Buckling of a rectangular composite orthotropic plate with two parallel free edges and the other two edges clamped and subjected to uniaxial compressive distributed load

The paper is concerned with the solution to the buckling problem of a plate having two opposite edges free and subjected to a uniform compressive load applied to another two fully clamped edges. At first glance, the problem might look simple, resembling the buckling of a compressed strip-beam. However, this is not the case. The buckled plate bends between the free edges as opposed to the beam buckling mode. The situation even more complicated when the plate material is not isotropic since the bending depends not only on the plate's aspect ratio but also on the elastic properties of the material. In this work, an analytical solution for such a buckling problem formulated for an orthotropic composite plate and based on the combined Kantorovich and generalised Galerkin methods is presented, and a compact analytical formula for the critical load is derived. The solution was verified by comparison with the finite element analysis.