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.

Bending Analysis of Piezoelectric Functionally Graded Material Plates Using HSDT

2019 ◽  
Vol 969 ◽  
pp. 116-121
Author(s):  
Ch. Naveen Reddy ◽  
M. Bhargav ◽  
T. Revanth
Keyword(s):  
Analytical Solution ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Deformation Theory ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Analytical Formulation ◽  
Simply Supported ◽  
Graded Material

This work investigates the complete analytical solution for functionally graded material (FGM) plates incorporated with smart material. The odjective of the present work is to determine bending characteristics of piezoelectric FGM plates with different geometrical parameters, voltages and boundary conditions for electro-mechanical loading. In this work an analytical formulation based on higher order shear deformation theory (HSDT) is presented for the piezoelectric FGM plates. The solutions are obtained in closed from using Navier’s technique for piezoelectric FGM plates a specific type of simply supported boundary conditions and pc code have been developed to find out the deflections and stresses for various parameters. All the solutions are plotted against aspect proportion, side to thickness proportion as a function of material variety parameter (n) and thickness coordinate for different voltages. The significant trends from the results are obtained.

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 Research on the dynamic buckling of functionally graded material plates under conditions of one edge fixed and three edges simply supported

2018 ◽  
Vol 38 ◽  
pp. 02013
Author(s):  
Wang Xin ◽  
Han Zhi Jun ◽  
Wu Ya Li
Keyword(s):  
Critical Load ◽  
Functionally Graded Material ◽  
Dynamic Buckling ◽  
Functionally Graded ◽  
Gradient Index ◽  
Mixing Rate ◽  
Analytical Expression ◽  
Simply Supported ◽  
Longitudinal Load ◽  
Graded Material

Based on the strain assumption and linear mixing rate of Vogit, the physical property parameter expression of functionally graded material plates is obtained. According to the theory of small deformation and Hamilton principle, the dynamic buckling governing equation of functionally graded material plates under longitudinal load is obtained. Using the method of trial function, the analytical expression of critical load and the buckling solution of the functionally graded material plate under conditions of one edge fixed and three edges simply supported is obtained. The analytical expression of critical load is numerically calculated by METLAB. The influence of geometric size, gradient index, modal order and material composition on critical load is discussed. The results show that the critical buckling load decreases exponentially with the increase of critical length, decreases with the increase of gradient index k, increases with the increase of modal order, and the elastic modulus of constituent materials has significant effect on the critical load. The higher-order buckling modes of functionally graded material plates are prone to occur under the condition of high longitudinal load.

Buckling of Simply Supported Piezoelectric FGM Plates Subjected to Electro-Mechanical Loading Using Higher-Order Shear Deformation Theory

2012 ◽  
Vol 622-623 ◽  
pp. 200-205
Author(s):  
Kamal M. Bajoria ◽  
Priyanka A. Jadhav
Keyword(s):  
Stability Analysis ◽  
Functionally Graded Material ◽  
Material Properties ◽  
Deformation Theory ◽  
Piezoelectric Effect ◽  
Volume Fraction ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Simply Supported ◽  
Graded Material

This paper investigates the stability analysis of plates made of functionally graded material (FGM) and integrated with piezoelectric actuator and sensor at top and bottom face subjected to electrical and mechanical loading. The finite element formulation is presented using degenerated shell element, von-Karman hypothesis, higher-order shear deformation theory and considering the piezoelectric effect. The governing equilibrium equation is derived using the principle of minimum energy and solution for critical buckling load is obtained by solving Eigen value problem. The material properties of the FGM plates are assumed to be graded along the thickness direction according to simple power-law distribution in terms of the volume fraction of the constituents, while the poison’s ratio is assumed to be constant. Stability analysis is carried out on simply supported plate made of newly introduced metal based functionally graded material (FGM) i.e. mixture of aluminum and stainless steel which exhibits the two different material properties in single material i.e. high corrosion resistance as well as high strength. Results show that the buckling strength of plate increases with increase in volume fraction indices through the thickness and it can be further improved with the help of piezoelectric effect.

Buckling analysis of circular functionally graded material plate having variable thickness under uniform compression by finite-element method

2007 ◽  
Vol 221 (11) ◽  
pp. 1241-1247 ◽  
Author(s):  
M H Naei ◽  
A Masoumi ◽  
A Shamekhi
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Functionally Graded Material ◽  
Variable Thickness ◽  
Buckling Analysis ◽  
Functionally Graded ◽  
Buckling Load ◽  
Simply Supported ◽  
Graded Material ◽  
Element Method

The current study presents the buckling analysis of radially-loaded circular plate with variable thickness made of functionally graded material. The boundary conditions of the plate is either simply supported or clamped. The stability equations were obtained using energy method based on Love-Kichhoff hypothesis and Sander's non-linear strain-displacement relation for thin plates. The finite-element method is used to determine the critical buckling load. The results obtained show good agreement with known analytical and numerical data. The effects of thickness variation and Poisson's ratio are investigated by calculating the buckling load. These effects are found not to be the same for simply supported and clamped plates.

scholarly journals A Stress Approach Model of Functionally Graded Shells

2020 ◽  
Vol 2020 ◽  
pp. 1-16
Author(s):  
Carlos Humberto Rubio Rascón ◽  
Alberto Díaz Díaz ◽  
Axel Fernando Domínguez Alvarado
Keyword(s):  
Finite Element ◽  
Stress Field ◽  
Functionally Graded Material ◽  
Degrees Of Freedom ◽  
Computational Cost ◽  
Good Alternative ◽  
Functionally Graded ◽  
Equilibrium Equations ◽  
Finite Element Calculations ◽  
Graded Material

This paper presents a model called SAM-FG (stress approach model of functionally graded shells) for linear elastic, thin, and moderately thick shells made of functionally graded materials. The model is an extension of the SAM-H model, originally created for homogeneous shells. Assuming that the material is orthotropic and that one of its orthotropic directions is the thickness direction, the extension consists in considering that the 3D compliance tensor may depend on the thickness coordinate. The model starts with a tunable polynomial approximation of the 3D stress field that contains the same generalized forces as SAM-H. This stress approximation verifies the 3D equilibrium equations and the stress boundary conditions at the faces of the shell. As in SAM-H, 5 generalized displacements appear in SAM-FG. By applying the Hellinger–Reissner functional and Reissner’s variational method, the generalized forces, strains, and equations in SAM-FG turn out to be the same as in SAM-H, except for the generalized constitutive equations. To prove the accuracy of the model, SAM-FG is first applied to a simply supported, functionally graded plate and its results are compared to other models. To validate the model for shell-like structures, SAM-FG results are compared to those obtained with solid finite element calculations for three case studies of structures subjected to an internal pressure. The first one deals with a hollow sphere made of an isotropic functionally graded material. The second case considers a hollow cylinder made of an orthotropic functionally graded material. In the last case, a catenoid with an isotropic functionally graded material is studied. In all cases, the mean displacements are correctly predicted, even if the main purpose of the SAM-FG model is not to calculate these fields accurately. The stress field approximations are very accurate, and since the implementation of the shell model in a finite element code would imply 5 degrees of freedom per node, SAM-FG is a good alternative to solid finite element calculations for the structural analysis of functionally graded shells with a reasonable computational cost.

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