First-order-theory-based thermoelastic stability of functionally graded material circular plates

AIAA Journal ◽  
2002 ◽  
Vol 40 ◽  
pp. 1444-1450 ◽  
Author(s):  
M. Najafizadeh ◽  
M. R. Eslami
Keyword(s):  
Functionally Graded Material ◽  
Order Theory ◽  
Functionally Graded ◽  
Circular Plates ◽  
First Order ◽  
First Order Theory ◽  
Graded Material

Probabilistic Analysis on the Uncertainty in Natural Frequency of Functionally Graded Material Beams

2019 ◽  
Vol 889 ◽  
pp. 484-488
Author(s):  
Van Thuan Nguyen ◽  
Duy Liem Nguyen
Keyword(s):  
Elastic Modulus ◽  
Natural Frequency ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Order Perturbation ◽  
First Order ◽  
Graded Material ◽  
Natural Frequency Analysis ◽  
Mcs Method ◽  
First Order Perturbation

This paper applies the stochastic finite element method (SFEM) to perform the natural frequency analysis of functionally graded material (FGM). It is assumed that the elastic modulus and width of the FGM beam vary along the thickness and width directions following exponential functions. The stochastic eigenvalue problem is solved independently by first-order perturbation and Monte Carlo simulation (MCS) method through changing elastic modulus as spatial randomness. The results show that the first-order perturbation method based SFEM produces a very close value to MCS method.

Analytical Solutions Using a Higher-Order Refined Theory for the Static Analysis of Functionally Graded Material Plates

2013 ◽  
Vol 705 ◽  
pp. 30-35
Author(s):  
K. Swaminathan ◽  
D.T. Naveenkumar
Keyword(s):  
Shear Deformation ◽  
Static Analysis ◽  
Functionally Graded Material ◽  
Analytical Solutions ◽  
Degrees Of Freedom ◽  
Order Theory ◽  
Higher Order ◽  
Functionally Graded ◽  
Simply Supported ◽  
Graded Material

Analytical formulations and solutions to the static analysis of simply supported Functionally Graded Material (FGM) plates hitherto not reported in the literature based on a higher-order refined shear deformation theory with nine degrees-of-freedom already reported in the literature are presented. This computational model incorporates the plate deformations which account for the effect of transverse shear deformation. The transverse displacement is assumed to be constant throughout the thickness. In addition, another higher order theory with five degrees-of-freedom and the first order theory already reported in the literature are also considered for comparison. The governing equations of equilibrium using all the computational models are derived using the Principle of Minimum Potential Energy (PMPE) and the analytical solutions are obtained in closed-form using Naviers solution technique. A simply supported plate with SS-1 boundary conditions subjected to transverse loading is considered for all the problems under investigation. The varying parameters considered are the side-to-thickness ratio, power law function, edge ratio and the degree of anisotropy. Correctness of the formulation and the solution method is first established and then extensive numerical results using all the models are presented which will serve as a bench mark for future investigations.

scholarly journals Analysis of Sigmoid Functionally Graded Material (S-FGM) Nanoscale Plates Using the Nonlocal Elasticity Theory

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
Woo-Young Jung ◽  
Sung-Cheon Han
Keyword(s):  
Elasticity Theory ◽  
Shear Deformation ◽  
Power Law ◽  
Functionally Graded Material ◽  
Nonlocal Elasticity ◽  
Nonlocal Elasticity Theory ◽  
Functionally Graded ◽  
Vibration Response ◽  
First Order ◽  
Graded Material

Based on a nonlocal elasticity theory, a model for sigmoid functionally graded material (S-FGM) nanoscale plate with first-order shear deformation is studied. The material properties of S-FGM nanoscale plate are assumed to vary according to sigmoid function (two power law distribution) of the volume fraction of the constituents. Elastic theory of the sigmoid FGM (S-FGM) nanoscale plate is reformulated using the nonlocal differential constitutive relations of Eringen and first-order shear deformation theory. The equations of motion of the nonlocal theories are derived using Hamilton’s principle. The nonlocal elasticity of Eringen has the ability to capture the small scale effect. The solutions of S-FGM nanoscale plate are presented to illustrate the effect of nonlocal theory on bending and vibration response of the S-FGM nanoscale plates. The effects of nonlocal parameters, power law index, aspect ratio, elastic modulus ratio, side-to-thickness ratio, and loading type on bending and vibration response are investigated. Results of the present theory show a good agreement with the reference solutions. These results can be used for evaluating the reliability of size-dependent S-FGM nanoscale plate models developed in the future.

Thermal Postbuckling of Imperfect Circular Functionally Graded Material Plates: Examination of Voigt, Mori–Tanaka, and Self-Consistent Schemes

2014 ◽  
Vol 137 (2) ◽  
Author(s):  
Y. Kiani ◽  
M. R. Eslami
Keyword(s):  
Functionally Graded Material ◽  
Initial Imperfection ◽  
Functionally Graded ◽  
Circular Plates ◽  
Equilibrium Equations ◽  
Simply Supported ◽  
Self Consistent ◽  
Nonlinear Equilibrium ◽  
Graded Material ◽  
Thermal Postbuckling

Thermal postbuckling of solid circular plates made of a through-the-thickness functionally graded material (FGM) is analyzed in this paper. Initial imperfection of the plate is also taken into account. Each thermomechanical property of the plate is assumed to be a function of the temperature and thickness coordinate. Equivalent properties of the FGM media are obtained based on three different homogenization schemes, namely, Voigt rule, Mori–Tanaka scheme, and self-consistent estimate. Temperature profile is assumed to be through-the-thickness direction only. The solution of the heat conduction equation is obtained using an iterative central finite difference scheme. Various types of thermal loadings, such as uniform temperature rise, temperature specified at surfaces, and heat flux, are considered. Nonlinear equilibrium equations of the plate are obtained by means of the conventional Ritz method. Solution of the resulting nonlinear equilibrium equations and temperature distribution are obtained simultaneously at each step of heating. It is shown that response of a perfect clamped FGM plate is of the bifurcation type of buckling with stable postbuckling equilibrium branch, whereas imperfect clamped and perfect/imperfect simply supported FGM plates do not reveal the bifurcation type of instability through the nonuniform heating process. Furthermore, amplitude of initial imperfection is an important factor on the equilibrium path of FGM circular plates, especially for simply supported ones.

scholarly journals A New Beam Model for Simulation of the Mechanical Behaviour of Variable Thickness Functionally Graded Material Beams Based on Modified First Order Shear Deformation Theory

Materials ◽  
2019 ◽  
Vol 12 (3) ◽  
pp. 404 ◽  
Author(s):  
Vu Nam ◽  
Pham Vinh ◽  
Nguyen Chinh ◽  
Do Thom ◽  
Tran Hong
Keyword(s):  
Mechanical Behavior ◽  
Functionally Graded Material ◽  
Variable Thickness ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Beam Model ◽  
First Order ◽  
Graded Material ◽  
Fgm Beam

There are many beam models to simulate the variable thickness functionally graded material (FGM) beam, each model has advantages and disadvantages in computer aided engineering of the mechanical behavior of this beam. In this work, a new model of beam is presented to study the mechanical static bending, free vibration, and buckling behavior of the variable thickness functionally graded material beams. The formulations are based on modified first order shear deformation theory and interpolating polynomials. This new beam model is free of shear-locking for both thick and thin beams, is easy to apply in computation, and has efficiency in simulating the variable thickness beams. The effects of some parameters, such as the power-law material index, degree of non-uniformity index, and the length-to-height ratio, on the mechanical behavior of the variable thickness FGM beam are considered.

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