• 首页关于本刊投稿须知期刊订阅编委会期刊合作查询检索English

查看全文   查看HTML全文 下载PDF阅读器  

  任争争,梅雨辰,李鸿晶.微分求积法在结构动力分析中的应用[J].震灾防御技术,2018,(4):829-838, DOI:10.11899/zzfy20180410.

微分求积法在结构动力分析中的应用
摘要:    微分求积法(DQM)是1种求解微分方程初(边)值问题的数值方法,通常以较小的计算工作量即可获得较高的数值精度。这种方法应用于工程领域时多用来解决梁、板等结构的静力分析或结构特征值分析等问题,即对边值问题的微分方程的求解。结构动力分析属于初值问题,荷载和结构反应都具有特殊性,直接套用DQM求解边值问题并不能获得问题的解。本文尝试利用微分求积原理建立求解结构动力反应的具体方法。借鉴单元法的思想,将荷载持时划分为若干个时步,在每个时步内对动态荷载和结构反应进行离散,然后用DQM对时步逐个进行求解,得到体系在整个时域内的反应过程。通过对3种不同自振周期的线弹性单自由度体系在不同频率简谐激励下反应的计算,阐释了本文方法的可行性以及高精度、高效率的特点,通过数值试验确定了时步内相对较优的节点数,并为时步长度的选取提供了建议。
作者单位
任争争 南京工业大学, 土木工程学院, 南京 211816 
梅雨辰 南京工业大学, 土木工程学院, 南京 211816 
李鸿晶 南京工业大学, 土木工程学院, 南京 211816 
关  键  词:结构  动力分析  微分求积法  初值问题  参数选择
DOI:10.11899/zzfy20180410
基金项目:国家自然科学基金(51478222),高等学校博士学科点专项科研基金(20123221110011)
收稿日期:2017-11-25
作者简介:任争争,女,生于1992年。硕士研究生。主要从事工程抗震研究。E-mail:876982248@qq.com
通讯作者:李鸿晶,男,生于1966年。教授。主要从事地震工程学研究。E-mail:hjing@njtech.edu.cn
The Application of Differential Quadrature Method in Structural Dynamic Analysis
Abstract:      The differential quadrature method (DQM) is a numerical technique of solving initial/boundary value problems of differential equations and capable of obtaining a higher numerical accuracy with a smaller calculation workload. This method is often used to solve the problems of structural static analysis of beams and slabs or eigenvalue analysis when it is applied to the engineering fields, which is to solve the differential equation of the boundary value problems. Dynamic analysis of structures is an initial value problem as well as particular loads and structural response. As a result, applying the DQ method of solving the boundary value problem directly cannot obtain solution of problem. The principle of differential quadrature is applied to establish the specific method of solving structural dynamic response in this paper. By analogizing the idea of unit method, the duration of the load is divided into many time steps and dynamic load and structure are discretized in each time step, then the response of the system can be solved in the whole time domain by employing the DQ method step by step. The feasibility of this method and the characteristics of high precision and high efficiency are expounded by calculating the response of three linear elastic single-freedom-degree system of different natural vibration periods excited by simple harmonic loads of different frequencies. By means of numerical experiment, the optimal meshing scheme is determined and the suggestion for the time step is given.
Keywords:  Structure  Dynamic analysis  Differential quadrature method  Initial value problem  Choices of parameters
关闭