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

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 (kappa(21)), 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 (kappa(13)) and transverse compression vs. shear load (kappa(23)) 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.