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Mathematical Problems in Engineering
Volume 2015, Article ID 646391, 12 pages
Research Article

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

Department of Mechanical Engineering, National Cheng Kung University, Tainan 701, Taiwan

Received 10 April 2015; Accepted 8 June 2015

Academic Editor: Bo-Qing Dong

Copyright © 2015 Sen-Yung Lee and Qian-Zhi Yan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.