||CMES: Computer Modeling in Engineering & Sciences, Vol. 30, No. 1, pp. 27-36, 2008
||Full length paper in PDF format. Size = 133,166 bytes
||beams, large deflection, nonlinear boundary conditions, shifting function method
||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.