Correspondence Relations Between Deflection, Buckling Load, and Frequencies of Thin Functionally Graded Material Plates and Those of Corresponding Homogeneous Plates

2015 ◽  
Vol 82 (11) ◽  
Author(s):  
Shi-Rong Li ◽  
Xuan Wang ◽  
Romesh C. Batra
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Plate Theory ◽  
Poisson Ratio ◽  
Functionally Graded ◽  
Thin Plates ◽  
Scaling Factors ◽  
Classical Plate Theory ◽  
Graded Material ◽  
Plane Membrane

Based on the classical plate theory (CPT), we derive scaling factors between solutions of bending, buckling and free vibration of isotropic functionally graded material (FGM) thin plates and those of the corresponding isotropic homogeneous plates. The effective material properties of the FGM plate are assumed to vary piecewise continuously in the thickness direction except for the Poisson ratio that is taken to be constant. The correspondence relations hold for plates of arbitrary geometry provided that the governing equations and boundary conditions are linear. When the stretching and bending stiffnesses of the FGM plate satisfy a relation, Poisson's ratio is constant and the boundary conditions are such that the in-plane membrane forces vanish, then there exists a physical neutral surface for the FGM plate that is usually different from the plate midsurface. Example problems studied verify the accuracy of scaling factors.

scholarly journals AN ANALYTICAL APPROACH ON THE BUCKLING ANALYSIS OF CIRCULAR, SOLID AND ANNULAR FUNCTIONALLY GRADED THIN PLATESGRADED THIN

1970 ◽  
Vol 41 (1) ◽  
pp. 7-14 ◽  
Author(s):  
H. Koohkan ◽  
A. Kimiaeifar ◽  
A. Mansourabadi ◽  
R. Vaghefi
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Thin Plates ◽  
Radial Compression ◽  
Power Functions ◽  
Classical Plate Theory ◽  
Buckling Loads ◽  
Various Boundary Conditions

In this paper, the buckling analysis of circular, solid and annular functionally graded thin plates under uniform radial compression loads is studied. The material properties through the thickness are assumed to be power functions of the thickness. Moreover, the stability equations based on the classical plate theory (CPT), are derived by using the Hamilton’s principle. The obtained coupled-PDEs are difficult to be used for evaluation of the buckling loads of annular plates with various boundary conditions. To resolve this difficulty, a coordinate transformation from the middle plane to a new position is done and as consequence the equations are decoupled. By using the forgoing equations, the buckling loads are determined. The procedure is done for both circular and annular FGM plates of various boundary conditions under uniform radial loads on the edges and the results are validated with one of references.Key Words: Buckling analysis; solid plate; annular plate; functionally graded materials.DOI: 10.3329/jme.v41i1.5357Journal of Mechanical Engineering, Vol. ME 41, No. 1, June 2010 7-14 

Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

2018 ◽  
Vol 233 (8) ◽  
pp. 2636-2662 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam ◽  
Vinayak Ranjan
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Functionally Graded Plate ◽  
Material Inhomogeneity ◽  
Power Law Exponent ◽  
Out Of Plane ◽  
Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

Nonlinear thermo-mechanical buckling of higher-order shear deformable porous functionally graded material plates reinforced by orthogonal and/or oblique stiffeners

2019 ◽  
Vol 233 (17) ◽  
pp. 6177-6196 ◽  
Author(s):  
Vu Hoai Nam ◽  
Nguyen Thi Phuong ◽  
Dang Thuy Dong ◽  
Nguyen Thoi Trung ◽  
Nguyen Van Tue
Keyword(s):  
Shear Deformation ◽  
Elastic Foundation ◽  
Functionally Graded Material ◽  
Thermal Environment ◽  
Plate Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Deformation Plate Theory ◽  
Graded Material ◽  
Post Buckling

In this paper, an analytical approach for nonlinear buckling and post-buckling behavior of stiffened porous functionally graded plate rested on Pasternak's elastic foundation under mechanical load in thermal environment is presented. The orthogonal and/or oblique stiffeners are attached to the surface of plate and are included in the calculation by improving the Lekhnitskii's smeared stiffener technique in the framework of higher-order shear deformation plate theory. The complex equilibrium and stability equations are established based on the Reddy's higher-order shear deformation plate theory and taken into account the geometrical nonlinearity of von Kármán. The solution forms of displacements satisfying the different boundary conditions are chosen, the stress function method and the Galerkin procedure are used to solve the problem. The good agreements of the present analytical solution are validated by making the comparisons of the present results with other results. In addition, the effects of porosity distribution, stiffener, volume fraction index, thermal environment, elastic foundation… on the critical buckling load and post-buckling response of porous functionally graded material plates are numerically investigated.

