Functionally Graded Hollow Sphere With Piezoelectric Internal and External Layers Under Asymmetric Transient Thermomechanical Loads

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Hollow Sphere ◽  
Legendre Polynomials ◽  
Radial Direction ◽  
Energy Equation ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Power Functions ◽  
Legendre Series ◽  
Piezoelectric Layers ◽  
Transient Thermal

In this paper, an analytical method is developed to obtain the solution for the two-dimensional (2D) (r,θ) transient thermal and mechanical stresses in a hollow sphere made of functionally graded (FG) material and piezoelectric layers. The FGM properties vary continuously across the thickness, according to the power functions of radial direction. The temperature distribution as a function of radial and circumferential directions and time is obtained solving the energy equation, using the method of separation of variables and Legendre series. The Navier equations are solved analytically using the Legendre polynomials and the system of Euler differential equations.

Solution for Equation of Two-Dimensional Transient Heat Conduction in Functionally Graded Material Hollow Sphere With Piezoelectric Internal and External Layers

2016 ◽  
Vol 139 (1) ◽  
Author(s):  
M. Jabbari ◽  
S. M. Mousavi ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Functionally Graded Material ◽  
Hollow Sphere ◽  
Transient Heat Conduction ◽  
Functionally Graded ◽  
Transient Temperature ◽  
Two Dimensional ◽  
Power Functions ◽  
Legendre Series ◽  
Graded Material

In this paper, an exact solution for the equation of two-dimensional transient heat conduction in a hollow sphere made of functionally graded material (FGM) and piezoelectric layers is developed. Transient temperature distribution, as a function of radial and circumferential directions and time with general thermal boundary conditions on the inside and outside surfaces, is analytically obtained for different layers, using the method of separation of variables and Legendre series. The results are the sum of transient and steady-state solutions that depend upon the initial condition for temperature and heat source, respectively. The FGM properties are assumed to depend on the variable r and they are expressed as power functions of r.

scholarly journals Two-Dimensional Stress Analysis of Thick Hollow Functionally Graded Sphere Under Non-Axisymmetric Mechanical Loading

2021 ◽  
Vol 6 (4) ◽  
pp. 1115-1126
Author(s):  
Sandeep Kumar Paul ◽  
Manoj Sahni
Keyword(s):  
Differential Equation ◽  
Steady State ◽  
Mechanical Loading ◽  
Radial Direction ◽  
External Pressure ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Legendre Series ◽  
Spherical Coordinate ◽  
Nonlinear Variation

In this paper, a functionally graded thick hollow sphere is considered for the analysis of two-dimensional steady state mechanical stress in the radial and circumferential directions under mechanical loading. Modulus of elasticity is varying with continuous nonlinear variation along the radial direction and Poisson’s ratio is kept as constant. The Legendre series and Euler differential equation are used to solve Navier equations. Geometry of the sphere is assumed in spherical coordinate system. Applying mechanical boundary conditions at inner and outer radii, we have carried out the analytical solutions for stresses, strains and displacements. In the numerical example, only internal pressure is varying along circumferential direction and external pressure is kept as zero. Displacements and mechanical stresses are presented graphically and the results are discussed numerically.

Thermohydrodynamic Analysis for Laminar Flow Journal Bearing

1978 ◽  
Vol 100 (4) ◽  
pp. 510-512 ◽  
Author(s):  
Z. S. Safar
Keyword(s):  
Heat Flow ◽  
Radial Direction ◽  
Energy Equation ◽  
Journal Bearing ◽  
Separation Of Variables ◽  
Isoperimetric Problem ◽  
Momentum Equation ◽  
Journal Bearings ◽  
The Third ◽  
Semianalytical Method

This paper describes a semianalytical method for solving the thermohydrodynamic problem in journal bearings. It is assumed that the shaft is isothermal and the bearing heat flow is in the radial direction. The momentum equation is reduced to ordinary differential equations by separation of variables. Two of the resulting equations are integrated directly, while the third equation is interpreted and solved as an isoperimetric problem. The energy equation with its boundary conditions is solved by the Galerkin Kantarovich method.

General Solution for Equation of Transient Heat Conduction in Functionally Graded Material Hollow Cylinder With Piezoelectric Internal and External Layers

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
M. Jabbari ◽  
M. A. Kiani
Keyword(s):  
Heat Conduction ◽  
Hollow Cylinder ◽  
Functionally Graded Material ◽  
Separation Of Variables ◽  
Transient Heat Conduction ◽  
Two Dimensions ◽  
Functionally Graded ◽  
Power Functions ◽  
Generalized Bessel Function ◽  
Graded Material

In this paper, the exact solution of the equation of transient heat conduction in two dimensions for a hollow cylinder made of functionally graded material (FGM) and piezoelectric layers is developed. Temperature distribution, as function of radial and circumferential directions and time, is analytically obtained for different layers, using the method of separation of variables and generalized Bessel function. The FGM properties are assumed to depend on the variable r, and they are expressed as power functions of r.

