Robust Design to Account for Geometric Imperfections in Small-Scale Structures

本研究的目的是开发一种设计方法与强大的形状和拓扑优化（RSTO），占各种形式的几何不确定性与制造小规模结构的缺陷。 该研究将提供一个基于水平集的动态拓扑设计模型，可以方便地捕获各种形式的局部和全局几何不确定性。 概率拓扑设计的计算框架将开发集成高性能的不确定性传播技术与现有的确定性拓扑优化方法。 该设计试验台通过光学超材料的设计解决了可持续能源的关键需求。 纳米制造和RSTO方法的无缝集成不需要几何边界的后处理，使用全功能原型提供了“硬件在环”验证。 如果成功的话，所提出的研究将把现有的确定性拓扑优化技术转化为几何不确定性下同时进行形状和拓扑优化的新方法。 虽然测试平台的重点是一个纳米工程系统，该方法是通用的，广泛适用于处理几何不确定性在微观，中观和宏观尺度上的几何变化有很大的影响，对产品性能。 这项研究的成果将为设计和纳米制造领域的多学科研究人员提供独特的研究和教育环境，同时在跨学科的学习环境中培养学生。从这项研究中开发的超材料设计应用将作为促进K-12工程意识的绝佳例子，说明工程中的新技术及其对创造可持续环境的影响。

The objective of this research is to develop a design methodology with robust shape and topology optimization (RSTO) that accounts for various forms of geometric uncertainties in association with imperfections in manufacturing small-scale structures. The research will provide a level-set based dynamic topological design model that conveniently captures various forms of local and global geometric uncertainties. A computational framework for probabilistic topology design will be developed to integrate high performance uncertainty propagation techniques with existing deterministic topology optimization methods. The design testbed addresses the critical demand in sustainable energy source through the design of optical metamaterials. The seamless integration of the nano-fabrication and the RSTO methodology that requires no post processing of geometry boundary offers 'hardware-in-the-loop' validation using fully functional prototypes. If successful, the proposed research will transform existing techniques in deterministic topology optimization to new methods for simultaneous shape and topology optimization under geometric uncertainties. Although the testbed is focused on a nano-engineered system, the methodology is general and widely applicable to handling geometric uncertainties at micro, meso, and macro scales where geometric variations have a large impact on product performance. The fruition of this research will offer a unique research and educational environment for multidisciplinary researchers across the fields of design and nano-manufacturing while training students in an interdisciplinary learning environment. The metamaterial design applications developed from this research will serve as excellent examples for promoting engineering awareness in K-12 by illustrating what is new in engineering and its impact on creating a sustainable environment.