Robust Structural Topology Optimization

拓扑优化是多功能工程结构面向目标生成设计的有力工具。与使用有限维参数几何模型的尺寸和形状优化方法相比，拓扑优化算法理论上可以在可能的拓扑的无限维空间中搜索最佳解。尽管在拓扑优化领域已经取得了重大进展，但目前使用的大多数方法都是基于隐含的确定性假设，即假设载荷条件、边界条件和材料本构性质是精确已知的。提出的研究计划将解决与鲁棒结构拓扑优化高效算法开发相关的关键基础、理论问题和计算挑战。在这个项目中使用的方法将包括求解随机线性弹性方程的有效数值格式与水平集方法相结合。该研究项目取得的进展将使设计人员能够充分利用先进增材制造技术的潜力，用于广泛的实际工程应用，其中性能稳健性是至关重要的设计要求。

Topology optimization is a powerful tool for goal-oriented generative design of multifunctional engineering structures. In contrast to size and shape optimization approaches that work with a finite-dimensional parametric geometry model, topology optimization algorithms can, in theory, search for the best solution in an infinite-dimensional space of possible topologies. Even though significant advances have been made in the field of topology optimization, most methods currently in use are based on the implicit assumption of determinism, i.e., the loading conditions, boundary conditions and material constitutive properties are assumed to be known precisely. The proposed research program will address the key fundamental, theoretical issues and computational challenges associated with the development of efficient algorithms for robust structural topology optimization. The methodology used in this project will involve efficient numerical schemes for solving the stochastic linear elasticity equations coupled with level-set methods. Advances made in this research program will enable designers to fully exploit the potential of advanced additive manufacturing techniques for a broad range of practical engineering applications where performance robustness is a crucial design requirement.