Mathematical Sciences: Duality Theory in Finite Deformation Nonsmooth Mechanics and Numerical Approaches

数学科学：有限变形非光滑力学中的对偶理论和数值方法

• 批准号: 9400565
• 负责人: David Gao
• 金额: $ 3万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1994
• 资助国家: 美国
• 起止时间: 1994-07-15 至 1997-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9400565&HistoricalAwards=false
• 关键词: Mathematical; Sciences; Duality; Theory; Finite

Gao 9400565 Based on the complementarity theory developed by Gao- Strang in 1988-89, the objective of this proposed research is to offer a comprehensive study on the duality theory in nonsmooth mechanics and the related numerical methods for finite deformation systems. Topics will include: (1) Nonsmooth plastic flow and structural limit analysis; (2) Nonlinear buckling analysis for plates and shells; (3) Control problems and optimal design of smart materials and structures; (4) Complementary finite element method for nonsmooth optimization. Finite deformation nonsmooth mechanics has been found more and more important applications in smart structural analysis, civil and aerospace engineering. Direct method for solving nonlinear and nonsmooth systems has always presented serious difficulties for mathematicians and engineers. The dual approach andcomplementary finite element method, however, possess a great of advantages. We can expect that the results of this proposed research will provide new insight to the nonsmooth mechanics, variational methods, finite deformation theory, nonlinear optimization theory and numerical methods.

Gao 9400565基于高斯特朗在1988年至1989年发展的互补理论，本研究的目的是全面研究非光滑力学中的对偶理论和有限变形系统的相关数值方法。内容包括：(1)非光滑塑性流动和结构极限分析；(2)板壳的非线性屈曲分析；(3)智能材料和结构的控制问题和优化设计；(4)非光滑优化的互补有限元方法。有限变形非光滑力学在智能结构分析、土木工程和航天工程中有着越来越重要的应用。求解非线性非光滑系统的直接方法一直是困扰数学家和工程技术人员的难题。然而，对偶方法和互补有限元方法具有很大的优势。可以预期，本文的研究结果将为非光滑力学、变分方法、有限变形理论、非线性优化理论和数值方法提供新的见解。