结构地震反应DQ解法的两种数值格式  

Two Numerical Schemes of Differential Quadrature Analysis Procedure for Response of the Earthquake-resistant Structures

作　　者：李鸿晶[1] 廖旭[1] 王通[2] 

机构地区：[1]南京工业大学土木工程学院,江苏南京210009 [2]同济大学土木工程防灾国家重点实验室,上海200092

出　　处：《应用基础与工程科学学报》2011年第5期758-766,共9页Journal of Basic Science and Engineering

基　　金：国家自然科学基金重大研究计划"重大工程的动力灾变"(90815013);地震行业科研专项经费项目(200808081)

摘　　要：通过对时间计算域的离散化将结构地震时程分析问题转化为一系列初值问题的求解,建立了一种基于DQ原理的结构地震反应高精度数值分析方法.为了使DQ原理能够应用于任意变化的地震地面加速度激励下的结构动力分析问题,提出了两种数值方案———单时步格式和多时步格式.单时步格式要求假定时步内地面加速度的分布模式,并且需要对时步进行网格剖分;多时步格式直接利用地面加速度的离散信息构造数值格式,一次运算可获得多个时刻的反应值.数值试验表明:两种数值格式均可以获得较高的数值精度.对于单时步格式,可以通过采用较大步距的方式降低结构动力分析的计算工作量;对于多时步格式,可以通过时步数量的合理选择达到提高计算效率的目的.Based on the step-by-step procedure,a high order numerical approach was presented for structural dynamic analysis subjected to earthquake induced ground motion using differential quadrature（DQ）rule in time domain.Total two numerical schemes,the single-step scheme and the multi-step scheme,were proposed for the DQ-based analysis procedure to achieve the seismic response of structures.For the single-step scheme,the DQ rule was used during each time step,and the dynamic response at the final point of the step was calculated from the initial conditions existing at the beginning of the step and from the history of earthquake ground acceleration over the step,but the distribution function of the ground acceleration during the step must be assumed and at least one additional sampling point had to be interpolated within the discrete time step to fit in with the needs of the DQ method.In another way,the DQ rule was used directly among a time interval consisting of a few time steps due to multi-step scheme,so the response values at more than one discrete time points may be obtained simultaneously.Results from numerical analysis showed that both the DQ-based analysis procedures could be used to achieve the time history of response of the seismic structures with a high level of accuracy.The time steps employed in the single-step procedure could usually be made a little longer to reduce the computational efforts,and the efficiency will be improved due to the multi-step procedure because several time steps have been contained within each interval in which the DQ rule is substituted to give a equivalent static equation for the solution of the seismic response.

关 键 词：结构 地震时程分析 DQ原理 单时步格式 多时步格式 

分 类 号：O39[理学—工程力学]