Collaborative Research: Optimal Design of Flaw-tolerant Structures and Material Microarchitectures via Stochastic Topology Optimization

拓扑优化是设计满足某些优化标准的结构和材料的计算过程，例如最小重量或最大刚度。这项技术在设计工程师中获得了巨大的吸引力，并已被证明可以识别有效使用材料带来前所未有的性能的设计。这项研究的目的是开发一种新的拓扑优化框架，能够设计出在存在几何不确定性的情况下具有健壮性的结构拓扑。考虑优化过程中的尺寸不确定性在许多工程应用中非常重要，例如，在涉及材料结构极端小型化的过程中，最优设计的物理实现通常受到很大的公差限制。将这项研究应用于包括添加剂制造在内的最先进的商业制造技术，将极大地影响建筑结构蜂窝材料的发展，并促进技术转移。这项研究的结果将被纳入马萨诸塞大学达特茅斯分校工程和应用科学博士项目的研究生课程。该项目将为马萨诸塞州大学达特茅斯分校(许多学生是第一代大学生)、加州大学欧文分校和约翰·霍普金斯大学的研究生和本科生提供培训。这项研究将产生一个新的设计优化框架，能够设计出在存在几何不确定性的情况下具有健壮性的结构拓扑。基于随机分析、不确定性表示和传播方法的新集成、高效的拓扑优化技术和基于逆均质化的材料设计框架，将探索一些策略。将开发连续结构和离散结构的随机拓扑优化框架，其中通过仔细合并节点和边界的不确定性来实现缺陷容限。计划采用新的方法来表征和表示几何不确定性，包括一项旨在仔细测量采用最先进的添加制造技术制造的建筑蜂窝材料中的典型几何缺陷的实验工作，并量化它们对宏观机械性能统计变化的影响。这项实验研究将为以容错为中心的拓扑优化框架的开发提供支持。

Topology optimization is a computational process for designing structures and materials that meet some optimality criteria, e.g. minimum weight or maximum stiffness. The technique has gained significant traction among design engineers and has been shown to identify designs where efficient use of materials resulted in unprecedented performance. The objective of this research is to develop a new topology optimization framework capable of designing structural topologies that are robust in the presence of geometric uncertainties. Accounting for dimensional uncertainties in the optimization process is of paramount importance in many engineering applications, for example in processes involving extreme miniaturization of the material architecture, where the physical realization of the optimal design is generally subjected to significant tolerances. The application of this research to state-of-the-art commercially available manufacturing technologies, including additive manufacturing, will greatly impact the development of architected cellular materials and promote technology transfer. Results of this research will be incorporated into graduate courses within the Engineering and Applied Science PhD program at the University of Massachusetts, Dartmouth. This project will provide training for graduate and undergraduate students at UMass Dartmouth (where many students are first generation college students), the University of California, Irvine and Johns Hopkins University.This research will result in a new design optimization framework capable of designing structural topologies that are robust in the presence of geometric uncertainties. A number of strategies will be explored based on novel integration of stochastic analysis and uncertainty representation and propagation methods with efficient topology optimization techniques and inverse homogenization-based material design frameworks. Stochastic topology optimization frameworks for both continuum and discrete structures will be developed where flaw-tolerance is achieved through careful incorporation of nodal and boundary uncertainties. Novel methodologies for the characterization and representation of geometric uncertainties are planned, including an experimental effort aimed at carefully measuring typical geometric flaws in architected cellular materials fabricated with state-of-the-art additive manufacturing techniques, and quantifying their impact on the statistical variations of the macroscopic mechanical properties. This experimental investigation will feed into the development of a topology optimization framework centered on flaw-tolerance.