Canonical Functions in Design Space

工程师们今天面临着前所未有的设计挑战和机遇，涉及新颖的应用和新的工程材料。通常只有有限的知识库可用于指导这些设计。除了来自优化的某些专门概念之外，缺乏一个通用的和有用的设计理论框架。一个严谨的力学理论，能够为一个复杂的问题确定可选的全局策略，这对设计工程师来说是非常有用的。在尝试开发新的理论和工具来帮助工程发现这种全球设计策略方面，已经取得了一些初步的成功。设计方案是通过寻找一组全局设计修改模式来产生的，这些模式会引起系统响应中相互正交的变化。每个正交方向称为规范设计方向。该提案要求支持继续测试梁是基于RITZ方法和符号计算（MACSYMA）。该方法的有限元实现和探索其在连续统问题中的应用将得到发展。这项工作将包括研究全局优化、拓扑优化和设计/响应关系的可视化方法。

Engineers are today faced with unprecedented design challenges and opportunities involving novel applications and new engineered materials. Often there is only a limited knowledge base available to guide these designs. Other than certain specialized concepts from optimization, a general and useful theoretical framework for design is lacking. A rigorous mechanics theory that is capable of identifying alternative global strategies for a complex problem would be very useful to design engineers. Some preliminary success had be forthcoming in an attempt to develop new theory and tools to help engineering discover such global design strategies. The design alternatives are generated by seeking a set of global design modification patterns which induce mutually orthogonal changes in the system response. Each orthogonal direction is termed a canonical design direction. This proposal requests support to continue to test the beams were based on the RITZ method and symbolic computation (MACSYMA). A finite element implementation of the method and explore its use in continuum problem will be developed. This work will include investigation of approaches to global optimization, optimization of topology, and visualization of design/response relations.