This paper investigates symmetrical buckling of orthotropic circular and annular plates of continuous variable thickness. Uniform compression loading is applied at the plate outer boundary. Thickness varies linearly along radial direction. Inner edge is free, while outer edge has different boundary conditions: clamped, simply and elastically restraint against rotation. The optimized Ritz method is applied for buckling analysis. In this method, a polynomial function that is based on static deformation of orthotropic circular plates in bending is used. Also, by employing an exponential parameter in deformation function, eigenvalue is minimized in respect to this parameter. The advantage of this procedure is simplicity, in comparison with other methods, while whole algorithm for solution can be coded for computer programming. The effects of variation of radius, thickness, different boundary conditions, ratio of radial Young modulus to circumferential one, and ratio of outer radius to inner one in annular plates on buckling load factor are investigated. The obtained results show that in plate with identical thickness, increasing of outer radius decreases the buckling load factor. Moreover, increase of thickness of the plates results in increase of buckling load factor. Manuscript profile

In this paper, the effect of elastic foundation on the out of plane displacement of functionally graded circular plates using differential transform method is presented. Differential transform method is a semi-analytical-numerical solution technique that is capable to solve various types of differential equations. Using this method, governing differential equations are transformed into recursive relations and boundary conditions are changed into algebraic equations. Since the problem of plates on elastic foundation have a great practical importance in modern engineering structures and Winkler foundation model is widely used, plate is assumed on Winkler elastic foundation. In this article functionally graded plate is considered in which material properties vary through the thickness direction by power-law distribution. Analysis results of out of plane displacement of plate on elastic foundation under uniform transverse loads are obtained in different terms of foundation stiffness, material properties and boundary conditions. In order to validate the solution technique, results obtained are compared with the results of the finite element method (FEM). Manuscript profile

In this paper, buckling of orthotropic rectangular plates under different loadings was investigated. For this reason, governing buckling equations for an isotropic plate were modified by applying constitutive equations of orthotropic materials. After obtaining the equations of orthotropic plates, Generalized Differential Quadrature method (GDQM) was applied on buckling equations and thus a set of Eigen value equations resulted. In order to solve this Eigen value problem, a computer program was developed using MATLAB software in a way that the influence of different parameters such as length to width ratio (aspect ratio), the number of layers, the angle of layers arrangement, material of layers, kind of loading and boundary conditions were included. A buckling load factor was calculated for simply supported and clamped supported plates. The results of GDQ method were compared with reported results from Rayleigh – Ritz method and with results from solving the Finite element using ANSYS 8.0 software. The comparison showed the accuracy of obtained result clearly. Manuscript profile

This paper investigates symmetrical buckling of orthotropic circular and annular plates of continuous variable thickness. Uniform compression loading is applied at the plate outer boundary. Thickness varies linearly along radial direction. Inner edge is free, while outer edge has different boundary conditions: clamped, simply and elastically restraint against rotation. The optimized RayLeigh-Ritz method is applied for buckling analysis. In this method, a polynomial function that is based on static deformation of orthotropic circular plates in bending is used. Also, byemploying an exponential parameter in deformation function, eigenvalue is minimized in respect to that parameter. The advantage of this procedure is simplicity in comparison with other methods, while whole algorithm for solution can be coded for computer programming. The effect of variation of radius, thickness, different boundary conditions, ratio of radial Young Modulus to circumferential one, ratio of outer radius to inner one in annular plates on critical buckling coefficient are investigated. The obtained results show that in plate with identical thickness, increasing of outer radius decreases the critical buckling coefficient. In addition increasing of thickness of the plates results in increase of critical buckling coefficient. Manuscript profile

In the present paper, the buckling problem of rectangular functionally graded (FG) plate with arbitrary edge supports is investigated. The present analysis is based on the classical plate theory (CPT) and large deformation is assumed for deriving stability equations. The plate is subjected to bi-axial compression loading. Mechanical properties of FG plate are assumed to vary continuously along the thickness of the plate according to differentvolume of fractionfunctions of constituents. These functions are assumed to have power law distributions. The displacement function is assumed to have the form of doubleFourier series, of which derivatives are legitimized using Stokes’ transformation method. The advantage of using this method is the capability of considering effect of anypossible combination of boundary conditionson the buckling loads. The out-plane displacement distribution is assumed using Fourier Sinus Series. This results in a general eigenvalue problem which can be used for evaluating the buckling load under different edge conditions, plate aspect ratios and various volume fraction functions. For generality of problem, plate is elastically restrained using some rotational and translational springs at four edges. Some numerical examples are presented and compared the to numerical results of finite element method using ABAQUS and other researchers’ results to validate the proposed method. It has been shown that there is good agreement between them Manuscript profile