薄板动力学相空间非传统Hamilton变分原理与辛算法  

UNCONVENTIONAL HAMILTON VARIATIONAL PRINCIPLE IN PHASE SPACE AND SYMPLECTIC ALGORITHM FOR DYNAMIC ANALYSIS OF THIN PLATES

作　　者：刘淼[1] 罗恩[2] 仲政[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092 [2]中山大学应用力学与工程系,广州510275

出　　处：《固体力学学报》2007年第2期207-211,共5页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金(10432030;10172097);高校博士点基金(20030558025)资助

摘　　要：将弹性薄板动力分析从Lagrange体系改换为Hamilton体系.通过罗恩提出的一条简单而统一的途径,建立了弹性薄板动力学的相空间非传统Hamilton变分原理,并从该原理推导出相应的Hamilton正则方程、边界条件与初始条件.然后基于这种相空间非传统Hamilton变分原理,提出弹性薄板动力响应分析的辛空间有限元-时间子域法,文中数值结果表明,这种方法的计算精度与效率都明显高于常用的Wilson-θ法和Newmark-β法.The Lagrange system for dynamic analysis of elastic thin plates is transferred to the Hamilton system. According to a simple and unified way proposed by Luo, the unconventional Hamilton variational principle in phase space for dynamics of elastic thin plates is established, and the Hamilton canonical equations, boundary and initial conditions can be derived from this variational principle. Based on the unconventional Hamilton variational principle, the symplectic space finite element-time subdomain method is proposed. From the results of the numerical example, it can be seen that the accuracy and the computational efficiency of the method excel obviously those of widely used Wilson-θ and Newmark-β method.

关 键 词：弹性薄板 HAMILTON体系 相空间非传统Hamilton变分原理 动力响应分析 辛空间有限元-时间子域法 

分 类 号：O343[理学—固体力学]