The paper is devoted to a simply supported rectangular plate subjected to two types of compressive edge loads. The first load is applied uniformly along a part of two opposite edges, the second one has a non-uniform distribution (defined by a half wave of the sin^k function). The critical load value of the plate is located between the values for uniformly distributed and concentrated load. Critical value of thickness of the plate is determined. The problem is solved by the orthogonalization method, and the results are compared with those of numerical analysis done by means of the finite element method.

The paper is devoted to buckling problem of an axially compressed generalized cylindrical sandwich panel and rectangular sandwich plate. The continuous variation of mechanical properties in thickness direction of the structures is assumed. The generalized theory of deformation of the straight line normal to the neutral surface is applied. The analytical model of this sandwich panel is elaborated. Three differential equations of equilibrium of this panel based on the principle of stationary potential energy are obtained. This system of equations is analytically solved and the critical load is derived. Moreover, the limit transformation of the sandwich panel to a sandwich rectangular plate is presented. The critical loads of the example cylindrical panels and rectangular plates are derived.