scholarly journals Thermal Analysis of a Functionally Graded Coating/Substrate System Using the Approximated Transfer Approach

Coatings ◽  
2019 ◽  
Vol 9 (1) ◽  
pp. 51 ◽  
Author(s):  
Hui Wang ◽  
Qinghua Qin
Keyword(s):  
Boundary Conditions ◽  
Heterogeneous Material ◽  
Fundamental Solutions ◽  
Kernel Functions ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Hybrid Finite Element Method ◽  
Polygonal Element ◽  
Graded Coating ◽  
Graded Material

As a heterogeneous material, functionally graded material (FGM) behaves as continuously changed material properties in certain directions from one composition to another, and hence it has received much more attention for biomedical applications and thermal protections to achieve innovative functions that conventional homogeneous material cannot accomplish. However, due to the particularly small thickness ratio of coating to substrate in practice, the conventional mesh discretization of the coating region is inefficient. To simplify the meshing procedure and increase the efficiency of analysis, the approximated transfer algorithm based on the concept of finite difference is developed for transferring boundary conditions applied on the coating surface to the interface of coating and substrate. As a result, only the substrate with transferred convection boundary conditions needs to be solved numerically, i.e., by the fundamental-solution based hybrid finite element method (HFS-FEM) with high accuracy and feasible polygonal element construction, in which only integrals along the element boundary are evaluated because of the application of fundamental solutions of the problem as kernel functions of interior approximated fields. Finally, numerical experiments including the single-layered, multi-layered and functionally graded coatings are carried out to verify the accuracy and applicability of the present method.

Forces on a Circular Hole Located in Functionally Graded Material

2011 ◽  
Vol 704-705 ◽  
pp. 631-635
Author(s):  
Xian Feng Wang ◽  
Feng Xing ◽  
Norio Hasebe
Keyword(s):  
Circular Hole ◽  
Constant Term ◽  
Complex Stress ◽  
Functionally Graded ◽  
Homogeneous Material ◽  
Dimensional Problem ◽  
Stress Components ◽  
Graded Material ◽  
Stress Functions ◽  
Stress Function Method

The complex stress function method is used in this study to formulate the 2-dimensional problem for nonhomogeneous materials. The Young’s modulus E varies linearly with the coordinate x and the Poisson’s ratio of the material is assumed constant and. The stress components and the boundary conditions are expressed in terms of two complex stress functions in explicit forms. It is noted that the constant term in stress functions has an influence on the stress components, which is different from the homogeneous material case. Subsequently, the problem of a nonhomogeneous plane containing a circular hole subjected to a uniform internal pressure is studied.

Vibration analysis of a thin functionally graded plate having an out of plane material inhomogeneity resting on Winkler–Pasternak foundation under different combinations of boundary conditions

2018 ◽  
Vol 233 (8) ◽  
pp. 2636-2662 ◽  
Author(s):  
Piyush Pratap Singh ◽  
Mohammad Sikandar Azam ◽  
Vinayak Ranjan
Keyword(s):  
Boundary Conditions ◽  
Power Law ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Pasternak Foundation ◽  
Functionally Graded Plate ◽  
Material Inhomogeneity ◽  
Power Law Exponent ◽  
Out Of Plane ◽  
Graded Material

In the present research article, classical plate theory has been adopted to analyze functionally graded material plate, having out of plane material inhomogeneity, resting on Winkler–Pasternak foundation under different combinations of boundary conditions. The material properties of the functionally graded material plate vary according to power law in the thickness direction. Rayleigh–Ritz method in conjugation with polynomial displacement functions has been used to develop a computationally efficient mathematical model to study free vibration characteristics of the plate. Convergence of frequency parameters (nondimensional natural frequencies) has been attained by increasing the number of polynomials of displacement function. The frequency parameters of the functionally graded material plate obtained by proposed method are compared with the open literature to validate the present model. Firstly, the present model is used to calculate first six natural frequencies of the functionally graded plate under all possible combinations of boundary conditions for the constant value of stiffness of Winkler and Pasternak foundation moduli. Further, the effects of density, aspect ratio, power law exponent, Young’s modulus on frequency parameters of the functionally graded plate resting on Winkler–Pasternak foundation under specific boundary conditions viz. CCCC (all edges clamped), SSSS (all edges simply supported), CFFF (cantilever), SCSF (simply supported-clamped-free) are studied extensively. Furthermore, effect of stiffness of elastic foundation moduli (kp and kw) on frequency parameters are analyzed. It has been observed that effects of aspect ratios, boundary conditions, Young’s modulus and density on frequency parameters are significant at lower value of the power law exponent. It has also been noted from present investigation that Pasternak foundation modulus has greater effect on frequency parameters as compared to the Winkler foundation modulus. Most of the results presented in this paper are novel and may be used for the validation purpose by researchers. Three dimensional mode shapes for the functionally graded plate resting on elastic foundation have also been presented in this article.

