Postbuckling of Elastic Beams Considering Higher Order Strain Terms

Nonlinear relations between the beam displacement and generalized strain measures, which have basic effects on postbuckling behavior of elastic beams, are presented. The complex coupling phenomena associated with the higher order strain terms is reviewed for the special case of planar and rectilinear pinned-pinned beams. Special consideration was made for the physical assumptions used in the various column-beam models. A natural hierarchy results yielding that all the higher order terms can, for a specific beam formulation, be steadily obtained by dissimilar polynomial approximations of the generalized strains. The asymptotic expansions method and the minimum energy criterion are used to perform analytical calculation of the postbifurcation equilibrium path at the neighborhood of a bifurcation point when only a unique buckling mode is assumed to occur. As a result, postbuckling branches are easily obtained even when accounting for both beam centerline extensional deformation and shear strain. They show that the critical load is scarcely affected by the higher order strain terms unlike the postbuckling paths which are found to be very sensitive to them.