Initial Postbuckling Behavior of Shear Deformable Symmetrically Laminated Beams

Abstract-Results for the initial postbuckling behavior of laminated beams are presented. Shear deformation effects are incorporated by relaxing certain assumptions of thin beam/plate theory. The analysis used is in the spirit of Koiter [Doctoral thesis, Delft, Amsterdam, English translation AFFDL-TR-70-25, (1970)], who developed asymptotic expressions for the potential energy in the neighborhood of the critical load in terms of a small parameter, which was identified as the amplitude of the buckling mode. The method adopted in the present paper is to use asymptotic expansion considerations to differential equations obtained via the principle of stationary potential energy. The effect of boundary conditions on the initial postbuckling response is studied by considering the two extreme cases of pinned-pinned and fully clamped boundary supports. An extensive parametric study is conducted to study the effects of mechanical properties, emerging as suitable non-dimensional groups from the derivation of the governing equations, on the initial postbuckling response. Finally, the effect of shape imperfections on the response of the beam is studied for certain example configurations that exhibit a limit load type of behavior.