Mechanical and thermal buckling analysis of functionally graded plates

Abstract

The mechanical and thermal buckling analysis of functionally graded ceramic–metal plates is presented in this study. The first-order shear deformation plate theory, in conjunction with the element-free kp-Ritz method, is employed in the current formulation. It is assumed that the material property of each plate varies exponentially through the thickness. The displacement field is approximated in terms of a set of mesh-free kernel particle functions. The bending stiffness is evaluated using a stabilized conforming nodal integration technique, and the shear and membrane terms are computed using a direct nodal integration method to eliminate the shear locking effects of very thin plates. The mechanical and thermal buckling behaviour of functionally graded plates with arbitrary geometry, including plates that contain square and circular holes at the centre, are investigated, as are the influence of the volume fraction exponent, boundary conditions, hole geometry, and hole size on the buckling strengths of these plates.

Introduction

Functionally graded materials (FGMs) are made of advanced composites in which the material properties vary continuously and smoothly in a structure. FGMs, which are usually made of metal and ceramic, possess two main properties: toughness and a high degree of temperature-resistance. These special characteristics make them preferable to conventional composite materials, which are subject to delamination, for engineering applications. Noda [1] carried out an extensive review of broad research topics related to FGMs, including thermoelastic and thermoinelastic problems, and corresponding parametric studies. Reddy and Chin [2] developed a finite element formulation for the dynamic thermoelastic responses of functionally graded cylinders and plates using the first-order shear deformation plate theory, and He et al. [3] investigated the vibration control of functionally graded plates (FGPs) mounted with integrated piezoelectric sensors and actuators. Liew et al. [4] carried out static and dynamic piezothermoelastic analysis for the active control of FGPs bonded with integrated piezoelectric sensors and actuators in thermal gradient environments. Reddy [5] proposed a finite element model based on the third-order deformation theory to investigate the static and dynamic responses of FGPs under mechanical and thermal loading, and Efraim and Eisenberger [6] investigated the vibrations of thick annular FGPs with variable thicknesses. Vel and Batra [7] reported a three-dimensional exact solution for the vibration of functionally graded rectangular plates.

In addition to these static and dynamic analyses, the buckling behaviour of FGPs has also attracted research interest. Feldman and Aboudi [8] carried out elastic buckling analysis of FGPs subjected to axial load and also investigated the optimal spatial distribution of the volume fraction to improve buckling resistance. Birman [9] provided buckling analysis of functionally graded hybrid composite plates, and Javaheri and Eslami [10] analyzed the thermal buckling of FGPs based on higher order theory. Liew et al. [11], [12] performed postbuckling analysis of FGPs subjected to thermo-electro-mechanical loading and also considered the thermal postbuckling of these plates. Yang and Shen [13] examined the nonlinear bending and postbuckling behaviour of FGPs subjected to combined transverse and in-plane loads using a semi-analytical approach, and Woo et al. [14] presented an analytical solution for the postbuckling behaviour of moderately thick FGM plates and shells under thermal and mechanical loading.

Recently, mesh-free methods have been widely applied to a variety of engineering analyses due to their flexibility. Studies include thin shell analysis [15], [16], the large deformation analysis of nonlinear structures [17] and the static and vibration analysis of FGMs [18], [19], [20]. In this paper, the buckling behaviour of FGPs under mechanical and thermal loading is investigated using the element-free kp-Ritz method [21], [22], [23], [24]. The formulation is based on the first-order shear deformation plate theory, and the material properties of the FGPs are assumed to vary continuously and smoothly through the thickness according to the power-law distribution of the volume fraction of the constituents. In the thermal buckling analysis of a FGP, the temperature is considered to vary only through the thickness direction and to be constant over any plane. A stabilized conforming nodal integration approach is employed to evaluate the plate bending stiffness, and the shear and membrane terms are estimated using a direct nodal integration method. When compared with Gauss integration, the proposed integration scheme shows better computational efficiency without shear locking for very thin plates. Moreover, this method is more effective for dealing with plates with complex geometry, especially plates with cutouts. The buckling behaviour of a variety of FGPs, including solid plates and plates with holes, is discussed, and the influence of the volume fraction exponent, hole size, and boundary condition on the buckling strength of these plates is also examined.