Optimum Configurations of Three-Dimensional Mechanical Components with Behavior and Geometry Constraints

这项研究的目标是开发公式和求解策略，以生成相对于包括功能和几何标准在内的性能衡量标准而言最优的机械部件的形状和拓扑。研究将着重于以下几个方面：数学上严格的公式，它被形式化地描述为优化问题，其中设计空间包括对结构的不同拓扑描述，以及二维和三维组件的不同结构理想化；包括对结构力学行为的局部功能约束的公式，如应力、变形和屈曲的测量；以及适合于解决上述形式的问题的计算程序的开发。调查旨在促进在包括形状和拓扑的设计配置空间中进行系统搜索。这种探索的目标不仅是产生改进的、最优的或接近最优的设计，而且还产生对这个复杂的设计空间的理解，以及一类有意义的设计限制对设计问题的可接受解的影响。这项研究将产生设计工具，能够为相当大的一类机械设计问题提出近乎最佳的配置。这些想法在汽车或航空航天等行业有许多可能的应用。如果成功，这些工具将提供仅有的几种适用于设计早期阶段的方法之一。

The goal of this research is to develop formulations and solution strategies to generate the shape and topology of mechanical components that are optimal with respect to measures of performance that include functional as well as geometric criteria. The research will emphasize the following: mathematically rigorous formulations, which are posed formally as optimization problems in which the design space includes different topological descriptions of the structure, as well as different structural idealizations of two and three dimensional components; optimization problems that incorporate geometry and topology constraints; formulations that include local functional constraints on the mechanical behavior of the structure, such as measures of stress, deformation, and buckling; and the development of computational procedures suitable for the solution of problems cast in the form outlined above. The investigation seeks to facilitate a systematic search in a space of design configurations that includes shape and topology. The goal of such exploration is not only the generation of improved, optimal or near optimal designs, but also the generation of understanding of this complex design space and of the effect that a meaningful class of design restrictions has on admissible solutions to the design problem. The investigation will produce tools for design capable of suggesting near-optimal configurations for a reasonably large class of mechanical design problems. There are many possible applications of these ideas in industries such as automotive or aerospace. These tools will, if successful, provide one of only a handful of methods that are applicable in the early stages of design.