BUCKLING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER MECHANICAL LOADING USING HIGHER ORDER FUNCTIONALLY GRADED STRIP

2013 ◽  
Vol 13 (06) ◽  
pp. 1350033 ◽  
Author(s):  
M. H. SHERAFAT ◽  
H. R. OVESY ◽  
S. A. M. GHANNADPOUR
Keyword(s):  
Volume Fraction ◽  
Plate Theory ◽  
Load Capacity ◽  
Plate Thickness ◽  
Higher Order ◽  
Functionally Graded ◽  
Biaxial Compression ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Ceramic Phase

This paper is concerned with buckling analyses of rectangular functionally graded plates (FGPs) under uniaxial compression, biaxial compression and combined compression and tension loads. It is assumed that the plate is a mixture of metal and ceramic that its properties changes as afunction according to the simple power law distribution through the plate thickness. The fundamental eigen-buckling equations for rectangular plates of functionally graded material (FGM) are obtained by discretizing the plate into some finite strips, which are developed on the basis of the higher order plate theory (HOPT). The solution is obtained by the minimization of the total potential energy. Numerical results fora variety of FGPs are given, and compared with the available results, wherever possible. The effects of thickness ratio, variation of the volume fraction of the ceramic phase through the thickness, aspect ratio, boundary conditions and also load distribution on the buckling load capacity of FGM plates are determined and discussed. It is found that the buckling behavior of FGM plates is particularly influenced by application of HOPT, especially when the plates are thick.

Large Deflection Behavior of Relatively Thick Functionally Graded Plates under Pressure Loads Using Higher Order Shear Deformation Theory

2011 ◽  
Vol 471-472 ◽  
pp. 709-714 ◽  
Author(s):  
Mohammad Homayoun Sadr-Lahidjani ◽  
Mohammad Hajikazemi ◽  
Mona Ramezani-Oliaee
Keyword(s):  
Shear Deformation ◽  
Deformation Theory ◽  
Large Deflection ◽  
Plate Theory ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Rectangular Plates ◽  
Functionally Graded Plates ◽  
Power Law Distribution

Large deflection analysis of thin and relatively thick rectangular functionally graded plates is studied in this paper. It is assumed that the mechanical properties of the plate, graded through the thickness, are described by a simple power law distribution in terms of the volume fractions of constituents. The plate is assumed to be under lateral pressure load. The fundamental equations for rectangular plates of FGM are obtained using the classical laminated plate theory (CLPT), first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT) for large deflection and the solution is obtained by minimization of the total potential energy.

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.

Free Vibration and Buckling Analysis of Functionally Graded Plates Resting on Elastic Foundation Using Higher Order Theory

2018 ◽  
Vol 18 (04) ◽  
pp. 1850049 ◽  
Author(s):  
Smita Parida ◽  
Sukesh Chandra Mohanty
Keyword(s):  
Free Vibration ◽  
Shear Deformation ◽  
Elastic Foundation ◽  
Volume Fraction ◽  
Plate Theory ◽  
Higher Order ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Pasternak Elastic Foundation

This paper deals with the free vibration and buckling analysis of functionally graded material (FGM) plates, resting on the Winkler–Pasternak elastic foundation. The higher order shear deformation plate theory (HSPT) is adopted for the realistic variation of transverse displacement through the thickness, using the power law distribution to describe the variation of the material properties. Both the effects of shear deformation and rotary inertia are considered. In the present model, the plate is discretised into [Formula: see text] eight noded serendipity quadratic elements with seven nodal degrees of freedom (DOFs). The validation study is carried out by comparing the calculated values with those given in the literature. The effects of various parameters like the Winkler and Pasternak modulus coefficients, volume fraction index, aspect ratio, thickness ratio and different boundary conditions on the behaviour of the FGM plates are studied.

scholarly journals A Novel Higher-Order Shear and Normal Deformable Plate Theory for the Static, Free Vibration and Buckling Analysis of Functionally Graded Plates

2017 ◽  
Vol 2017 ◽  
pp. 1-20 ◽  
Author(s):  
Shi-Chao Yi ◽  
Lin-Quan Yao ◽  
Bai-Jian Tang
Keyword(s):  
Natural Frequencies ◽  
Plate Theory ◽  
Closed Form Solution ◽  
Higher Order ◽  
Form Solution ◽  
Functionally Graded ◽  
The Novel ◽  
Functionally Graded Plates ◽  
Graded Materials ◽  
Different Shapes

Closed-form solution of a special higher-order shear and normal deformable plate theory is presented for the static situations, natural frequencies, and buckling responses of simple supported functionally graded materials plates (FGMs). Distinguished from the usual theories, the uniqueness is the differentia of the new plate theory. Each individual FGM plate has special characteristics, such as material properties and length-thickness ratio. These distinctive attributes determine a set of orthogonal polynomials, and then the polynomials can form an exclusive plate theory. Thus, the novel plate theory has two merits: one is the orthogonality, where the majority of the coefficients of the equations derived from Hamilton’s principle are zero; the other is the flexibility, where the order of the plate theory can be arbitrarily set. Numerical examples with different shapes of plates are presented and the achieved results are compared with the reference solutions available in the literature. Several aspects of the model involving relevant parameters, length-to-thickness, stiffness ratios, and so forth affected by static and dynamic situations are elaborate analyzed in detail. As a consequence, the applicability and the effectiveness of the present method for accurately computing deflection, stresses, natural frequencies, and buckling response of various FGM plates are demonstrated.

