Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions

Sen-Yung Lee, Qian Zhi Yan

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton's principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.

Original languageEnglish
Article number646391
JournalMathematical Problems in Engineering
Volume2015
DOIs
Publication statusPublished - 2015 Jan 1

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Curved Beam
Timoshenko Beam
Nonlinear Boundary Conditions
Static analysis
Static Analysis
Boundary conditions
Differential equation
Hamilton's Principle
Characteristic equation
Boundary Problem
Mathematical Modeling
Deflection
Nonlinear Problem
Governing equation
Analytical Solution
Differential equations
Nonlinearity
Valid

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Engineering(all)

Cite this

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Exact Static Analysis of In-Plane Curved Timoshenko Beams with Strong Nonlinear Boundary Conditions. / Lee, Sen-Yung; Yan, Qian Zhi.

In: Mathematical Problems in Engineering, Vol. 2015, 646391, 01.01.2015.

Research output: Contribution to journalArticle

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AB - Analytical solutions have been developed for nonlinear boundary problems. In this paper, the shifting function method is applied to develop the static deflection of in-plane curved Timoshenko beams with nonlinear boundary conditions. Three coupled governing differential equations are derived via the Hamilton's principle. The mathematical modeling of the curved beam system can be decomposed into a complete sixth-order ordinary differential characteristic equation and the associated boundary conditions. It is shown that the proposed method is valid and performs well for problems with strong nonlinearity.

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