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.

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.

Magneto-electro-elastic vibration of moderately thick FG annular plates subjected to multi physical loads in thermal environment using GDQ method by considering neutral surface

2019 ◽  
Vol 233 (10) ◽  
pp. 2140-2159 ◽  
Author(s):  
Ehsan Arshid ◽  
Ali Kiani ◽  
Saeed Amir
Keyword(s):  
Boundary Conditions ◽  
Natural Frequencies ◽  
Thermal Environment ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Elastic Vibration ◽  
Functionally Graded ◽  
Mode Shapes ◽  
Neutral Surface ◽  
Sensors And Actuators

The vibration analysis of an annular plate made up of functionally graded magneto-electro-elastic materials subjected to multi physical loads is presented. The plate is in thermal environment and temperature is distributed non-uniformly in its thickness direction. In addition, the plate is assumed moderately thick, the material properties vary through the thickness, and the exact neutral surface position is determined and took into account. According to Hamilton’s principle and the first-order shear deformation theory, the governing motion equations are extracted. Numerical results for various boundary conditions are obtained via the generalized differential quadrature method and are validated in simpler states with those of the literature. The effects of different parameters such as material property gradient index, multi physical loads, temperature variations, boundary conditions and geometric specifications of the plate on the natural frequencies and mode shapes are investigated. Temperature changes have little effect on the natural frequencies and the effect of electric potential on them is opposite of magnetic one. In other words, by increasing the magnetic potential, the rigidity of the plate increases too, and the frequency increases. The results of this study are useful to design more efficient sensors and actuators used in the smart or intelligent structures.

Buckling analysis of functionally graded annular sector plates resting on elastic foundations

2010 ◽  
Vol 225 (2) ◽  
pp. 312-325 ◽  
Author(s):  
A Naderi ◽  
A R Saidi
Keyword(s):  
Boundary Conditions ◽  
Elastic Foundation ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Elastic Foundations ◽  
Annular Sector ◽  
Sector Plate ◽  
Annular Sector Plate

In this study, an analytical solution for the buckling of a functionally graded annular sector plate resting on an elastic foundation is presented. The buckling analysis of the functionally graded annular sector plate is investigated for two typical, Winkler and Pasternak, elastic foundations. The equilibrium and stability equations are derived according to the Kirchhoff's plate theory using the energy method. In order to decouple the highly coupled stability equations, two new functions are introduced. The decoupled equations are solved analytically for a plate having simply supported boundary conditions on two radial edges. Satisfying the boundary conditions on the circular edges of the plate yields an eigenvalue problem for finding the critical buckling load. Extensive results pertaining to critical buckling load are presented and the effects of boundary conditions, volume fraction, annularity, plate thickness, and elastic foundation are studied.

NONLINEAR BENDING ANALYSIS OF FUNCTIONALLY GRADED PLATES UNDER PRESSURE LOADS USING A FOUR VARIABLE REFINED PLATE THEORY

2014 ◽  
Vol 11 (04) ◽  
pp. 1350062 ◽  
Author(s):  
MOHAMED ATIF BENATTA ◽  
ABDELHAKIM KACI ◽  
ABDELOUAHED TOUNSI ◽  
MOHAMMED SID AHMED HOUARI ◽  
KARIMA BAKHTI ◽  
...  
Keyword(s):  
Shear Stress ◽  
Shear Deformation ◽  
Transverse Shear ◽  
Plate Theory ◽  
Functionally Graded ◽  
Shear Stresses ◽  
Functionally Graded Plates ◽  
Refined Plate Theory ◽  
Von Karman ◽  
Von Kármán

