深梁动力响应分析的一种辛算法  

A Symplectic Algorithm for Dynamic Response Analysis of Timoshenko Beam

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,广东广州510275 [2]广东省建筑科学研究院,广东广州510500 [3]广州市建筑科学研究院,广东广州510440

出　　处：《中山大学学报（自然科学版）》2010年第4期33-37,共5页Acta Scientiarum Naturalium Universitatis Sunyatseni

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深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。用这种辛算法分析了4种支承条件下深梁的动力响应问题。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 modem dual-comple- mentarity, the unconventional Hamilton-type variational principle in phase space for dynamics of Timoshenko beam with linear damping is 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 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 obviously improve those of widely used Wilson-θand Newmark-β methods.

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：O322[理学—一般力学与力学基础]