拉压刚度不同桁架的动力参变量变分原理和保辛算法

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振动与冲击 ›› 2013, Vol. 32 ›› Issue (4) : 179-184.

论文

拉压刚度不同桁架的动力参变量变分原理和保辛算法

高强，张洪武，张亮，钟万勰

作者信息 +

Dynamic Parametric Variational Principle and Symplectic Algorithm for Truss with Different Tensional and Compressional Stiffness

Gao Qiang, Zhang Hongwu, Zhang Liang, Zhong Wanxie

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摘要

对于一些展开结构，为达到其设计性能，必须采用特殊的索、膜结构，这些索、膜部件表现出不同的拉压性质。具有拉、压不同性质的材料或结构的力学分析，体现出较强的非线性特征，需要针对这类问题发展有效的求解算法。本文建立了由拉压刚度不同杆单元组成的桁架结构的动力学参变量变分原理，将拉压刚度不同桁架问题的非线性动力分析转换为线性互补问题求解。结合时间有限元方法构造了求解此问题的保辛数值积分方法，此方法不需要迭代和刚度矩阵更新，避免了迭代求解方法的收敛问题，计算过程稳定、高效。

Abstract

For deployable structures, some special structures, such as cable and membrane, are used to achieve the design performance. These cable and membrane components show different tensile and compressive properties. The difference in tension and compression brings strong nonlinear behavior and effective numerical methods are needed. Dynamic parametric variational principle for truss with different stiffness in tension and compression is established and the nonlinear analysis of the truss can be transformed into a complementarity problem. Based on the time finite element method, a symplectic method for solving this problem is established. The numerical method proposed in this paper is stable and efficient, and does not need interaction and update of stiffness matrix.

导出引用

高强;张洪武;张亮;钟万勰. 拉压刚度不同桁架的动力参变量变分原理和保辛算法[J]. 振动与冲击, 2013, 32(4): 179-184

Gao Qiang;Zhang Hongwu;Zhang Liang;Zhong Wanxie. Dynamic Parametric Variational Principle and Symplectic Algorithm for Truss with Different Tensional and Compressional Stiffness[J]. Journal of Vibration and Shock, 2013, 32(4): 179-184