Low-Velocity Impact on a Functionally Graded Circular Thin Plate

2006 ◽  
Author(s):  
Pantele Chelu ◽  
Liviu Librescu
Keyword(s):  
Plate Theory ◽  
Equation System ◽  
Functionally Graded ◽  
Low Velocity Impact ◽  
Thin Plates ◽  
Low Velocity ◽  
Alternative Analysis ◽  
Velocity Impact ◽  
Graded Material ◽  
The Impact

In this paper, an alternative analysis strategy based on a Wavelet-Galerkin scheme specially tailored to solve impact problems of functionally graded orthotropic thin plates subjected to low-velocity impact is presented. The plate considered to be circular, is assumed to be clamped on its lateral edge and has internal supports of rigid, elastic and viscoelastic types. The material properties of the plate are represented in the form of exponential functions of the thickness coordinate. A rigid spherical indenter impacts the plate. The study is based on the classical lamination plate theory (CLT). An advanced contact law of the Hertzian type is adopted. A nonlinear Volterra integral equation system is obtained in the following unknown functions: the impact force and the dynamic reaction forces at the rigid, elastic and viscoelastic internal point supports. Numerical simulations displaying the contact force, the transversal displacement and the penetration depth are graphically presented, and pertinent conclusions regarding the implications of incorporation of graded material systems are outlined.

Exact Relationships between Eigenvalues of FGM Circular Plates Based on RPT and those of Isotropic Homogeneous Circular Plates Based on CPT

2007 ◽  
Vol 353-358 ◽  
pp. 3002-3005
Author(s):  
Lian Sheng Ma ◽  
Lei Wu
Keyword(s):  
Eigenvalue Problem ◽  
Plate Theory ◽  
Functionally Graded ◽  
Classical Solutions ◽  
Transverse Shear Deformation ◽  
Axisymmetric Vibration ◽  
Circular Plates ◽  
Third Order ◽  
Classical Plate Theory ◽  
Graded Material

Based on the mathematical similarity of the eigenvalue problem of the Reddy’s third-order plate theory (RPT) and the classical plate theory (CPT), relationships between the solutions of axisymmetric vibration or buckling of functionally graded material (FGM) circular plates based on RPT and those of isotropic homogeneous circular plates based on CPT are presented, from which one can easily obtain the RPT solutions of axisymmetric vibration or buckling of FGM circular plates expressed in terms of the well-known CPT solutions of isotropic circular plates without much tedious mathematics. Effects of rotary inertia are not considered in the present analysis. The relationships obtained from the present analysis may be used to check the validity, convergence and accuracy of numerical results of FGM plates based on RPT, and also show clearly the intrinsic features of the effect of transverse shear deformation on the classical solutions.

NONLINEAR MECHANICAL BENDING OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOADS WITH VARIOUS BOUNDARY CONDITIONS

2011 ◽  
Vol 02 (02) ◽  
pp. 237-258 ◽  
Author(s):  
MOHAMMAD TALHA ◽  
B. N. SINGH
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Strain ◽  
Various Boundary Conditions ◽  
Transverse Loads ◽  
Nonlinear Mechanical ◽  
Graded Material ◽  
Mechanical Bending

Nonlinear mechanical bending of functionally graded material (FGM) plates under transverse loads with various boundary conditions are presented. The material properties of the FGM plates are graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The theoretical nonlinear finite element formulations are based on the higher-order shear deformation theory, with a special modification in the transverse displacement in order to estimate the parabolic distribution of transverse shear strains through the plate thickness. The Green–Lagrange nonlinear strain–displacement relation with all higher-order nonlinear strain terms is included to account for the large deflection response of the plate. The fundamental equations for FGM plates with traction-free boundary conditions on the top and bottom faces of the plate are accomplished using variational approach. Results have been achieved using a C0 continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence and comparison studies have been performed to ascertain the effectiveness of the present model. Numerical results are highlighted for different thickness ratios, aspect ratios, and role played by the constituent volume fraction index with different boundary conditions.

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