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

WU Ying; LI Shi-rong; TENG Zhao-chun

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Article Navigation > Applied Mathematics and Mechanics > 2003 > 24(9): 984-990

WU Ying, LI Shi-rong, TENG Zhao-chun. Post-Buckling of a Cantilever Rod with Variable Cross-Sections Under Combined Load[J]. Applied Mathematics and Mechanics, 2003, 24(9): 984-990.

Citation:

WU Ying, LI Shi-rong, TENG Zhao-chun. Post-Buckling of a Cantilever Rod with Variable Cross-Sections Under Combined Load[J]. Applied Mathematics and Mechanics, 2003, 24(9): 984-990.

Citation:

WU Ying, LI Shi-rong, TENG Zhao-chun. Post-Buckling of a Cantilever Rod with Variable Cross-Sections Under Combined Load[J]. Applied Mathematics and Mechanics, 2003, 24(9): 984-990.

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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

Received Date: 2001-06-28
Rev Recd Date: 2003-05-28
Publish Date: 2003-09-15

Abstract

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

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References(17)

References

[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.