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Applied Mathematics and Mechanics (English Edition) ›› 2008, Vol. 29 ›› Issue (7): 933-941 .doi: https://doi.org/10.1007/s10483-008-0712-x

• Articles • 上一篇    下一篇

翘曲空间曲线梁自然坐标精确解

朱莉莉 1,2, 赵颖华1   

  1. 1.大连海事大学 道路与桥梁工程研究所，辽宁 大连 116026；
    2.大连交通大学 机械工程学院，辽宁 大连 116028
  • 收稿日期:2008-01-14 修回日期:2008-04-28 出版日期:2008-07-03 发布日期:2008-01-01
  • 通讯作者: 赵颖华

Exact solution for warping of spatial curved beams in natural coordinates

ZHU Li-li 1,2, ZHAO Ying-hua1   

  1. 1. Institute of Road and Bridge Engineering, Dalian Maritime University,Dalian 116026, Liaoning Province, P. R. China;
    2. School of Mechanical Engineering, Dalian Jiaotong University,Dalian 116028, Liaoning Province, P. R. China
  • Received:2008-01-14 Revised:2008-04-28 Online:2008-07-03 Published:2008-01-01
  • Contact: ZHAO Ying-hua

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摘要： 基于现有空间曲线桥梁理论，考虑与扭转有关的翘曲变形和横向剪切变形的影响，建立了自然标架下空间曲线梁的内力和变形的解析解答。将该解答应用于受均布扭矩和竖向分布荷载的平面曲线梁的分析，将所得结果与Heins解答进行比较，证明了理论的正确，并应用该理论分析了解析式中翘曲和横向剪切变形项的影响。

关键词: 自然坐标, 曲线梁, 翘曲, 复杂荷载, 解析解

Abstract: The purpose of the paper is to present an exact analytical solution of a spatial curved beam under multiple loads based on the existing theory. The transverse shear deformation and torsion-related warping effects are taken into account. By using this solution, a plane curved beam subjected to uniform vertical loads and torsions is analyzed. Accuracy and efficiency of present
theory are demonstrated by comparing its numerical results with Heins' solution. Furthermore, the effects of the transverse shear deformation and torsion-related warping on deformation of the beam are discussed.

Key words: curved beam, multiple loads, warping, natural coordinate, analytical solution

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