Open Access

ARTICLE

Exact Large Deflection Solutions for Timoshenko Beams with Nonlinear Boundary Conditions

by Sen Yung Lee¹, Shin Yi Lu², Yen Tse Liu², Hui Chen Huang²

1 Corresponding author. Tel: +886-6-2757575 ext.62150; E-mail: sylee@mail.ncku.edu.tw. Distinguished Professor, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China
2 Graduate students, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China

Computer Modeling in Engineering & Sciences 2008, 33(3), 293-312. https://doi.org/10.3970/cmes.2008.033.293

Abstract

A new analytic solution method is developed to find the exact static deflection of a Timoshenko beam with nonlinear elastic boundary conditions for the first time. The associated mathematic system is shifted and decomposed into six linear differential equations and at most four algebra equations. After finding the roots of the algebra equations, the exact solution of the nonlinear beam system can be reconstructed. It is shown that the proposed method is valid for the problem with strong nonlinearity. Examples, limiting studies and numerical analysis are given to illustrate the analysis. The exact solutions are compared with the perturbation solutions. The influence of the nonlinear spring constant and the slenderness ration on the errors of the perturbation solutions is evaluated.

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