动力学平衡方程的辛两步求解算法  

Symplectic two-step algorithms of FE dynamic equations

作　　者：杨蓉[1] 邢誉峰[1] 

机构地区：[1]北京航空航天大学固体力学研究所,北京100083

出　　处：《计算力学学报》2008年第6期882-886,共5页Chinese Journal of Computational Mechanics

摘　　要：基于线性多步方法的构造格式和辛变换,给出了动力学方程的两种辛两步法求解格式,它们分别具有四阶精度和二阶精度,但都只有二阶格式的计算量,因此四阶辛两步法具有较大的应用价值。对两种辛两步法和解析解进行了数值比较,证明了二阶精度辛两步格式在一定条件下就是欧拉中点保辛算法,或δ=0.5和α=0.25的Newmark辛格式。Two symplectic two-step solution algorithms of finite element dynamics equilibrium equations are presented, one of which has the fourth order accuracy, the phase is forward, and the accuracy of the other is the second order, the phase is backward. The calculation work of the fourth order two-step methods is not larger than that of Newmark symplectic method whose accuracy is of the second order, so there is an advantage of the fourth order two-step symplectic algorithm in the application to the practical calculation. The phase errors of the fourth order algorithm are compared in detail with that of Newmark symplectic method. Numerical results are given to illustrate the accuracy of the newly constructed twostep algorithms by comparing the obtained dynamic responses and energy with that of symplectic Newmark and analytical methods.

关 键 词：辛算法 多步法 直接积分方法 相位 

分 类 号：O343[理学—固体力学]