Exact Large Deflection Solutions for Timoshenko Beams with Nonlinear Boundary Conditions
Sen Yung Lee; Shin Yi Lu; Yen Tse Liu; and Hui Chen Huang

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 33, No. 3, pp. 293-312, 2008
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Keywords Timoshenko beams, static deflection, nonlinear boundary conditions, shifting function method, perturbation solution.
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.
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