Elasticity Solutions for Annular Plates of Functionally Graded Materials Subjected to a Uniform Load

2011 ◽  
Vol 261-263 ◽  
pp. 853-857
Author(s):  
Bo Yang ◽  
Xin Zhang ◽  
Han Yu Yu
Keyword(s):  
Boundary Conditions ◽  
Complex Variable ◽  
Plate Theory ◽  
Theory Of Elasticity ◽  
Functionally Graded ◽  
Transverse Load ◽  
Functionally Graded Plates ◽  
Uniform Load ◽  
Classical Plate Theory ◽  
Elasticity Solutions

England (2006) proposed a novel theory to study the bending problem of isotropic functionally graded plates subjected to transverse biharmonic loads. His theory is extended here to functionally graded plates of transversely isotropic materials. Using the complex variable method, the governing equations of three plate displacements appearing in the expansions of the displacement field are formulated based on the three-dimensional theory of elasticity for a transverse load satisfying the biharmonic equation. The solutions may be expressed in terms of four analytic functions of the complex variable, in which the unknown constants can be determined from the boundary conditions similar to that in the classical plate theory(CPT). The elasticity solutions of an FGM annular plate under a uniform load are derived. A comparison of the present results for a uniform load with existing solutions is made and good agreement is observed. The influence of boundary conditions, material inhomogeneity and radius-to-radius ratio on the plate deflection and stresses are studied numerically.

scholarly journals Multiparametric Analytical Solution for the Eigenvalue Problem of FGM Porous Circular Plates

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 429 ◽  
Author(s):  
Krzysztof Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Equations Of Motion ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as a linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the neglected effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

Nonlinear Random Vibration of Functionally Graded Plates

2010 ◽  
Author(s):  
Vedat Dogan
Keyword(s):  
Random Vibration ◽  
Plate Theory ◽  
Random Excitation ◽  
Functionally Graded ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Classical Plate Theory ◽  
Nonlinear Random Vibration ◽  
Time Domain Response ◽  
Stationary Random Processes

The nonlinear random vibration of functionally graded plates under random excitation is presented. Material properties are assumed to be independent of temperature. The plates are assumed to have isotropic, two-constituent material distribution through the thickness. The modulus of elasticity, thermal expansion coefficient and density vary according to a power-law distribution in terms of the volume fractions of the constituents. The Classical Plate Theory (CPT) is employed for analytical formulations. Geometric nonlinearity due to in-plane stretching and von Karman type is considered. A Monte Carlo simulation of stationary random processes, multi-mode Galerkin-like approach, and numerical integration procedures are used to develop linear and nonlinear response solutions of clamped functionally graded plates. Uniform temperature distributions through the plate are assumed. Numerical results include time domain response histories, root mean square (RMS) values and response spectral densities. Effects of material composition and temperature rise are also investigated.

Refined hyperbolic shear deformation plate theory

2014 ◽  
Vol 229 (15) ◽  
pp. 2675-2686 ◽  
Author(s):  
K Nareen ◽  
RP Shimpi
Keyword(s):  
Shear Deformation ◽  
Plate Theory ◽  
Plate Thickness ◽  
Three Dimensional ◽  
Theory Of Elasticity ◽  
Governing Equations ◽  
Dimensional Theory ◽  
Classical Plate Theory ◽  
Shear Deformation Plate Theory ◽  
Elasticity Solutions

The paper presents a novel shear deformation plate theory involving only two variables. Taking a cue from exact three-dimensional theory of elasticity solutions for a plate, hyperbolic functions are used for describing displacement variation across plate thickness. The theory involves only two governing equations, which are uncoupled for statics and are only inertially coupled for dynamics. The shear stress free surface conditions are satisfied. No shear correction factor is required. The theory is variationally consistent, has a strong similarity with classical plate theory, and is simple, yet accurate. Illustrative examples for free vibration and for static flexure demonstrate the effectiveness of the theory.

