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CONTENTS
Volume 5, Number 4, December 2016
 

Abstract
In this article, the buckling responses of functionally graded curved (spherical, cylindrical, hyperbolic and elliptical) shell panels under elevated temperature load are investigated numerically using finite element steps. The effective material properties of the functionally graded shell panel are evaluated using Voigt´s micromechanical model through the power-law distribution with and without temperature dependent properties. The mathematical model is developed using the higher-order shear deformation theory in conjunction with Green-Lagrange type nonlinear strain to consider large geometrical distortion under thermal load. The efficacy of the proposed model has been checked and the effects of various geometrical and material parameters on the buckling load are analysed in details.

Key Words
FGM; thermal buckling; single/doubly curved panel; HSDT; ANSYS

Address
Vishesh R. Kar: Department of Design and Automation, School of Mechanical Engineering, VIT University Vellore: 632014, India

Subrata K. Panda: Department of Mechanical Engineering, National Institute of Technology, Rourkela: 769008, India

Trupti R. Mahapatra: School of Mechanical Engineering, KIIT University, Bhubaneswar: 751024, India

Abstract
In this paper, a higher order shear and normal deformation theory is presented for functionally graded material (FGM) plates. By dividing the transverse displacement into bending, shear and thickness stretching parts, the number of unknowns and governing equations for the present theory is reduced, significantly facilitating engineering analysis. Indeed, the number of unknown functions involved in the present theory is only five, as opposed to six or even greater numbers in the case of other shear and normal deformation theories. The present theory accounts for both shear deformation and thickness stretching effects by a hyperbolic variation of ail displacements across the thickness and satisfies the stress-free boundary conditions on the upper and lower surfaces of the plate without requiring any shear correction factor. Equations of motion are derived from Hamilton&aqute;s principle. Analytical solutions for the bending and free vibration analysis are obtained for simply supported plates. The obtained results are compared with three-dimensional and quasi- three-dimensional solutions and those predicted by other plate theories. It can be concluded that the present theory is not only accurate but also simple in predicting the bending and free vibration responses of functionally graded plates.

Key Words
Functionally Graded Material; power law index; Higher-order Shear Deformation Theory; Navier solution

Address
Belkacem Adim and Tahar Hassaine Daouadji: Departement de genie civil , Universite Ibn Khaldoun Tiaret; BP 78 Zaaroura, 14000 Tiaret, Algerie

Belkacem Adim and Tahar Hassaine Daouadji: Ibn Khaldoun de Tiaret, Algerie

Abstract
Thermo-mechanical buckling problem of functionally graded (FG) nanoplates supported by Pasternak elastic foundation subjected to linearly/non-linearly varying loadings is analyzed via the nonlocal elasticity theory. Two opposite edges of the nanoplate are subjected to the linear and nonlinear varying normal stresses. Elastic properties of nanoplate change in spatial coordinate based on a powerlaw form. Eringen´s nonlocal elasticity theory is exploited to describe the size dependency of nanoplate. The equations of motion for an embedded FG nanoplate are derived by using Hamilton principle and Eringen´s nonlocal elasticity theory. Navier´s method is presented to explore the influences of elastic foundation parameters, various thermal environments, small scale parameter, material composition and the plate geometrical parameters on buckling characteristics of the FG nanoplate. According to the numerical results, it is revealed that the proposed modeling can provide accurate results of the FG nanoplates as compared some cases in the literature. Numerical examples show that the buckling characteristics of the FG nanoplate are related to the material composition, temperature distribution, elastic foundation parameters, nonlocality effects and the different loading conditions.

Key Words
anoplates buckling; functionally graded material; linear and nonlinear varying loading; thermal loading; Pasternak foundation; nonlocal elasticity theory; Navier´s method

Address
Department of Mechanical Engineering, Faculty of Engineering, Imam Khomeini International University, Postal code: 3414916818, Qazvin, Iran


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