The correct derivation of the buckling equations of the shear-deformable FGM plates for the extended Kantorovich method

This article presents the derivation of elastic buckling equations and boundary conditions shear-deformable plates in frame extended Kantorovich method (EKM). Surveying literature shows that those stability are often obtained using a wrong by confusing them with linear equilibrium condition. work aims at providing correct is built on Buckling derived for three different plate theories, namely, first-order shear deformation theory (FSDT), refined-FSDT, refined (RPT). first to implement EKM based theory. Also, it time refined-FSDT analysis. For generic FGM plates, FSDT both found be simple contain only lateral displacements/rotations variations. On other hand, RPT, have coupled in-plane displacement variations, even if physical neutral taken as reference plane. The considered rectangular under general loads. properties continuously varying through its thickness which assumed change smoothly separable function two directions. von Kármán nonlinearity considered. according Trefftz criterion, variational calculus. solution methods out scope this article, however, brief strategy presented.