Buckling and postbuckling of a nonlinearly elastic column

formula, bifurcation, limit load, finite disturbance buckling The classical problem of buckling of an inextensible elastic column, under the action of a compressive force is examined. The column is made of nonlinearly elastic material for which the stress-strain relation is represented by the Ludwick constitutive law. An approximative formula for determination of the force at immediate post-buckling is given. Further post-buckling solutions are obtained for different values of the nonlinearity parameter by numerical integration using the Runge-Kutta-Fehlberg algorithm, and are pre-sented in non-dimensional diagrams. It is shown that no bifurcation point is found in the case of nonlinearly elastic column