夹层梁动力响应分析的一种辛算法  

A Symplectic Algorithm for Dynamic Response Analysis of Sandwich Beams

作　　者：章学军[1,2] 黄伟江[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]广东省建筑科学研究院,广州510500 [3]广州市建筑科学研究院,广州510440

出　　处：《建筑科学》2010年第1期56-59,63,共5页Building Science

基　　金：国家自然科学基金资助项目(10172097;10772203)

摘　　要：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况下Reissner夹层梁动力学的相空间非传统Hamilton型变分原理。这种变分原理不仅能反映此类动力学初值—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。文中用这种辛算法进行了四种支承条件下夹层梁的动力响应分析。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 unconven- tional Hamilton-type variational principle in phase space for dynamics of Reissner sandwich 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 in- terpolation polynomials as approximation to the time subdomain. The numerical results show that this new method is obviously superior to the widely used Wilson-θ and Newmark-β methods in the stability, convergence, computational accuracy and efficiency.

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：TU311.4[建筑科学—结构工程] TU323.3