Exact Large Deflection of Beams with Nonlinear Boundary Conditions
Sen Yung Lee; Sheei Muh Lin; Chien Shien Lee; Shin Yi Lu; and Yen Tse Liu

Source CMES: Computer Modeling in Engineering & Sciences, Vol. 30, No. 1, pp. 27-36, 2008
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Keywords beams, large deflection, nonlinear boundary conditions, shifting function method
Abstract An analytic solution method, namely the shifting function method, is developed to find the exact large static deflection of a beam with nonlinear elastic springs supports at ends for the first time. The associated mathematic system is a fourth order ordinary differential equation with nonlinear boundary conditions. It is shifted and decomposed into five 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. Finally, examples and limiting studies are given to illustrate the analysis.
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