作　　者： ; ; ;

机构地区： 中山大学工学院应用力学与工程系

出　　处： 《力学学报》 2007年第5期672-677,共6页

摘　　要： 提出了求解非齐次动力方程特解的一种精细数值积分法,该方法与通解精细积分法具有相同精度.首先选取一个积分形式的非齐次方程特解,将积分区域划分为2^N份,并对之进行精细的数值积分;然后针对载荷为多项式、指数函数及三角函数的情况,将积分求和转化为一个递推过程,按此只需n次矩阵乘法就能计算出积分和,从而得到非齐次方程的特解.该方法的优点是能与通解的精细积分过程有机地结合起来,具有极高的精度和效率,同时还具有较广泛的适用范围.算例结果证明了该方法的有效性. 　A precise time integration（PTI）method proposed by Zhong WX for structural dynamics is widely used in solving structural dynamic equation and heat conduction equation.The merit of PTI is that it not only can take advantage of the full computer precision for general solution of ordinary differential homogeneous equation but is usually independent of time step length.However,difficulties arise when the algorithm is used for non-homogeneous dynamic systems.So far there is no such a method to calculate the particular solution as precise and efficient as PTI.Based on the basic idea of PTI,a general precise time integration method（GPTI） is presented to calculate the particular solution of non-homogeneous equation.Firstly,Duhamel＇s integral form of The special solution of non-homogeneous equation is given.And the domain of integration is separated into 2^N sections.Secondly,when the non-homogeneous term is polynomial,exponential function or trigonometric function,the integration can be converted to a recursion.So the particular solution in the form of integration is precisely obtained by only n-times matrix multiplication.In this paper,the process of PTI for general solution and that of GPTI for particular solution are closely integrated.For the latter can make full use of the middle result of the former,this combination is of a high computational merit.A simple further amendment to the particular solution is given.The amended particular solution of non-homogeneous equations is almost as precise as the general solution of homogeneous equation attained by PTI.The GPTI can be put into broad applications for the following two reasons.First,some methods become invalid for a requirement of calculating the inverse matrix,which sometimes is unstable,or even impossible.And in GPTI,the inverse matrix calculation is avoided. Second,when the non-homogeneous term is polynomials,trigonometric function or the exponential function, GPTI can be applied directly;for other forms of non-homogeneous term,they normally can be ex

关 键 词： 结构动力分析 精细积分 指数矩阵运算 数值积分 递推算法

领　　域： [理学] [理学]