弹性地基梁动力响应分析的一种辛算法  

A Symplectic Algorithm for Dynamic Response Analysis of Elastic Foundation Beams

作　　者：黄伟江 

机构地区：[1]广州市建筑科学研究院,广州510440

出　　处：《广州建筑》2007年第4期13-16,共4页GUANGZHOU ARCHITECTURE

摘　　要：本文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弹性地基梁动力学的相空间(挠度、动量)非传统Hamilton型变分原理。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Lagrange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弹性地基梁的动力响应问题。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Wilson-θ法和Newmark-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 elastic foundation beam with linear damping is established, which can fully characterize the initial-boundary-value problem of this dynamics. And its Euler function has symplectic structure character. Based on this variational principle in phase space, a symplectic space finite element - time subdomain method is 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：TU470.3[建筑科学—结构工程]