Open Access

ARTICLE

Exact Large Deflection of Beams with Nonlinear Boundary Conditions

Sen Yung Lee¹, Sheei Muh Lin², Chien Shien Lee³, Shin Yi Lu³, Yen Tse Liu³
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 Professor, Department of Mechanical Engineering, Kun Shan University, Tainan, Taiwan, Republic of China
3 Graduate students, Department of Mechanical Engineering, National Cheng Kung University, Tainan, Taiwan, Republic of China

Computer Modeling in Engineering & Sciences 2008, 30(1), 27-36. https://doi.org/10.3970/cmes.2008.030.027

Abstract

An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five 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. Finally, examples and limiting studies are given to illustrate the analysis.

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Keywords

beams, large deflection, nonlinear boundary conditions, shifting function method

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