中文核心期刊
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中国科技核心期刊
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Journal of Chongqing Jiaotong University(Natural Science)

Journal of Chongqing Jiaotong University(Natural Science) ›› 2008, Vol. 27 ›› Issue (4): 502-507.

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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. 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

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. 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
  • 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)

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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

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

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