弹性梁动力响应分析的一种辛算法

A Symplectic Algorithm for Dynamic Response Analysis of Elastic Beams

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自然辛结构。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。文中算例的计算结果表明 ,这种新方法的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 beam with linear damping is established, which can fully characterize the initial_boundary_value problem of this dynamics. And its Euler equations possess natural symplectic structure. 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 computational accuracy and efficiency of this new method excel obviously those of widely used Wilson_ θ method and Newmark_ β method.