Robust Structural Topology Optimization

拓扑优化是面向目标的多功能工程结构创成式设计的有力工具。与使用有限维参数几何模型的尺寸和形状优化方法不同，拓扑优化算法在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很大的进展，但目前使用的大多数方法都是基于确定性的隐含假设，即假设载荷条件、边界条件和材料的本构性质是精确的。拟议的研究计划将解决与开发稳健结构拓扑优化的高效算法相关的关键基础、理论问题和计算挑战。本项目所使用的方法将包括求解随机线弹性方程的有效数值格式和Level-Set方法。这一研究计划取得的进展将使设计师能够充分挖掘先进添加剂制造技术的潜力，用于广泛的实际工程应用，在这些应用中，性能稳健性是关键的设计要求。

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.