Two-Dimensional Stresses in a Hollow FG Sphere with Heat Source

2011 ◽  
Vol 264-265 ◽  
pp. 700-705 ◽  
Author(s):  
Amir Hossein Mohazzab ◽  
Mohsen Jabbari
Keyword(s):  
Steady State ◽  
Heat Source ◽  
Power Law ◽  
Thermal Stresses ◽  
Circumferential Stress ◽  
Functionally Graded ◽  
Power Functions ◽  
Legendre Series ◽  
Thermal Boundary Conditions ◽  
Power Law Index

This work studied the theoretical solution for axisymmetric steady-state mechanical and thermal stresses in hollow functionally graded spheres with respect to heat source. The material properties of the FG sphere change continuously across the thickness direction according to the power functions of radial direction. The steady-state temperature, displacements, and stresses are derived due to the general mechanical and thermal boundary conditions as function of radial and circumferential directions. The temperature and Navier equations are solved analytically, using Taylor and Legendre series. With increasing the power law indices the temperature distribution due to heat source is decreased. Circumferential stress and radial displacement due to heat source are decreased as the power law index increases.

scholarly journals Mechanical and Thermal Stresses in a FGPM Hollow Cylinder due to Radially Symmetric Loads

2011 ◽  
Vol 2011 ◽  
pp. 1-9 ◽  
Author(s):  
M. Jabbari ◽  
M. Meshkini ◽  
M. R. Eslami
Keyword(s):  
Fourier Series ◽  
Heat Conduction ◽  
Steady State ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Functionally Graded ◽  
Power Functions ◽  
One Dimensional ◽  
Complex Fourier Series

The general solution of steady-state on one-dimensional Axisymmetric mechanical and thermal stresses for a hollow thick made of cylinder Functionally Graded porous material is developed. Temperature, as functions of the radial direction with general thermal and mechanical boundary-conditions on the inside and outside surfaces. A standard method is used to solve a nonhomogenous system of partial differential Navier equations with nonconstant coefficients, using complex Fourier series, rather power functions method and solve the heat conduction. The material properties, except poisson's ratio, are assumed to depend on the variable , and they are expressed as power functions of .

scholarly journals Three-Dimensional Piezothermoelastic Stress of a Finite Functionally Graded Cylindrical Shell with Piezoelectric Layer

2013 ◽  
Vol 2013 ◽  
pp. 1-13 ◽  
Author(s):  
Yong-gang Kang ◽  
Zhong-qi Wang ◽  
Gongnan Xie
Keyword(s):  
Cylindrical Shell ◽  
Fourier Series ◽  
Material Properties ◽  
Piezoelectric Layer ◽  
Radial Direction ◽  
Electric Displacement ◽  
Three Dimensional ◽  
Functionally Graded ◽  
Simply Supported ◽  
Piezoelectric Layers

Three-dimensional piezothermoelastic solutions for a finite functionally graded cylindrical shell with piezoelectric layer are carried out in this paper. The cylindrical shell is simply supported at four end edges and is subjected to axisymmetric thermomechanical loads. The piezoelectric layers are polarized along radial direction as a sensor. The material properties are assumed to be temperature independent and radially dependent but are assumed to be homogeneous in each layer; the variables are expanded in Fourier series to satisfy the boundary conditions and multilayer approach is used. Numerical results of mullite/molybdenum functionally graded cylindrical shell are presented; the temperature change, stresses, electric potential, and electric displacement distributions are given and briefly discussed.

General Solution for Mechanical and Thermal Stresses in a Functionally Graded Hollow Cylinder due to Nonaxisymmetric Steady-State Loads

2003 ◽  
Vol 70 (1) ◽  
pp. 111-118 ◽  
Author(s):  
M. Jabbari ◽  
S. Sohrabpour ◽  
M. R. Eslami
Keyword(s):  
Steady State ◽  
Material Properties ◽  
Thermal Stresses ◽  
Separation Of Variables ◽  
Functionally Graded ◽  
Two Dimensional ◽  
Power Functions ◽  
Complex Fourier Series ◽  
Graded Material ◽  
Thick Cylinder

In this paper, the general theoretical analysis of two-dimensional steady-state thermal stresses for a hollow thick cylinder made of functionally graded material is developed. The temperature distribution is assumed to be a function of radial and circumferential directions with general thermal and mechanical boundary conditions on the inside and outside surfaces. The material properties, except Poisson’s ratio, are assumed to depend on the variable r and they are expressed as power functions of r. The separation of variables and complex Fourier series are used to solve the heat conduction and Navier equations.

Thermomechanical Analysis in FG Rotating Hollow Disk

2011 ◽  
Vol 110-116 ◽  
pp. 148-154 ◽  
Author(s):  
A. R. Khorshidvand ◽  
M. Jabbari
Keyword(s):  
Heat Conduction ◽  
Material Properties ◽  
Radial Direction ◽  
Thermal Stresses ◽  
Energy Equation ◽  
Elliptic Cylinder ◽  
Thermomechanical Analysis ◽  
Functionally Graded ◽  
Exponential Functions ◽  
Graded Materials

In this paper, mechanical and thermal stresses of rotating hollow disks composed of functionally graded materials (FGMs) is presented. The material properties for FG are expressed as nonlinear exponential functions through the radius of disk and Poisson’s ratio is taken to be constant. The temperature distribution is derived from first law thermodynamics by solving energy equation, general thermal and mechanical boundary conditions are assumed on the inside and outside surfaces of the disk. Heat conduction and Navier equations of a FGM disk are expressed in elliptic cylinder coordinates system and solved analytically. The results are shown for displacement and stresses components along the radial direction.

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