NUMERICAL SOLUTIONS OF ENERGY-CONSERVING TIME INTEGRATION METHODS
LI Yan1;WU Bin2;OU Jinping2,3
（1 College of Petroleum Engineering, China University of Petroleum(Beijing), Beijing 102249, China; 2 School of Civil Engineering, Harbin Institute of Technology, Harbin 150090, China; 3 Dalian University of Technology, Dalian 116024, China）
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.
2010, Vol. 29 