A New Higher Order Shear Deformation Model for Static Behavior of Functionally Graded Plates

2013 ◽  
Vol 5 (03) ◽  
pp. 351-364 ◽  
Author(s):  
Tahar Hassaine Daouadji ◽  
Abdelouahed Tounsi ◽  
El Abbes Adda Bedia
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Volume Fraction ◽  
Higher Order ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Deformation Model ◽  
Functionally Graded Plates ◽  
Static Behavior

AbstractIn this paper, a new displacement based high-order shear deformation theory is introduced for the static response of functionally graded plate. Unlike any other theory, the number of unknown functions involved is only four, as against five in case of other shear deformation theories. The theory presented is variationally consistent, has strong similarity with classical plate theory in many aspects, does not require shear correction factor, and gives rise to transverse shear stress variation such that the transverse shear stresses vary parabolically across the thickness satisfying shear stress free surface conditions. The mechanical properties of the plate are assumed to vary continuously in the thickness direction by a simple power-law distribution in terms of the volume fractions of the constituents. Numerical illustrations concerned flexural behavior of FG plates with Metal-Ceramic composition. Parametric studies are performed for varying ceramic volume fraction, volume fraction profiles, aspect ratios and length to thickness ratios. The validity of the present theory is investigated by comparing some of the present results with those of the classical, the first-order and the other higher-order theories. It can be concluded that the proposed theory is accurate and simple in solving the static behavior of functionally graded plates.

Buckling of Functionally Graded Circular/Annular Plates Based on the First-Order Shear Deformation Plate Theory

2004 ◽  
Vol 261-263 ◽  
pp. 609-614 ◽  
Author(s):  
L.S. Ma ◽  
Tie Jun Wang
Keyword(s):  
Shear Deformation ◽  
Material Properties ◽  
Volume Fraction ◽  
Plate Theory ◽  
Plate Thickness ◽  
Shear Deformation Theory ◽  
Outer Radius ◽  
Functionally Graded ◽  
First Order ◽  
Annular Plates

Based on the first-order shear deformation theory of plate, governing equations for the axisymmetric buckling of functionally graded circular/annular plates are derived. The coupled deflections and rotations in the pre-buckling state of the plates are neglected in analysis. The material properties vary continuously through the thickness of the plate, and obey a power law distribution of the volume fraction of the constituents. The resulting differential equations are numerically solved by using a shooting method. The critical buckling loads of circular and annular plates are obtained, which are compared with those obtained from the classical plate theory. Effects of material properties, ratio of inter to outer radius, ratio of plate thickness to outer radius, and boundary conditions on the buckling behavior of FGM plates are discussed.

Nonlinear Vibrations of Pressurized Functionally Graded Plates Using Higher-Order Thickness Stretching Theory

2014 ◽  
Author(s):  
F. Alijani ◽  
M. Amabili
Keyword(s):  
Nonlinear Vibrations ◽  
Equations Of Motion ◽  
Three Dimensional ◽  
Shear Deformation Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Numerical Continuation ◽  
Normal Strain ◽  
Rectangular Plates ◽  
Functionally Graded Plates

Nonlinear vibrations of moderately thick functionally graded (FG) rectangular plates are investigated by considering a higher-order shear deformation theory that takes into account the thickness deformation effect. The geometrically nonlinear strain-displacement relationships are derived retaining full non-linear terms in the in-plane and transverse displacements and the three-dimensional constitutive equations are used by removing the assumption of zero transverse normal strain. The plate is assumed to have immovable boundary conditions at the edges. The equations of motion are obtained by using multi-modal energy approach. A code based on pseudo arc-length continuation and collocation scheme is utilized for numerical continuation and bifurcation analysis. Results show that higher-order thickness deformation theories yield a significant accuracy improvement for nonlinear vibrations of highly pressurized functionally graded plates.

A New Trigonometric Higher-Order Shear and Normal Deformation Theory for Functionally Graded Plates

2016 ◽  
Author(s):  
Ankit Gupta ◽  
Mohammad Talha
Keyword(s):  
Boundary Conditions ◽  
Deformation Theory ◽  
Volume Fraction ◽  
Higher Order ◽  
Functionally Graded ◽  
Transverse Displacement ◽  
Functionally Graded Plates ◽  
Power Law Distribution ◽  
Normal Deformation ◽  
3 Dimensional

In the present study, a new trigonometric higher-order shear and normal deformation theory is proposed and implemented to investigate the free vibration characteristics of functionally graded material (FGM) plates. The present theory comprises the nonlinear variation in the in-plane and transverse displacement and accommodates, both shear deformation and thickness stretching effects. It also satisfies the stress-free boundary conditions on the top and bottom surfaces of the plate without requiring any shear correction factor. The governing equations are derived using the variational principle. The effective mechanical properties of FGM plates are assumed to vary according to a power law distribution of the volume fraction of the constituents. Poisson’s ratios of FGM plates are assumed constant. The numerical solution has been obtained using an efficient displacement based C0 finite element model with eight degrees of freedom per node. The computed results are compared with 3-dimensional and quasi-3-dimensional solutions and those projected by other well-known plate theories. Natural frequencies of the functionally graded plates with various side-to-thickness ratios, boundary conditions, and volume fraction index ‘n’ have been computed. It can be concluded that the proposed model is not only accurate but also simple in predicting the vibration behavior of functionally graded plates.

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