Abstract
Based on the geometrically nonlinear 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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Euler L.De Curvis Elasticis, Methodus Inveniendi Lineas Maximi Minimive Proprietate Ganudentes [M]. Lausanne & Geneva, 1744.
Lagrange J L.Qeuvres de Lagrange [M]. Vol 2. Paris: Gauthier-Villars, 1868,125–170.
Love A E H.Treaties on the Mathematical Theory of Elasticity [M] New York: Dever, 1927.
Timoshenko S P, Gere J M.Theory of Elastic Stability [M]. 2nd Ed. New York: MacGraw-Hill, 1961.
Wang, C Y. Post-buckling of a clamped-simply supported elastica [J].International Journal of Non-Linear Mechanics, 1997,32(6):1115–1122.
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.
Lee K. Post-buckling of uniform cantilever column under a combined load [J]International Journal of Non-Linear Mechanics, 2001,36(5):813–816.
CHENG Chang-jun, ZHU Zheng-you.Bifurcation and Buckling of Structures [M]. Lanzhou: Lanzhou University Press, 1991. (in Chinese)
ZHU Zheng-you, CHENG Zhang-jun.Computational Method for Bifurcation Problems [M]. Lanzhou: Lanzhou University Press, 1989. (in Chinese)
LI Shi-rong, LI Zhong-ming. A quantitative study of the assumption that the axis is inextensible in analysis of post-buckling of compressed rods [J].Journal of Lanzhou University (Natural Science), 1997,33(4):42–46. (in Chinese)
LI Shi-rong, YANG Jing-ning. An analysis of post-buckling of extensible rods with variable sections and clamped-simply supported ends[J].Journal of Computational Mechanics, 2000,17(1):114–118. (in Chinese)
LI Shi-rong, CHENG Chang-jun. Analysis of thermal post-buckling of heated elastic rods [J].Applied Mathematics and Mechanics (English Ed) 2000,21(2):133–140.
LI Shi-rong, Thermal post-buckling of asymmetrically supported elastic rods [J]Engineering Mechanics, 2000,17(5):115–120. (in Chinese)
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.
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.
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.
William H P, Brain P F, Sao A T,et al.Numerical Recipes—the Art of Scientific Computing [M]. London: Cambridge University Press, 1986.
Author information
Authors and Affiliations
Additional information
Communicated by SHEN Hui-shen
Foundation item: the Basic Research Program of National Science and Technology Ministry (2001CCA04300)
Biography: WU Ying (1967≈), Associate Professor (E-mail: wying36@163.com)
Rights and permissions
About this article
Cite this article
Ying, W., Shi-rong, L. & Zhao-chun, T. Post-buckling of a cantilever rod with variable cross-sections under combined load. Appl Math Mech 24, 1111–1118 (2003). https://doi.org/10.1007/BF02437643
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02437643