A Novel Technique for Nonlinear Analysis of Beams on Two-parameter Elastic Foundations

Postbuckling, nonlinear bending, and nonlinear vibration analyses are presented for a simply supported Euler–Bernoulli beam resting on a two-parameter elastic foundation. The nonlinear model is introduced by using the exact expression of the curvature. Two kinds of end conditions, namely movable and immovable, are considered. The nonlinear equation of motion, including beam–foundation interaction, is derived separately for these two kinds of end conditions. The analysis uses a two-step perturbation technique to determine the postbuckling equilibrium paths of an axially loaded beam, the static large deflections of a bending beam subjected to a uniform transverse pressure, and the nonlinear frequencies of a beam with or without initial stresses. The numerical results confirm that the foundation stiffness has a significant effect on the nonlinear behavior of Euler–Bernoulli beams. The results also reveal that the end condition has a great effect on the nonlinear bending and nonlinear vibration behaviors of Euler–Bernoulli beams with or without elastic foundations.