Large-Scale Structural Optimization Using New Duality Based Methods

9523127饶本研究的主要目的是发展一类新的建模和计算方法来解决某些非常大规模的结构优化问题。特别是离散结构的拓扑设计，这是应用优化领域中最重要和最具挑战性的问题之一。这些新方法基于数学对偶原理，迄今为止已在弹性结构的最大刚度设计和塑性结构的最小重量设计两类应用中取得了显著的成功。这项工作将大大拓宽问题的类别，在那里类似的基于对偶性的方法可以应用。该项目的主要组成部分是由于各种应用程序中的原始对偶变换而产生的新的建模能力，以及利用所得最小-最大公式结构的高效，特定问题的非光滑算法。为了推进现代设计技术的前沿，研究人员不断寻求科学和数学工具，通过这些工具可以有效地计算出令人满意的（即可行的）甚至是最优的设计。虽然这在工程学科的各个领域都有许多非常成功的应用，但直到最近这些基于对偶性的方法出现之前，与离散结构的拓扑或配置设计相关的一类问题仍然没有得到明显的解决。这些方法的进一步发展将代表应用设计优化方面的重大进步，并将展示如何为各种汽车，民用和航空航天应用中的静态和动态承重结构生成新的和可证明的最佳拓扑。

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.