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Applied Mathematics and Mechanics >

2011 , Vol. 32 >Issue 6: 719 - 728

DOI: https://doi.org/10.1007/s10483-011-1451-x

Articles

Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure

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  • 1. Department of Computer Science and Technology, Shanghai Normal University, Shanghai 200234, P. R. China;
    2. College of Mechanical Engineering, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China;
    3. Department of Mechanics, College of Sciences, Shanghai University, Shanghai 200444, P. R. China

Received date: 2010-12-24

  Revised date: 2011-04-15

  Online published: 2011-06-01

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Abstract

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

Cite this article

ZHU Yuan-Yuan;HU Yu-Jia;CHENG Chang-Jun . Analysis of nonlinear stability and post-buckling for Euler-type beam-column structure[J]. Applied Mathematics and Mechanics, 2011 , 32(6) : 719 -728 . DOI: 10.1007/s10483-011-1451-x

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