非线性动力分析避免状态矩阵求逆的精细积分多步法  

PRECISE INTEGRATION MULTI-STEP METHOD FOR NONLINEAR DYNAMIC EQUATIONS TO AVOID CALCULATING INVERSE OF STATE MATRIX

作　　者：王海波[1] 余志武[1] 陈伯望[2] 

机构地区：[1]中南大学土木建筑学院,长沙410075 [2]湖南城市学院土木工程学院,湖南益阳413000

出　　处：《振动与冲击》2008年第4期105-107,116,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金资助项目(50438020,10572153);湖南省教育厅资助科研项目(05B063,05A070)

摘　　要：将精细积分法和预估-校正Adams-Bashforth-Moulton多步法相结合,提出了高精度的精细积分多步法,对非线性动力状态方程进行求解,避免了对状态矩阵求逆。该方法与精确值和现有Adams多步法进行比较,数值计算结果表明该方法是一种高精度、高效率和稳定性较好的方法。该方法可方便地进行不同阶次的积分运算。Combining the precise integration method and Adams-Bashforth-Moulton predict-correct multi-step method,a highly precise integration method for nonlinear dynamic equations is put forward.It is a multi-step method to avoid calculating the inverse of the state matrix.Compared with the present Adams-Bashforth-Moulton method,the numerical results show that the proposed method is more highly accurate and efficient,capable of keeping computation stability,and suitable for different order numerical inteqrations.

关 键 词：非线性动力方程 多步法 预估一校正Adams—Bashforth—Moulton法 精细积分法 预估一校正法 

分 类 号：TU311.3[建筑科学—结构工程] O322[理学—一般力学与力学基础]