能量守恒逐步积分方法数值解研究

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振动与冲击 ›› 2010, Vol. 29 ›› Issue (5) : 16-19,3.

论文

能量守恒逐步积分方法数值解研究

李妍1;吴斌2;欧进萍2,3

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NUMERICAL SOLUTIONS OF ENERGY-CONSERVING TIME INTEGRATION METHODS

LI Yan1;WU Bin2;OU Jinping2,3

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文章历史 +

摘要

由于能量守恒逐步积分方法对非线性结构具有很好的无条件稳定性，对Simo能量法、Hughes能量法两类能量守恒逐步积分方法进行了研究，以期获得适合非线性结构的最优算法。首先对两种方法的平衡方程进行对比，分析了它们保证系统能量守恒进而保证无条件稳定的方式。然后从理论上研究了两种方法求解动态平衡方程时得到的数值解,结果表明Simo能量法的平衡方程有唯一解，而Hughes能量法存在多解从而可能会导致求解时出现不合理解。数值算例结果验证了理论分析的正确性，同时表明Simo能量法的计算效率优于Hughes能量法和经典的平均加速度法。理论分析与数值算例结果表明Simo能量法优于Hughes能量法和平均加速度法。

Abstract

Two energy-conserving time integration methods developed by Simo and Hughes respectively are studied due to their excellent unconditional stability for general nonlinear structures, with the purpose of obtaining the optimal method. Firstly the ways of conserving system energy, hence ensuring unconditional stability, are analyzed by comparing the equilibrium equations of the two methods. Then numerical solutions of the two methods applied to solving dynamical balance equations are studied theoretically. The theoretical analyses show that the balance equation of Simo method has the only one solution, while Hughes method may induce multiple solutions which may lead to unreasonable solution when solving balance equations. The results of numerical example demonstrate the correction of the theoretical analyses and show higher computation efficiency of Simo method than Hughes method and typical average acceleration method. The results of theoretical analyses and numerical example exhibit advantages of Simo method over Hughes method and average acceleration method.

导出引用

李妍;吴斌;欧进萍;. 能量守恒逐步积分方法数值解研究[J]. 振动与冲击, 2010, 29(5): 16-19,3

LI Yan;WU Bin;OU Jinping;. NUMERICAL SOLUTIONS OF ENERGY-CONSERVING TIME INTEGRATION METHODS[J]. Journal of Vibration and Shock, 2010, 29(5): 16-19,3