厚板动力响应分析的一种辛算法  

A SYMPLECTIC ALGORITHM FOR DYNAMIC RESPONSE ANALYSIS OF THICK PLATE

作　　者：黄伟江[1,2] 章学军[1,3] 罗恩[1] 

机构地区：[1]中山大学应用力学与工程系,广州510275 [2]广州市建筑科学研究院有限公司,广州510440 [3]广东省建筑科学研究院,广州510500

出　　处：《动力学与控制学报》2010年第2期155-159,共5页Journal of Dynamics and Control

基　　金：国家自然科学基金资助项目(10172097;10772203)~~

摘　　要：将厚板动力分析从Lagrange体系改换为Hamilton体系.根据古典阴阳互补和现代对偶互补的基本思想,首次建立了线性阻尼情形下厚板动力学的相空间非传统Hamilton变分原理.这种变分原理不仅能反映这种动力学初值—边值问题的全部特征,而且它的欧拉方程具有辛结构的特征.基于该变分原理,提出一种称之为辛空间有限元—时间子域法的辛算法.这种新方法是由空间域采用有限元法与时间子域采用La-grange插值多项式插值的时间子域法相结合而成.文中用这种辛算法分析了四种支承条件下厚板的动力响应问题.算例的计算结果表明,这种新方法的稳定性、收敛性、计算精度和效率都明显高于国际上常用的W ilson-θ法和Newm ark-β法.According to the basic idea of classical yin-yang complementarity and modern dual-complementarity,the unconventional Hamilton-type variational principle in phase space for dynamics of thick plate with linear damping was established,which can fully characterize the initial-boundary-value problem of this dynamics.And it＇s Euler function has symplectic structure character.Based on this variational principle in phase space,a symplectic space finite element-time subdomain method was presented.This new method is the result of combining finite element method in space domain with time subdomain method by applying the Lagrange interpolation polynomials as approximation to the time subdomain.The numerical results show that the stability,convergence,computational accuracy and efficiency of this new method excel obviously those of widely used Wilson-θ method and Newmark-β method.

关 键 词：相空间 非传统HAMILTON型变分原理 初值—边值问题 辛算法 动力响应 

分 类 号：O302[理学—力学]