NONLINEAR MECHANICAL BENDING OF FUNCTIONALLY GRADED MATERIAL PLATES UNDER TRANSVERSE LOADS WITH VARIOUS BOUNDARY CONDITIONS

2011 ◽  
Vol 02 (02) ◽  
pp. 237-258 ◽  
Author(s):  
MOHAMMAD TALHA ◽  
B. N. SINGH
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Functionally Graded ◽  
Nonlinear Strain ◽  
Various Boundary Conditions ◽  
Transverse Loads ◽  
Nonlinear Mechanical ◽  
Graded Material ◽  
Mechanical Bending

Nonlinear mechanical bending of functionally graded material (FGM) plates under transverse loads with various boundary conditions are presented. The material properties of the FGM plates are graded in the thickness direction according to a simple power-law distribution in terms of the volume fractions of the constituents. The theoretical nonlinear finite element formulations are based on the higher-order shear deformation theory, with a special modification in the transverse displacement in order to estimate the parabolic distribution of transverse shear strains through the plate thickness. The Green–Lagrange nonlinear strain–displacement relation with all higher-order nonlinear strain terms is included to account for the large deflection response of the plate. The fundamental equations for FGM plates with traction-free boundary conditions on the top and bottom faces of the plate are accomplished using variational approach. Results have been achieved using a C0 continuous isoparametric Lagrangian finite element with 13 degrees of freedom per node. Convergence and comparison studies have been performed to ascertain the effectiveness of the present model. Numerical results are highlighted for different thickness ratios, aspect ratios, and role played by the constituent volume fraction index with different boundary conditions.

FE Analysis of Functionally Graded Material Plate during Debonding Case with Different Boundary Conditions

2014 ◽  
Vol 627 ◽  
pp. 57-60 ◽  
Author(s):  
Wasim M.K. Helal ◽  
Dong Yan Shi
Keyword(s):  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Volume Fraction ◽  
Maximum Shear Stress ◽  
Functionally Graded ◽  
Von Mises Stress ◽  
Sigmoid Function ◽  
Different Boundary Conditions ◽  
Graded Material ◽  
The Relationship

Functionally graded materials (FGMs) have become helpful in our engineering applications. Analysis of functionally graded material (FGM) plate during debonding case with different boundary conditions is the main purpose of this investigation. Elastic modulus (E) of functionally graded (FG) plate is assumed to vary continuously throughout the height of the plate, according the volume fraction of the constituent materials based on a modified sigmoid function, but the value of Poisson coefficient is constant. In this research, the finite element method (FEM) is used in order to show the shape of a plate made of FGM during debonding case with different boundary conditions. In the present investigation, the displacement value applied to the FGM plate is changed in order to find the relationship between the maximum von Mises stress and the displacement. Also, the relationship between the maximum shear stress and the displacement is carried out in the present work. The material gradient indexes of the FGM plate are changed from 1 to 10. The stress distributions around the debonding zone with all the material gradient indexes of the FGM plate are investigated in this work.

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.

Bending deflection and stress analyses in a thin functionally graded material skew plate with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined in-plane and uniform lateral loads using the extended Kantorovich method

2021 ◽  
pp. 095440622199068
Author(s):  
Ahmad Mamandi
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Boundary Conditions ◽  
Functionally Graded ◽  
Kantorovich Method ◽  
Different Boundary Conditions ◽  
Extended Kantorovich Method ◽  
Skew Plate ◽  
Pasternak Elastic Foundation ◽  
Graded Material

In this study, bending deflection and stress analyses have been conducted for a thin skew plate made of functionally graded material (FGM) with different boundary conditions on the Winkler–Pasternak elastic foundation and under combined loads including uniform transverse load, normal and shear in-plane forces, and planar body forces. The Cartesian partial differential equation governing the bending deflection of the skew plate has been converted into a partial differential equation in oblique coordinates using the conversion relations. Then, by employing the variational principle and residual weighted Galerkin method and using the Extended Kantorovich Method (EKM), the equation has been converted to a set of linear differential equations in terms of two functions in the longitudinal and transverse directions of the oblique plate, and afterward, the equation has been solved using the iterative solution method. Different boundary conditions in a combined form of simply and clamped supports have been investigated and their effects on bending deflection and generated in-plane normal and shear stresses are discussed.

scholarly journals Free vibration analysis of 2D-FGM truncated conical shell resting on Winkler–Pasternak foundations based on FSDT

2014 ◽  
Vol 229 (5) ◽  
pp. 818-839 ◽  
Author(s):  
A Asanjarani ◽  
S Satouri ◽  
A Alizadeh ◽  
MH Kargarnovin
Keyword(s):  
Free Vibration ◽  
Boundary Conditions ◽  
Functionally Graded Material ◽  
Conical Shell ◽  
Shear Deformation Theory ◽  
Functionally Graded ◽  
Geometrical Parameters ◽  
Two Dimensional ◽  
Graded Material ◽  
Truncated Conical Shell

Based on the first-order shear deformation theory, this paper focuses on the free vibration behavior of two-dimensional functionally graded material truncated conical shells resting on Winkler–Pasternak foundations. The materials are assumed to be isotropic and inhomogeneous in the length and thickness directions of truncated conical shell. The material properties of the truncated conical shell are varied in these directions according to power law functions. The derived governing equations are solved using differential quadrature method. Convergence of this method is checked and the fast rate of convergence is observed. The primary results of this study are obtained for ( SS− SL), ( CS− CL), and ( CS− SL) boundary conditions and compared with those available in the literatures. Furthermore, effects of geometrical parameters, material power indexes, mechanical boundary conditions, Winkler and Pasternak foundation moduli on the nondimensional frequency parameters of the two-dimensional functionally graded material truncated conical shell are studied.

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