自然弯扭梁广义翘曲坐标的求解

虞爱民; 易明

自然弯扭梁广义翘曲坐标的求解

虞爱民¹,
易明²

1.
同济大学教育部固体力学重点实验室,上海 200092;2.同济大学汽车学院,上海 200092

详细信息

作者简介:
虞爱民(1948- ),男,江苏人,教授(联系人.Tel:+86-21-62276787;E-mail:aimin.yu@163.com)

中图分类号: TB125
计量
- 文章访问数: 2711
- HTML全文浏览量: 193
- PDF下载量: 553
- 被引次数: 0
出版历程
- 收稿日期: 2002-12-10
- 修回日期: 2004-06-11
- 刊出日期: 2004-10-15

Solution of Generalized Coordinate for Warping for Naturally Curved and Twisted Beams

YU Ai-min¹,
YI Ming²

1.
Key Labor atory of Solid Mechanics of MOE,Tongji University, Shanghai 0009, P. R. China;

摘要

摘要: 提出了自然弯扭梁受复杂载荷作用时静力分析的一种理论方法，重点在于对控制方程的求解，其中考虑了与扭转有关的翘曲变形和横向剪切变形的影响．在特殊的情况下，可以比较容易地得到这些方程的解答，包括各种内力、应力、应变和位移的计算．算例给出了平面曲梁受水平和垂直分布载荷作用时广义翘曲坐标的求解方法．计算结果表明，求得的应力和位移的理论值和三维有限元结果非常接近．此外，该理论不限于具有双对称横截面的自然弯扭梁，同样可推广至具有一般横截面形状的情况．
- 自然弯扭梁 /
- 圣维南扭转翘曲函数 /
- 广义翘曲坐标 /
- 最小势能原理 /
- 变分方程
Abstract: A theoretical method for static analysis of naturally curved and twisted beams under complicated loads was presented,with special attention devoted to the solving process of governing equations which take into account the effects of torsion-related warping as well as transverse shear deformations.These governing equations,in special cases,can be readily solved and yield the solutions to the problem.The solutions can be used for the analysis of the beams,including the calculation of various internal forces,stresses,strains and displacements.The present theory will be used to investigate the stresses and displacements of a plane curved beam subjected to the action of horizontal and vertical distributed loads.The numerical results obtained by the present theory are found to be in very good agreement with the results of the FEM results.Besides,the present theory is not limited to the beams with a double symmetric cross section,it can also be extended to those with arbitrary crosssectional shape.
- naturally curved and twisted beam /
- St.Venant torsional warping function /
- generalized coordinate for warping /
- the minimum potential energy principal /
- variational equation

HTML全文

参考文献(11)

[1]	Ie C A,Kosmatka J B.On the analysis of prismatic beams using first-order warping functions[J].International Journal of Solids and Structures,1992，29(7):879—891. doi: 10.1016/0020-7683(92)90023-M
[2]	Zu J W-Z.Han R P S.Dynamic response of a spinning Timoshenko beam with general boundary conditions and subjected to a moving load[J].Journal of Applied Mechanics,1994,61(1):152—160. doi: 10.1115/1.2901390
[3]	Wang C M,Lam K Y,He X Q,et al.Large deflection of an end supported beam subjected to a point load[J].International Journal of Solids and Structures,1997,32(1):63—72.
[4]	Nayfeh Ali H,Perngjin F Pai.Non-linear non-planar parametric responses of an inextensional beam[J].International Journal of Non-Linear Mechanics,1989，24(2):139—158. doi: 10.1016/0020-7462(89)90005-X
[5]	Gummadi L N B,Palazotto A N.Large strain analysis of beams and arches undergoing rotations[J].International Journal of Non-Linear Mechanics,1998，33(4):615—645. doi: 10.1016/S0020-7462(97)00033-4
[6]	William Paulsen H.Eigenfrequencies of curved Euler-Bernoulli beam structures with dissipative joints[J].Quarterly of Applied Mathematics,1995,53(2):259—271.
[7]	Washizu K. Some considerations on a naturally curved and twisted slender beam[J].Journal of Mathematics and Physics,1964,43(2):111—116.
[8]	熊汉伟，张培源.空间曲杆有限元分析[J].重庆大学学报，1997，20(4)：31—36.
[9]	朱渝春，张涪源，严波.封闭薄壁截面空间曲杆的双力矩[J].应用数学和力学，1999，20(12)：1252—1258.
[10]	Timoshenko S,Goodier J N.Theory of Elasticity[M].New York:McGraw-Hill,1951.
[11]	Timoshenko S.Vibration Problems in Engineering[M].New York:Wiley,1974.