单步块格式在结构动力响应分析中的应用  

Application of Single-Step Block Format in Structural Dynamic Response Analysis

作　　者：付兆隆 刘冬兵 徐光晨 王永 FU Zhao-long;LIU Dong-bing;XU Guang-chen;WANG Yong(Electric and New Energy Institute,China Three Gorges University,Yichang Hubei 443002,China;College of Mathematics and Computer,Panzhihua University,Panzhihua Sichuan 617000,China;UHV Converter Station Branch of State Grid Shanghai Municipal Electric Power Company,Shanghai 201413,China)

机构地区：[1]三峡大学电气与新能源学院,湖北宜昌443002 [2]攀枝花学院数学与计算机学院,四川攀枝花617000 [3]国网上海市电力公司特高压换流站分公司,上海201413

出　　处：《计算机仿真》2024年第11期380-385,415,共7页Computer Simulation

基　　金：四川省科技厅应用基础研究项目(2019YJ0683);攀枝花学院校级项目(202207);攀枝花学院院级项目(Y2021-03);国网上海市电力公司科技项目(B3090V220001)。

摘　　要：动力时程响应的典型计算方法都是低阶数值算法,其对计算步长比较敏感,通常要采用较小的计算步长才能满足动力响应分析精度要求。为此将单步块格式用于多自由度阻尼体系的动力响应分析中。借鉴积分求微法的基本思想,将动力方程非齐次项Duhamel积分项转换成一个微分方程,并采用单步块格式进行求解,同时采用精细积分法来计算各时间节点的矩阵指数,对于一个给定的时间段,s级的单块块格式可以同时计算出s个时间步长的动态响应,因此具有较高并行计算度,且具有较强数值稳定性且保持显式算法的特征。数值试验结果表明,上述算法具有较强数值稳定性,数值计算精度高,在较大的时间步长下具有较高的计算效率且计算结果稳定可靠。The typical calculation methods of dynamic time history response are low-order numerical algorithms,which are more sensitive to the calculation step size,and usually a smaller calculation step size is required to meet the accuracy requirements of the dynamic response analysis.In this paper,the one-step block method is used in the dy-namic response analysis of a multi-degree-of-freedom damping system.Drawing lessons from the basic idea of the integration differential method,the Duhamel integral term of the non-homogeneous term of the dynamic equation is converted into a differential equation,and the one-step block method is used to solve the problem.At the same time,the precise integration method is used to calculate the matrix exponent of each time node.For a given period,the s-stage one block scheme can calculate the dynamic response of s time-steps at the same time,so it has a high degree of parallel computing,and has strong numerical stability and maintains the characteristics of an explicit algorithm.Numerical test results show that the algorithm has strong numerical stability,high numerical calculation accuracy,high calculation efficiency under a large time step,and stable and reliable calculation results.

关 键 词：动力响应分析 单步块格式 矩阵指数 高阶算法 

分 类 号：TP301.6[自动化与计算机技术—计算机系统结构]