A galerkin procedure for localized buckling of a strut on a nonlinear elastic foundation

Working from the governing differential equation a Galerkin procedure has been developed to model the localized buckle pattern of an elastic strut on a nonlinear elastic (softening) Winkler foundation. The choice of trial functions comes directly from a perturbation study about the critical point, the actual shape being determined by the eigenvalues of the linearized equation. A good comparison has been achieved with independently obtained numerical solutions using only a few modes. Other measures of the accuracy of the approximate solutions have also proven to be favourable.