Exact large deflection solutions for Timoshenko beams with nonlinear boundary conditions

Sen-Yung Lee, Shin Yi Lu, Yen Tse Liu, Hui Chen Huang

Research output: Contribution to journalArticle

14 Citations (Scopus)

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.

Original languageEnglish
Pages (from-to)293-312
Number of pages20
JournalCMES - Computer Modeling in Engineering and Sciences
Volume33
Issue number3
Publication statusPublished - 2008

Fingerprint

Large Deflection
Timoshenko Beam
Nonlinear Boundary Conditions
Algebra
Perturbation Solution
Boundary conditions
Exact Solution
Numerical analysis
Differential equations
Analytic Solution
Linear differential equation
Deflection
Numerical Analysis
Limiting
Roots
Nonlinearity
Valid

All Science Journal Classification (ASJC) codes

  • Software
  • Modelling and Simulation
  • Computer Science Applications

Cite this

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Exact large deflection solutions for Timoshenko beams with nonlinear boundary conditions. / Lee, Sen-Yung; Lu, Shin Yi; Liu, Yen Tse; Huang, Hui Chen.

In: CMES - Computer Modeling in Engineering and Sciences, Vol. 33, No. 3, 2008, p. 293-312.

Research output: Contribution to journalArticle

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