Postbuckling Behavior of Beams on Two-parameter Elastic Foundation

The postbuckling behavior of beams on a two-parameter elastic foundation subjected to axial forces is investigated. Based on the strain energy expression, a two-node nonlinear beam element is formulated. The element includes the effects of shear deformation, foundation deflection in both the horizontal and vertical directions. The bracketing procedure and the iterative Newton–Raphson method with arc-length control technique are adopted to compute the critical loads and equilibrium paths of the beams with various boundary conditions. The numerical results show that the critical load and the postbuckling behavior are not only governed by the foundation stiffness, but by the foundation deflection in the horizontal direction also. The postbuckling characteristics of the beams are altered by ignoring the foundation deflection in the horizontal direction. A detail investigation is carried out to highlight the influences of the partial support by the foundation and the beam slenderness on the critical load and the postbuckling behavior.