High-Resolution 3D Topology Optimization via Multi-Density Higher-Order Elements

该奖项的研究目标是创造一种高效的计算机方法，用于三维(3D)结构的高分辨率拓扑优化，以便对3D中的精细细节进行拓扑优化。该方法通过将拓扑表示与分析元素解耦，提高了拓扑设计的效率和分辨率。更具体地说，我们将创建一种新的方法：使用高效的高阶单元进行分析，并在每个单元中嵌入多个密度变量以实现高分辨率的拓扑表示。因此，我们的研究目的是了解分析单元的顺序和每个单元内密度变量的分布如何影响最终的设计分辨率、分析效率和优化稳定性，并在此基础上进一步开发出一种能够高效、稳定地进行高分辨率三维拓扑优化的形式化方法。从理论上讲，本研究将为拓扑优化提供一种新的方法：使用高阶多密度单元。它代表了传统上只使用单密度线性单元的拓扑优化方法的重大转变。实际上，这项研究将为三维结构的高分辨率拓扑优化提供一种有效的方法，而现有方法的成本过高。这项研究将对汽车、航空航天、制造业等迫切需要进行三维结构拓扑优化的行业产生积极的影响。由此产生的方法，当应用于混合动力汽车开发的多物理系统时，将为现代汽车系统的进步提供关键的使能技术。该方法还将能够利用附加制造能力，以成本效益的方式制造以前难以制造、拓扑优化的几何形状，从而大幅提高航空和运输行业的性能。

The research objective of this award is to create an efficient computer method for high-resolution topology optimization of structures in three-dimension (3D) so that fine details in 3D can be topologically optimized. The new approach aims to improve the efficiency and resolution of topological design by decoupling the topology representation from the analysis elements. More specifically, we will create a new method: using efficient higher-order elements for analysis and embedding multiple density variables in each element for high-resolution topology representation. Our research objective is thus to understand how the order of the analysis elements and the distribution of density variables within each element affect the resulting design resolution, the analysis efficiency and optimization stability, and upon which to further develop a formal method that enables efficient and stable high-resolution 3D topology optimization.Successful completion of this research would result in both theoretical breakthroughs and practical advances in topology optimization. Theoretically, this research would offer a new method for topology optimization: the use of higher-order multi-density elements. It represents a significant shift in topology optimization methods where traditionally only single-density linear elements are used. Practically, this research would lead to an efficient method for high resolution topology optimization of 3D structures, which is prohibitively expensive with existing methods. This research would positively impact a host of industries ranging from automotive, aerospace to manufacturing industry where topology optimization of 3D structures are urgently needed. The resulting method, when applied to multiphysics systems in hybrid-vehicle development, would provide a key enabling technology for the advancement of modern vehicle systems. The method would also enable the utilization of additive manufacturing capability to cost-effectively fabricate previously difficult to-manufacture, topologically optimized geometries for substantial performance improvements in aviation and transportation industry.