Levy solution for buckling analysis of functionally graded plates based on a refined plate theory

2013 ◽  
Vol 227 (12) ◽  
pp. 2649-2664 ◽  
Author(s):  
Huu-Tai Thai ◽  
Brian Uy
Keyword(s):  
Boundary Conditions ◽  
Plate Theory ◽  
Coupling Effect ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Neutral Surface ◽  
Functionally Graded Plates ◽  
Refined Plate Theory

This article presents analytical solutions for buckling analysis of functionally graded plate based on a refined plate theory. Based on the refined shear deformation theory, the position of neutral surface is determined and the governing stability equations based on neutral surface are derived. There is no stretching–bending coupling effect in the neutral surface-based formulation, and consequently, the governing equations and boundary conditions of functionally graded plates based on neutral surface have the simple forms as those of isotropic plates. The closed-form solutions of buckling load are obtained for rectangular plates with various boundary conditions. The accuracy of neutral surface-based model is verified by comparing the obtained results with those reported in the literature. Finally, parameter studies are carried out to study the effects of power law index, thickness ratio, and aspect ratio on the critical buckling load of functionally graded plates.

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 Exact Analytical Solution for Free Axisymmetric and Non-Axisymmetric Vibrations of FGM Porous Circular Plates

2018 ◽  
Author(s):  
Krzysztof Kamil Żur ◽  
Piotr Jankowski
Keyword(s):  
Boundary Conditions ◽  
Circular Plate ◽  
Special Functions ◽  
Plate Theory ◽  
Exact Analytical Solution ◽  
Free Vibration Analysis ◽  
Functionally Graded ◽  
Circular Plates ◽  
Classical Plate Theory ◽  
Coupled Equations

Free vibration analysis of the porous functionally graded circular plates has been presented on the basis of classical plate theory. The three defined coupled equations of motion of the porous functionally graded circular/annular plate were decoupled to one differential equation of free transverse vibrations of plate. The one universal general solution was obtained as linear combination of the multiparametric special functions for the functionally graded circular and annular plates with even and uneven porosity distributions. The multiparametric frequency equations of functionally graded porous circular plate with diverse boundary conditions were obtained in the exact closed-form. The influences of the even and uneven distributions of porosity, power-law index, diverse boundary conditions and the negligibled effect of the coupling in-plane and transverse displacements on the dimensionless frequencies of the circular plate were comprehensively studied for the first time. The formulated boundary value problem, the exact method of solution and the numerical results for the perfect and imperfect functionally graded circular plates have not yet been reported.

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 

Static Analysis of Moderately Thick Functionally Graded Plates With Various Boundary Conditions

2010 ◽  
Author(s):  
Nastaran Shahmansouri ◽  
Mohammad Mohammadi Aghdam ◽  
Kasra Bigdeli
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Closed Form Solution ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Various Boundary Conditions ◽  
Fg Plates ◽  
Ode Systems

The present study investigates static analyses of moderately thick FG plates. Using the First Order Shear Deformation Theory (FSDT), functionally graded plates subjected to transversely distributed loading with various boundary conditions are studied. Effective mechanical properties which vary from one surface of the plate to the other assumed to be defined by a power law form of distribution. Different ceramic-metal sets of materials are studied. Solution of the governing equations, including five equilibrium and eight constitutive equations, is obtained by the Extended Kantorovich Method (EKM). The system of thirteen Partial Differential Equations (PDEs) in terms of displacements, rotations, force and moment resultants are considered as multiplications of separable function of independent variables x and y. Then by successful utilization of the EKM these equations are converted to a double set of ODE systems in terms of x and y. The obtained ODE systems are then solved iteratively until final convergence is achieved. Closed form solution is presented for these ODE sets. It is shown that the method is very stable and provides fast convergence and highly accurate predictions for both thin and moderately thick plates. Comparison of the normal stresses at various points of rectangular plates and deflection of mid-point of the plate are presented and compared with available data in the literature. The effects of the volume fraction exponent n on the behavior of the normalized deflection, moment resultants and stresses of FG plates are also studied. To validate data for analysis fully clamped FG plates, another analysis was carried out using finite element code ANSYS. Close agreement is observed between predictions of the EKM and ANSYS.

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