【摘要】 根据对偶互补的思想,建立了网架结构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。基于该变分原理,空间域采用有限元法与时间子域采用三次样条函数插值的时间子域法相结合,构造了求解网架结构动力响应的一种辛算法,给出了逐步递推计算格式。数值算例结果表明,这种新方法的稳定性、计算精度和效率都明显高于Wilson-θ法和Newmark-β法。更多还原

【Abstract】 According to the basic idea of dual-complementarity,the unconventional Hamilton-type variational principle in phase space for dynamic analysis of space truss structure was introduced,which can fully characterize this kind of dynamic initial-boundary-value problems.In addition,its Euler equation is of symplectic structure character.Based on this vairiational principle,a symplectic algorithm was presented,combining the finite element method in space domain with the time subdomain method,in which the cubic spline interpolation was applied as approximation.The results of numerical examples show that the method is a highly efficient method with better computational performance and superior ability of stability compared with Wilson-θ and Newmark-β methods.更多还原