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

拓扑优化是设计结构和材料以满足某些优化标准的计算过程，例如最小重量或最大刚度。该技术在设计工程师中获得了显著的吸引力，并已被证明可以识别设计，其中有效利用材料导致前所未有的性能。本研究的目的是开发一种新的拓扑优化框架，能够在存在几何不确定性的情况下设计具有鲁棒性的结构拓扑。考虑优化过程中的尺寸不确定性在许多工程应用中是至关重要的，例如在涉及材料结构极端小型化的过程中，其中最优设计的物理实现通常受到很大的公差。将这项研究应用于最先进的商业制造技术，包括增材制造，将极大地影响建筑细胞材料的发展，并促进技术转移。这项研究的结果将被纳入麻省大学达特茅斯分校工程与应用科学博士课程的研究生课程。该项目将为麻省大学达特茅斯分校（其中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。这项研究将产生一种新的设计优化框架，能够设计在几何不确定性存在下具有鲁棒性的结构拓扑。一些策略将基于随机分析和不确定性表示和传播方法的新颖集成与有效的拓扑优化技术和基于逆均质化的材料设计框架进行探索。将开发连续和离散结构的随机拓扑优化框架，其中通过仔细结合节点和边界不确定性来实现容错。规划了几何不确定性表征和表示的新方法，包括旨在仔细测量用最先进的增材制造技术制造的蜂窝结构材料中的典型几何缺陷的实验工作，并量化它们对宏观力学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发展提供支持。

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.