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

这项研究的目标是开发配方， 解决方案的战略，以产生的形状和拓扑结构， 机械部件，最佳的措施， 性能，包括功能以及几何标准。 该研究将强调以下几点： 严格的公式，这是正式提出的优化， 其中设计空间包括不同拓扑的问题 结构的描述，以及不同的结构 二维和三维元件的理想化;优化 包含几何和拓扑约束的问题; 包括局部功能约束的公式 结构的机械性能，例如应力的测量， 变形和屈曲;以及计算 程序适合于解决问题的形式铸造 上面概述的。 调查旨在促进系统搜索， 包括形状和拓扑结构的设计配置空间。 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， 对这个复杂的设计空间的理解 一个有意义的设计限制类， 设计问题的解决方案。 调查将产生 能够建议接近最佳配置的设计工具 对于相当大的一类机械设计问题。 那里 这些想法有很多可能的应用， 如汽车或航空航天。 这些工具如果成功， 提供了少数几种适用于 设计的早期阶段。

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.