Timoshenko组合梁动力特性与瞬态响应的求积元分析  

Quadrature element analysis on dynamic characteristics and transient responses of Timoshenko composite beams

作　　者：李晓伟[1] 何光辉 LI Xiaowei;HE Guanghui(Songjiang Campus,Shanghai Open University,Shanghai 201600,China;School of Port and Transportation Engineering,Zhejiang Ocean University,Zhoushan 316022,China)

机构地区：[1]上海开放大学松江分校,上海201600 [2]浙江海洋大学港航与交通运输工程学院,浙江舟山316022

出　　处：《振动与冲击》2018年第18期257-265,共9页Journal of Vibration and Shock

基　　金：国家自然科学基金青年科学基金(51606168);上海开放大学2018年度学科研究课题(KX1815)

摘　　要：为了提高有限元法(FEM)在部分作用组合梁动力特性与瞬态响应分析中的计算效率。通过微分求积法离散组合梁基本未知量及其导数,利用Timoshenko组合梁动力问题的虚功原理建立其自由振动与瞬态分析的微分求积元方程;为了便于对比新建的求积元法(QEM)与FEM的计算效率,同时给出了抛物线插值位移法有限单元方程,在验证所建立的有限元与求积元算法正确性的基础上,对比了FEM与QEM在组合梁自由振动特征值分析与直接积分法地震时程分析中的计算效率。数值结果表明:QEM较FEM在组合梁固有频率分析中提速可达479倍,在地震时程分析中可提速42倍。Aiming at improving the efficiency of finite element method(FEM)in the dynamic characteristics and transient responses analyses of partial-interaction composite beams,firstly,the primary unknowns and their derivatives of the composite beams were discretized by the differential quadrature method,and the differential quadrature element equations were formulated,using the principle of virtual work on the Timoshenko composite beams’dynamic problem.For comparing the analysis efficiency between the proposed quadrature element method(QEM)and FEM,parabolic interpolation finite element equations were also provided.Then,the computational efficiency of FEM and QEM were compared through the eigenvalue analysis on free vibration and the direct integration analysis on seismic time-history,after the verification of the proposed FEM and QEM algorithms.The numerical results show that comparing with the FEM,the efficiency of the natural frequency analysis is increased by 479 times by using the presented QEM and that for the time-history response prediction by 42 times.

关 键 词：Timoshenko组合梁 微分求积元 有限元 动力分析 CPU时间 

分 类 号：TU311[建筑科学—结构工程]