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。该项目将致力于开发在不确定载荷条件下的稳健结构拓扑优化的新算法。这是一个重要的主题，因为大多数真实世界的结构设计问题都涉及由于运行环境的波动而导致的载荷条件的不确定性。忽视这种不确定性可能是灾难性的，并导致不可预见的在役故障。这个项目中将要开发的算法将基于由奈尔教授的小组开发的锚定ANOVA Petrov-Galerkin投影方案。这项工作将扩展到处理线弹性力学，并将开发随机伴随灵敏度分析功能。将使用水平集公式来演变最优拓扑，并将进行详细的数值研究，以对针对一系列问题开发的算法的性能进行基准测试。

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.