Buckling analysis of sandwich plates with functionally graded skins using a new quasi‐3D hyperbolic sine shear deformation theory and collocation with radial basis functions

Abstract

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:

Thermal and thermomechanical postbuckling of FGM sandwich plates resting on elastic foundations with tangential edge constraints and temperature dependent properties

“…Basing on a higher order shear deformation theory and a two-step perturbation technique, nonlinear dynamic and postbuckling responses of mid-plane symmetric FGM sandwich plates have been analyzed by Shen and Li [25] and Wang and Shen [26,27] including the effects of elastic foundations. Neves et al [28][29][30] used meshless methods based on some shear deformation plate theories to analyze the bending, free vibration and linear buckling behavior of isotropic and FGM sandwich plates. Also, Lurlaro et al [31] made use of a refined zigzag theory for bending and free vibration analysis of FGM sandwich plates.…”

Analysis of functionally graded sandwich plates using a new first-order shear deformation theory

“…Neves [8][9][10] developed HSDT to predict the behavior of FG sandwich plates. Recently, Xiang et al [11] analyzed the free vibration of FG sandwich plates using a nth-order shear deformation theory and a meshless method, while Sobhy [12] investigated the buckling and free vibration of FG sandwich plates using various HSDTs.…”

“…It is should be noted that HSDTs are highly computational cost due to involving in many unknowns (e.g., theories Neves et al [9][10] with nine unknowns and Natarajan and Manickam [7] with thirteen unknowns). To reduce computational cost, HSDTs with four unknowns were recently developed for FG sandwich plates (see Refs.…”

Analytical solution for thermal buckling analysis of rectangular plates with functionally graded coatings

“…(7) and (13) one can obtain the following relations in which Eq. (21) and imperfection have been accounted as…”

“…Yanga and Shen [12] carried out a study in the large defection and postbuckling behavior of FG plates subjected to transverse and in-plane loadings. Neves et al [13,14] investigated the buckling analysis of sandwich plates with functionally graded skins and sandwich beams using a new quasi-3D hyperbolic. The critical buckling load of functionally graded plates containing a crack using classical plate theory (CPT) through the finite element method has been obtained by Amiri Rad et al [15].…”