结构动力方程求解中隐式格式向显式格式的转换  

Transformation of implicit method to explicit method for solving structural dynamic equation

作　　者：李常青[1,2] 楼梦麟[2] 蒋丽忠[1] 

机构地区：[1]中南大学土木工程学院建筑工程系,长沙410000 [2]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《振动与冲击》2012年第13期91-94,共4页Journal of Vibration and Shock

基　　金：国家自然科学基金(51078355;50938008);中南大学自由探索计划资助

摘　　要：以广义加速度隐式算法为例,指出常用隐式算法可转换为显式算法。转换过程主要包括三个步骤:首先是对隐式求解的耦联线性方程组的系数矩阵取逆,然后将此逆矩阵在单位矩阵附近进行级数展开,最后进行级数截断。以常加速度方法的显式化过程为例,详细阐述隐式算法转换为显式算法的过程,着重介绍级数展开的项数对计算精度的影响,以及转换过程中时间步长必须同时满足算法的稳定性和级数收敛条件。揭示隐式算法与显式算法之联系,使可按高精度隐式算法得到与其相伴随的高精度显式算法。Taking the generalized acceleration method as an example, it was proved that implicit method could be transformed to associated explicit method by solving the inverse of coefficient matrix and then through series expansion and series truncation of the inverse matrix. The corresponding transformation process with respect to the constant acceleration method was detailedly described. After revealing the relationship between implicit method and explicit method, a kind of implicit methods with high accuracy and efficiency could be obtained.

关 键 词：广义线性加速度法 动力分析 显式算法 隐式算法 稳定性 

分 类 号：O321[理学—一般力学与力学基础]