网架结构动力分析的三次样条辛算法

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (15) : 89-94.

论文

网架结构动力分析的三次样条辛算法

李纬华，王堉，罗恩

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A cubic spline symplectic algorithm for dynamic analysis of space truss structure

LI Wei-hua, WANG Yu, LUO En

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文章历史 +

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。

Abstract

According to the basic idea of dual-complementarity, the unconventional Hamilton-type variational principle in phase space for dynamics of space truss structure is established, which can fully characterize the initial-boundary-value problem of this dynamics．In addition, the Euler function of this variation principle has symplectic structure character．Based on this vairiational principle, a symplectic algorithm which is the result of combining finite element method in space domain with time subdomain method by applying the cubic spline interpolation as approximation to the time subdomain is conducted. The results of numerical example show that the method is a highly efficient method with better computational performance and superior ability of stability compared to Wilson-θ and Newmark-β methods.

导出引用

李纬华;王堉;罗恩. 网架结构动力分析的三次样条辛算法[J]. 振动与冲击, 2013, 32(15): 89-94

LI Wei-hua;WANG Yu;LUO En. A cubic spline symplectic algorithm for dynamic analysis of space truss structure[J]. Journal of Vibration and Shock, 2013, 32(15): 89-94