Large-Scale Structural Optimization Using New Duality Based Methods

使用新的对偶性方法进行大规模结构优化

• 批准号: 9523127
• 负责人: Jagannatha Rao
• 金额: $ 24.99万
• 依托单位: University of Houston
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-10-01 至 2000-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9523127&HistoricalAwards=false
• 关键词: Large; Scale; Structural; Optimization; Using

9523127 Rao The principal objective of this research is to develop a new class of modeling and computational methods to solve certain very large-scale structural optimization problems. In particular, the focus is on the topology design of discrete structures, which are recognized as one of the most important and challenging problems in the field of applied optimization. These new methods are based on the principles of mathematical duality and have so far been deployed with remarkable success in two application classes: the maximum stiffness design of elastic structures and the minimum weight design of plastic structures. This work will significantly broaden the class of problems where similar duality-based methods can be applied. The major components of this project are the new modeling capability due to primal-dual transformations in various applications and the efficient, problem specific nonsmooth algorithms that exploit the structure of the resulting min-max formulations. In advancing the frontiers of modern design techniques, researchers are constantly seeking scientific and mathematical tools by which satisfactory (i.e., feasible) or even optimal designs can be efficiently computed. While this has lead to numerous very successful applications in a wide cross-section of engineering disciplines, the class of problems related to the topology or configuration design of discrete structures had remained distinctly unsolved until the recent emergence of these duality-based methods. Further development of these methods will represent a significant advance in applied design optimization, and will show how new and provably optimum topologies can be generated for static and dynamic load-bearing structures in a variety of automotive, civil and aerospace applications.

小行星9523127 本研究的主要目标是开发一类新的建模和计算方法来解决某些超大规模结构优化问题。 特别是，重点是离散结构的拓扑设计，这是公认的应用优化领域中最重要和最具挑战性的问题之一。 这些新的方法是基于数学对偶的原则，迄今已部署在两个应用类显着的成功：弹性结构的最大刚度设计和塑性结构的最小重量设计。 这项工作将显着扩大类的问题，类似的基于对偶的方法可以应用。该项目的主要组成部分是新的建模能力，由于原始对偶变换在各种应用程序和高效，具体问题的非光滑算法，利用结构的最小最大配方。 在推进现代设计技术前沿的过程中，研究人员不断寻求科学和数学工具，通过这些工具，可行的）或甚至最优的设计可以被有效地计算。 虽然这导致了许多非常成功的应用在广泛的横截面的工程学科，这类问题的拓扑结构或配置设计的离散结构仍然明显未解决，直到最近出现的这些对偶为基础的方法。 这些方法的进一步发展将代表应用设计优化的一个重大进步，并将展示如何在各种汽车，民用和航空航天应用中为静态和动态承载结构生成新的和可证明的最佳拓扑结构。