NUMERICAL SOLUTIONS OF ENERGY-CONSERVING TIME INTEGRATION METHODS

LI Yan;WU Bin;OU Jinping;

Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (5) : 16-19,3.

PDF(1552 KB)
PDF(1552 KB)
Journal of Vibration and Shock ›› 2010, Vol. 29 ›› Issue (5) : 16-19,3.
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NUMERICAL SOLUTIONS OF ENERGY-CONSERVING TIME INTEGRATION METHODS

  • LI Yan1;WU Bin2;OU Jinping2,3
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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.

Key words

energy-conserving time integration method / numerical stability / numerical solution / computation efficiency of iteration / nonlinear

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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
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