有用。该项目将关注在不确定载荷条件下鲁棒结构拓扑优化的新算法的发展。这是一个重要的话题，因为大多数现实世界的结构设计问题都涉及到由于工作环境波动而导致的加载条件的不确定性。忽略这种不确定性可能会造成潜在的灾难性后果，并导致无法预见的服务故障。在这个项目中开发的算法将基于锚定ANOVA Petrov-Galerkin投影方案，该方案由Nair教授的团队开发。这项工作将扩展到处理线性弹性静力学和随机伴随灵敏度分析能力将得到发展。将使用水平集公式来发展最优拓扑，并进行详细的数值研究，以基准测试在一系列问题上开发的算法的性能。

Structural topology optimization is a flexible tool that has proven to be particularly useful in the conceptual and preliminary design stages. This project will be concerned with the development of new algorithms for robust structural topology optimization under uncertain loading conditions. This is an important topic since most real-world structural design problems involve uncertainty in the loading conditions due to fluctuations in the operating environment. Ignoring this uncertainty can be potentially disastrous and lead to unforeseen in-service failure. The algorithms to be developed in this project will be based on the anchored ANOVA Petrov-Galerkin projection scheme developed by Professor Nair's group. This work will be extended to deal with linear elastostatics and stochastic adjoint sensitivity analysis capabilities will be developed. A level-set formulation will used to evolve the optimal topology and detailed numerical studies will be conducted to benchmark the performance of the algorithms developed on a range of problems.