近似平衡多项式加速度动力显式算法  

Pseudo-balance polynomial acceleration explicit method

作　　者：李常青[1,2] 楼梦麟[2] 余志武[2] 蒋立忠[1] 

机构地区：[1]中南大学,长沙410075 [2]同济大学,上海200092

出　　处：《应用力学学报》2011年第5期475-479,553,共5页Chinese Journal of Applied Mechanics

基　　金：自然科学基金(5107835550938008);中央高校基本科研业务费基金(20117Q008)

摘　　要：利用已知初始时刻的信息,建立一种可以取到任意阶高精度的多项式加速度单步隐式算法。在该隐式方法中,待求解方程组系数矩阵中质量阵的系数远远大于阻尼阵和刚度阵的系数,略去非对角阻尼阵和非对角刚度阵对方程组的影响,得到一种近似平衡多项式加速度动力显式计算方法。此方法的精度主要由加速度多项式插值的项数、步长、质量阵的条件数、质量刚度比(质量阵和刚度阵的范数之比)决定。在此基础上给出了这种算法的通式,进行了精度分析,结果表明:如果时间步长h足够短,n次加速度近似平衡动力显式算法的精度可以达到O(hn+1)。算例采用5次加速度近似平衡显式算法,计算结果的精确性证明了本算法的可行性。Based on the known initial condition and known outer force history,a general formula of high order single-step conditional stable implicit polynomial acceleration method is presented in this paper,and it is shown that when higher order polynomial is used,higher accuracy can be achieved and the algorithm becomes more stable.In the linear equation set to be solved in the implicit method,mass matrix has a dominant 'weight' than damp and stiffness matrices.The off-diagonal parts of damp matrix and stiffness matrix are neglected;a pseudo-balance polynomial acceleration explicit method is derived.This explicit method’s accuracy depends on factors such as order of polynomial,time step size,condition number of the mass matrix,ratio of the norm of mass matrix to that of the stiffness matrix.If time step is small enough,pseudo-balance n-th order polynomial acceleration explicit method has a accuracy of O(h n+1).A 5th order polynomial acceleration explicit method is applied to a numerical example of two degree-of-freedom system and the accuracy of computation results prove the feasibility of this pseudo-balance polynomial acceleration explicit method.

关 键 词：多项式加速度方法 时程分析 显式算法 近似平衡 

分 类 号：O321[理学—一般力学与力学基础]