Analytic Static Deflection Solutions of Beams Resting on Strong Nonlinear Elastic Foundations

The analytic static deflection solutions of beams resting on nonlinear elastic foundations are developed by the modified Adomian method. If the applied force function is an analytic function, then the deflection function can be derived and expressed in Maclaurin series. A recurrence relation for the coefficients of the Maclaurin series is derived. It is shown that the proposed solution method is accurate and efficient. The solution method can be successfully applied to the problem with strong nonlinearity. The results are also compared with those obtained by the perturbation method. It is found that the error of the perturbation solution will increase not only when the nonlinear parameter is increased but also when the applied load is increased.