The novelty of this paper is the use of four variable refined plate theory for nonlinear analysis of plates made of functionally graded materials. The plates are subjected to pressure loading and their geometric nonlinearity is introduced in the strain–displacement equations based on Von–Karman assumptions. Unlike any other theory, the theory presented gives rise to only four governing equations. Number of unknown functions involved is only four, as against five in case of simple shear deformation theories of Mindlin and Reissner (first shear deformation theory). The plate properties are assumed to be varied through the thickness following a simple power law distribution in terms of volume fraction of material constituents. The theory presented is variationally consistent, 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 fundamental equations for functionally graded plates are obtained using the Von–Karman theory for large deflection and the solution is obtained by minimization of the total potential energy. Numerical results for functionally graded plates are given in dimensionless graphical forms; and the effects of material properties on deflections and stresses are determined. The results obtained for plate with various thickness ratios using the theory are not only substantially more accurate than those obtained using the CPT, but are almost comparable to those obtained using higher order theories having more number of unknown functions.

scholarly journals Mechanical Buckling Analysis of Saturated Porous Functionally Graded Elliptical Plates Subjected to In-Plane Force Resting on Two Parameters Elastic Foundation Based on HSDT

2020 ◽  
Vol 142 (4) ◽  
Author(s):  
Mohammad Hossein Sharifan ◽  
Mohsen Jabbari
Keyword(s):  
Elastic Foundation ◽  
Ritz Method ◽  
Shear Deformation Theory ◽  
Potential Energy Function ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Critical Buckling Load ◽  
Mechanical Buckling ◽  
Two Parameters

Abstract In this paper, mechanical buckling analysis of a functionally graded (FG) elliptical plate, which is made up of saturated porous materials and is resting on two parameters elastic foundation, is investigated. The plate is subjected to in-plane force and mechanical properties of the plate assumed to be varied through the thickness of it according to three different functions, which are called porosity distributions. Since it is assumed that the plate to be thick, the higher order shear deformation theory (HSDT) is employed to analyze the plate. Using the total potential energy function and using the Ritz method, the critical buckling load of the plate is obtained and the results are verified with the simpler states in the literature. The effect of different parameters, such as different models of porosity distribution, porosity variations, pores compressibility variations, boundary conditions, and aspect ratio of the plate, is considered and has been discussed in details. It is seen that increasing the porosity coefficient decreases the stiffness of the plate and consequently the critical buckling load will be reduced. Also, by increasing the pores' compressibility, the critical buckling load will be increased. Adding the elastic foundation to the structure will increase the critical buckling load. The results of this study can be used to design more efficient structures in the future.

Buckling Analysis of FGM Thick Beam under Different Boundary Conditions Using GDQM

2012 ◽  
Vol 433-440 ◽  
pp. 4920-4924 ◽  
Author(s):  
Fatemeh Farhatnia ◽  
Mohammad Ali Bagheri ◽  
Amin Ghobadi
Keyword(s):  
Boundary Conditions ◽  
Volume Fraction ◽  
Differential Quadrature Method ◽  
Shear Deformation Theory ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Governing Equations ◽  
Graded Materials ◽  
Generalized Differential ◽  
Thick Beam

In this paper, buckling analysis of functionally graded (FG) thick beam under different conditions is presented. Based on the first order shear deformation theory, governing equations are obtained for Thimoshenko beam which is subjected to mechanical loads. In functionally graded materials (FGMs) the material properties obeying a simple power law is assumed to vary through thickness. In order to solve the buckling differential equations, Generalized Differential Quadrature Method (GDQM) is employed and thus a set of eigenvalue equations resulted. For solving this eigenvalue problem, a computer program was developed in a way that the influence of different parameters such as height to length ratio, various volume fraction functions and boundary conditions were included. Non-dimensional critical stress was calculated for simply-simply, clamped-simply and clamped-clamped supported beams. The results of GDQ method were compared with reported results from solving the Finite element too. The comparison showed the accuracy of obtained results clearly in this work.

A new four-variable refined plate theory for thermal buckling analysis of functionally graded sandwich plates

2011 ◽  
Vol 14 (1) ◽  
pp. 5-33 ◽  
Author(s):  
Mohamed Bourada ◽  
Abdelouahed Tounsi ◽  
Mohammed Sid Ahmed Houari ◽  
El Abbes Adda Bedia
Keyword(s):  
Plate Theory ◽  
Thermal Buckling ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Sandwich Plates ◽  
Refined Plate Theory
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