结构动力方程的离散精细积分格式  

Discrete precise time-integration method for structural dynamic analysis

作　　者：孙建鹏[1,2] 李青宁[1] 

机构地区：[1]西安建筑科技大学土木工程学院,陕西西安710055 [2]西部建筑科技国家重点实验室(筹),陕西西安710055

出　　处：《西安建筑科技大学学报（自然科学版）》2010年第1期42-46,共5页Journal of Xi'an University of Architecture & Technology(Natural Science Edition)

基　　金：陕西省自然科学基础研究计划项目(2005E236);陕西省教育厅专项科研计划项目(05JK235)

摘　　要：精细积分方法在数值上能够得到逼近于精确解的结果,但是对于非齐次动力方程涉及到矩阵求逆的困难,计算精度取决于非齐次项的拟合精度等问题.提出了离散精细积分格式,将非齐次动力方程转化为齐次动力方程,在实施精细积分过程中不必进行矩阵求逆.整个积分方法的精度取决于非奇次项的离散时间步长.这种方法理论上可实现任意高精度,而且计算效率较高,数值例题显示了方法的有效性.The precise time-integration method can give precise numerical results approaching the exact solution at the integration points. However, difficulty arises when the algorithm is applied to the non-homogeneous dynamic systems due to the inverse matrix calculation and the simulation of the applied loading. A new precise time-integration method i.e. the discrete precise time-integration method is proposed. The original equations are converted into homogeneous equations, thus the new method avoids the inverse matrix calculation. The accuracy of the method depends on the length of the timestep. The order of aceuracy is controllable in the method. Numerical examples are given to demonstrate the validity and efficiency of the method.

关 键 词：精细积分 离散时间步长 中值法 均值法 黄金分割法 

分 类 号：TU311.3[建筑科学—结构工程]