Optimal Topology Design under Fabrication and Demand Uncertainties

该奖项的研究目标是开发考虑小规模结构制造缺陷和需求不确定性的最佳设计方法。在工程设计中，有一种自然的趋势，即突破现有材料的容量极限或采用新的高性能材料。虽然这通过使用更稀疏和细长的元素来提高效率，但设计也变得更容易受到可能影响响应的缺陷的影响。该研究将通过将制造和需求的不确定性纳入拓扑优化方法来解决这一问题，拓扑优化是一种新兴的设计工具，用于优化跨设计领域的材料分布。pi将利用系统不确定性模型与拓扑优化算法中使用的数学形式之间的关系。此外，方法将探讨识别那些参数的不确定性对设计有主要影响。为了确保这些方法可以实际应用，制造被包括在工作范围内。制造样品的测试结果将用于量化制造误差，并为更新不确定性模型提供反馈。如果成功，这项研究的结果将有助于设计具有优化和/或定制可靠性的高效结构。潜在的应用包括高性能材料微结构、柔性机构和可调电容器。不确定性理论下的优化将被纳入一般（非启发式）拓扑优化方法，以确保结果的广泛影响。该项目的教育计划包括本科和研究生教育的课程开发和研究机会。它还包括巴尔的摩理工高中的工程设计推广活动。研究人员将利用拓扑优化的视觉吸引力来吸引本科生和高中生参与该项目提供的研究机会。

The research objective of this award is to develop optimal design methodologies that account for manufacturing defects and demand uncertainties in small-scale structures. In engineering design, there is a natural tendency to push the limits of capacity of existing materials or employ new high performance materials. While this increases efficiency by using more sparse and slender elements, the designs also become more susceptible to flaws that may impair response. The research will address this issue by incorporating fabrication and demand uncertainties into methods of topology optimization, which is an emerging class of design tools for optimizing material distribution across a design domain. The PIs will exploit the relationships between the model for the system uncertainties and the mathematical forms used in the algorithms for topology optimization. Furthermore, methods will be explored for identifying those parameters whose uncertainties have a dominant influence on design. To ensure that the methods can be practically applied, fabrication is included in the scope of work. Tests results from fabricated specimens will be used to quantify fabrication errors and provide feedback for updating the uncertainty models. If successful, the results of this research will facilitate design of efficient structures with optimized and/or tailored reliability. Potential applications include high performance material microstructures, compliant mechanisms, and tunable capacitors. The optimization under uncertainty theory will be incorporated into a general (non-heuristic) topology optimization methodology to ensure wide impact of the results. The educational plan of the project includes curriculum development and research opportunities for undergraduate and graduate education. It also includes engineering design outreach activities to Baltimore Polytechnic High School. The investigators will leverage the visually appealing aspects of topology optimization to attract undergraduates and high school students to research opportunities provided by the project.