An analytical solution for out-of-plane deflection of a curved Timoshenko beam with strong nonlinear boundary conditions

Sen-Yung Lee, Q. Z. Yan

Research output: Contribution to journalArticle

5 Citations (Scopus)

Abstract

This paper presents a simple method for finding the analytical solution for nonlinear boundary problems. The shifting function method is applied to developing the static deflection of an out-of-plane curved Timoshenko beam with nonlinear boundary conditions. Considering the out-of-plane motion of a uniform curved Timoshenko beam of constant radius R and a doubly symmetric cross section, three coupled governing differential equations are derived via Hamilton’s principle. After some simple arithmetic operations, the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. An example is given to illustrate the analysis and show that the proposed method performs very well for problems with strong nonlinearity.

Original languageEnglish
Pages (from-to)3679-3694
Number of pages16
JournalActa Mechanica
Volume226
Issue number11
DOIs
Publication statusPublished - 2015 Nov 26

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Boundary conditions
Differential equations

All Science Journal Classification (ASJC) codes

  • Computational Mechanics
  • Mechanical Engineering

Cite this

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An analytical solution for out-of-plane deflection of a curved Timoshenko beam with strong nonlinear boundary conditions. / Lee, Sen-Yung; Yan, Q. Z.

In: Acta Mechanica, Vol. 226, No. 11, 26.11.2015, p. 3679-3694.

Research output: Contribution to journalArticle

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AB - This paper presents a simple method for finding the analytical solution for nonlinear boundary problems. The shifting function method is applied to developing the static deflection of an out-of-plane curved Timoshenko beam with nonlinear boundary conditions. Considering the out-of-plane motion of a uniform curved Timoshenko beam of constant radius R and a doubly symmetric cross section, three coupled governing differential equations are derived via Hamilton’s principle. After some simple arithmetic operations, the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. An example is given to illustrate the analysis and show that the proposed method performs very well for problems with strong nonlinearity.

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