Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure

ZHU Yuan-yuan; HU Yu-jia; CHENG Chang-jun

doi:10.3879/j.issn.1000-0887.2011.06.004

Volume 32 Issue 6

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ZHU Yuan-yuan, HU Yu-jia, CHENG Chang-jun. Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure[J]. Applied Mathematics and Mechanics, 2011, 32(6): 674-682. doi: 10.3879/j.issn.1000-0887.2011.06.004

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Analysis of Non-Linear Stability and Post-Buckling for the Euler-Type Beam-Column Structure

doi: 10.3879/j.issn.1000-0887.2011.06.004

1.
Department of Computer Science and Technology, Shanghai Normal University, Shanghai 200234, P. R. China;

Received Date: 2010-12-24
Rev Recd Date: 2011-01-14
Publish Date: 2011-06-15

Abstract

Abstract

Based on the assumption of finite deformation,the Hamilton variational principle was extended to a nonlinear elastic Euler-type beam-column structure located on a nonlinear elastic foundation,and the corresponding 3-dimension mathematical model for analyzing the non-linear mechanical behaviors of structures was established,in which the effects of rotation inertia,non-linearity of material and geometry were considered.As application,the non-linear stability and the post-buckling for a linear elastic beam with equal cross-section and located on an elastic foundation were analyzed,here,one end of beam was fully fixed,and the other was partially fixed and subjected to an axial force.A new numerical technique was proposed to calculate the trivial solution,bifurcation points and bifurcation solutions by the shooting method and Newton-Raphson interactive method.The first and the second bifurcation points and the corresponding bifurcation solutions were calculated successfully.The effects of foundation resistances and inertia moments on the bifurcation points were considered.
- beam-column structure,
- Hamilton variational principle,
- nonlinear stability,
- shooting method and Newton-Raphson interactive method,
- post-bulking

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References(7)

References

[1]	陈至达. 杆、板、壳大变形理论[M]. 北京:科学出版社，1994.( CHEN Zhi-da. Finite Deformation Theory for Rods, Plates and Shells[M]. Beijing: Science Press, 1994. (in Chinese))
[2]	Antman S S. The Theory of Rods[M]. Handbuch der Physik, Vol VI a/2. Heidelberg, Berlin: Springer-Verlag, 1972.
[3]	朱媛媛, 三浦房纪, 朱正佑. 弹性地基HDAJ接头桩的非线性稳定性分析[J].力学季刊, 2005, 26(2): 216-223.(ZHU Yuan-yuan, Miura Fusanori, ZHU Zheng-you. Non-linear stability analysis for HDAJ spliced piles in elastic ground [J]. Chinese Quarterly of Mechanics, 2005, 26(2): 216-223. (in Chinese))
[4]	高杉, 朱媛媛, 朱正佑. 具有初始弯曲的桩基稳定性分析[J]. 上海大学学报(自然科学版), 2009, 15(3):290-295.(GAO Shan, ZHU Yuan-yuan, ZHU Zheng-you. Analysis of stability of pile with initial bending [J]. Journal of Shanghai University(Natural Science), 2009, 15(3): 290-295. (in Chinese))
[5]	胡育佳, 朱媛媛, 程昌钧. 在动载荷作用下框架结构大变形分析的微分代数方法[J]. 应用数学和力学,2008, 29(4):398-408.(HU Yu-jia, ZHU Yuan-yuan, CHENG Chang-jun. Differential-algebraic approach to large deformation analysis of frame structures subjected to dynamic loads[J]. Applied Mathematics and Mechanics(English Edition), 2008, 29(4):441-452.)
[6]	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.(ZHU Zheng-you, CHENG Chang-jun. Numerical Methods for Bifurcation Problems[M]. Lanzhou: Press of Lanzhou University, 1989. (in Chinese))
[7]	Arnold V I. Dynamical Systems Ⅵ, Singularity Theory Ⅰ: Local and Global Theory[M]. Encyclopaedia of Mathematical Sciences. Berlin: Springer-Verlag, 1993.