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A hyperbolic sine shear deformation theory is used for the linear buckling analysis of functionally graded plates. The theory accounts for through-the-thickness deformations.The buckling governing equations and boundary conditions are derived using Carrera's Unified Formulation and further interpolated by collocation with radial basis functions. The collocation method is truly meshless, allowing a fast and simple discretization of equations in the domain and on the boundary.A numerical investigation has been conducted considering and neglecting the thickness stretching effects on the buckling of sandwich plates with functionally graded skins. Numerical results demonstrate the high accuracy of the present approach. Problem formulationConsider a rectangular sandwich plate of plan-form dimensions a and b and uniform thickness h. The co-ordinate system is taken such that the x-y plane coincides with the midplane of the plate (z ∈ [−h/2, h/2]).The sandwich core is a ceramic material and skins are composed of a functionally graded material across the thickness direction. The bottom skin varies from a metal-rich surface (z = h 0 = −h/2) to a ceramic-rich surface while the top skin face varies from a ceramic-rich surface to a metal-rich surface (z = h 3 = h/2) as illustrated in Fig. 1. The volume fraction of the ceramic phase is obtained from a simple rule of mixtures as:

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A new enhanced strain element, based on the definition of extra compatibles modes of deformation added to the standard four-node finite element, is initially presented. The element is built with the objective of addressing incompressible problems and avoiding locking effects. By analysing at the element level the deformation modes which form a basis for the incompressible subspace the extra modes of deformation are proposed in order to provide the maximum possible dimension to that subspace. Subsequently another new element with more degrees of freedom is formulated using a mixed method. This is done by including an extra field of variables related to the derivatives of the displacement field of the extra compatible modes defined previously. The performance of the elements proposed is assessed in linear and non-linear situations.

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