轴向复合载荷作用下变截面悬臂弹性立柱后屈曲分析

吴莹; 李世荣; 滕兆春

轴向复合载荷作用下变截面悬臂弹性立柱后屈曲分析

兰州理工大学理学院, 兰州 730050

基金项目: 科技部基础研究重大项目前期预研专项基金资助项目(2001CCA04300)

详细信息

作者简介:
吴莹(1967- ),女,安徽灵壁人,副教授(E-mail:wying36@163.com).

中图分类号: O343
计量
- 文章访问数: 1995
- HTML全文浏览量: 66
- PDF下载量: 600
- 被引次数: 0
出版历程
- 收稿日期: 2001-06-28
- 修回日期: 2003-05-28
- 刊出日期: 2003-09-15

Post-Buckling of a Cantilever Rod with Variable Cross-Sections Under Combined Load

School of Sciences, Lanzhou University of Technology, Lanzhou 730050, P.R.China

摘要

摘要: 基于轴线可伸长弹性杆的几何非线性理论,建立了同时作用端部轴向集中荷载和沿轴线作用分布轴向载荷的变截面弹性悬臂柱的后屈曲控制方程。采用打靶法直接求解了所得强非线性边值问题,给出了截面线性变化的圆截面柱的二次平衡路径及其过屈曲位形曲线。
- 变截面柱 /
- 复合载荷 /
- 轴线伸长 /
- 过屈曲 /
- 打靶法
Abstract: Based on the geometrically non-linear theory of axially extensible elastic rods, the governing equations of post-buckling of a clamped-free rod with variable cross-sections, subjected to a combined load, a concentrated axial load P at the free end and a non-uniformly distributed axial load q,are established. By using shooting method, the strong nonlinear boundary value problems are numerically solved. The secondary equilibrium paths and the post-buckling configurations of the rod with linearly varied cross-sections are presented.
- rod with variable cross-section /
- axial extensibility /
- post-buckling /
- shooting method /
- numerical solution

HTML全文

参考文献(17)

[1]	Euler L.De Curvis Elasticis, Methodus Inveniendi Lineas Maximi Minimive Proprietate Ganudentes[M].Lausanne & Geneva, 1744.
[2]	Lagrange J L. Qeuvres de Lagrange[M].Vol 2.Paris:Gauthier-Villars, 1868,125-170.
[3]	Love A E H.Treaties on the Mathematical Theory of Elasticity[M].New York:Dever, 1927.
[4]	Timoshenko S P,Gere J M.Theory of Elastic Stability[M].2nd Ed. New York:MacGraw-Hill,1961.
[5]	Wang C Y.Post-buckling of a clamped-simply supported elastica[J].International Journal of Non-Linear Mechanics,1997,32(6):1115-1122.
[6]	Plaut R H,Suherman S,Dillard D A,et al.Deflections and buckling of a bent elastics in contact with a flat surface[J].International Journal of Solids and Structures,1999,36(8): 1209-1229.
[7]	Lee K. Post-buckling of uniform cantilever column under a combined load[J].International Journal of Non-Linear Mechanics, 2001,36(5):813-816.
[8]	程昌钧,朱正佑.结构的分叉与屈曲[M].兰州:兰州大学出版社,1991.
[9]	朱正佑,程昌钧.分支问题的数值计算方法[M].兰州:兰州大学出版社,1989.
[10]	李世荣,李中明.压杆过屈曲分析中轴线无伸长假设的定量讨论[J].兰州大学学报(自然科学版),1997,33(4):42-46.
[11]	李世荣,杨静宁.固支-简支变截面杆的过屈曲模型及其数值解[J].计算力学学报,2000,17(1):114-118.
[12]	李世荣,程昌钧.加热弹性杆热屈曲分析[J].应用数学和力学,2000,21(2):119-125.
[13]	李世荣.非对称支承弹性杆的热过屈曲[J].工程力学,2000,17(5):115-120.
[14]	LI Shi-rong,ZHOU You-he,ZHENG Xiao-jing.Thermal post-buckling of a heated elastic rod with pinned-fixed ends[J].Journal of Thermal Stresses, 2002, 25(1):45-56.
[15]	Coffin D W,Bloom F.Elastica solution for the hygrothermal buckling of a beam[J].International Journal of Non-Linear Mechanics,1999,34(5):935-947.
[16]	Filipich C P,Rosales M B.A further study on the post-buckling of extensible elastic rods[J].International Journal of Non-Linear Mechanics, 2000,35(5):997-1022.
[17]	William H P,Brain P F,Sao A T,et al.Numerical Recipes-the Art of Scientific Computing[M].London: Cambridge University Press, 1986.