剪切效应梁单元刚度和质量矩阵的推导及应用

重庆交通大学学报（自然科学版） ›› 2008, Vol. 27 ›› Issue (4): 502-507.

剪切效应梁单元刚度和质量矩阵的推导及应用

杜柏松¹, 项海帆², 葛耀君², 朱乐东²

1. 重庆交通大学土木建筑学院, 重庆 400074;
2. 同济大学桥梁工程系, 上海 200092

收稿日期:2007-04-06 修回日期:2008-03-06 出版日期:2008-08-20 发布日期:2016-11-07
作者简介:杜柏松(1976-),男,湖北英山人,副教授,博士后,研究方向:桥梁加固与施工监控。E-mail:sbaisongdu@gmail.com;手机:13668008956。
基金资助:
国家自然科学基金项目(50538050)

Derivation and Application of 3D-Beam's Element Stiffness and Mass Matrix with Shear Effect

DU Bai-song¹, XIANG Hai-fan², GE Yao-jun², ZHU Le-dong²

1. School of Civil Engineering & Architecture, Chongqing Jiaotong University, Chongqing 400074, China;
2. Department of Bridge Engineering, Tongji University, Shanghai 200092, China

Received:2007-04-06 Revised:2008-03-06 Online:2008-08-20 Published:2016-11-07

摘要/Abstract

摘要： 从工程梁理论中的梁位移微分方程出发直接推导出考虑剪切效应的空间梁单元的刚度矩阵,并从动力荷载的虚功原理出发推导出考虑剪切效应的其质量矩阵。编制了简单的有限元程序去验证,通过计算实例分别比较考虑剪切效应和不考虑剪切效应对结构固有频率的影响,结果表明在剪切系数较大时,不考虑剪切效应会引起较大的误差。

关键词: 剪切效应, 单元刚度矩阵, 单元质量矩阵, 剪切系数

Abstract: 3D-beam's displacement's differential equation was used to deduce the element stiffness matrix with shear effect,and dynamical load's principle of virtual work was employed to illustrate the 3D-beam's element mass matrix.A valued example was represented to demonstrate the influence of natural frequency between shear effect and non-shear effect respectively.The results indicate that it's necessary to consider the shear effect when the structures' shear coefficients can't be ignored.

Key words: shear effect, element stiffness matrix, element mass matrix, shear coefficient

中图分类号:

U441

杜柏松, 项海帆, 葛耀君, 朱乐东. 剪切效应梁单元刚度和质量矩阵的推导及应用[J]. 重庆交通大学学报（自然科学版）, 2008, 27(4): 502-507.

DU Bai-song, XIANG Hai-fan, GE Yao-jun, ZHU Le-dong. Derivation and Application of 3D-Beam's Element Stiffness and Mass Matrix with Shear Effect[J]. Journal of Chongqing Jiaotong University(Natural Science), 2008, 27(4): 502-507.