Approximate closed-form solution for buckling of orthotropic plates with longitudinal edges elastically restrained against rotation

Abstract

A simple trigonometric series is first introduced to satisfy the longitudinal edges with the clamped-simply supported (CS) condition, while the deformation shape function along the transverse direction is uniquely constructed through a weighted combination of three kinds of trigonometric series to meet the arbitrarily elastically restrained boundary condition against rotation. Approximate closed-form solution for buckling behavior of the orthotropic plates under compression, in-plane shear or combined shear and compression is further presented based on the Galerkin​ method. The transverse edges of the considered orthotropic plates are simply supported, while the opposite longitudinal edges are arbitrarily elastically restrained against rotation to different degree. In particular, the explicit closed-form buckling solutions for the long orthotropic plates under the respective pure in-plane shear and pure compression are obtained. The validity study demonstrates that the relative error of compressive buckling load with a maximum difference of 7% decreases with the increasing of the transverse vs. longitudinal compression load parameter (κ21), while the relative error of critical shear buckling load with a maximum difference of 10% decreases with an increase in the longitudinal compression vs. shear load (κ13) and transverse compression vs. shear load (κ23) parameters. The present approximate closed-form solution is effective and relatively accurate for performing the buckling analysis of orthotropic plates with the longitudinal edges arbitrarily elastically-restrained against rotation, and it can be used in simplified discrete plate analysis of thin-walled composite structures to predict their local buckling strength.