Buckling and post‐buckling of a nonlinearly elastic column

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 presented in non‐dimensional diagrams. It is shown that no bifurcation point is found in the case of nonlinearly elastic column.