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

该奖项的研究目标是创建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，以便可以对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，我们将创建一个新的方法：使用有效的高阶元素进行分析，并在每个元素中嵌入多个密度变量，以实现高分辨率的拓扑表示。因此，我们的研究目标是了解分析元素的顺序和每个元素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一种形式化的方法，使高效、稳定的高-该研究的成功完成，将对拓扑学的理论突破和实际应用起到积极的推动作用优化.从理论上讲，本研究为拓扑优化提供了一种新的方法：使用高阶多密度单元。它代表了拓扑优化方法的重大转变，传统上只使用单密度线性元件。实际上，这项研究将导致一个有效的方法，高分辨率的拓扑优化的3D结构，这是昂贵的与现有的方法。这项研究将积极影响从汽车，航空航天到制造业的许多行业，这些行业迫切需要3D结构的拓扑优化。由此产生的方法，当应用于多物理场系统的混合动力汽车的发展，将提供一个关键的使能技术，为现代车辆系统的进步。该方法还将使得能够利用增材制造能力来成本有效地制造先前难以制造的拓扑优化的几何形状，以用于航空和运输工业中的实质性性能改进。

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.