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.

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 .

Nonaxisymmetric Mechanical and Thermal Stresses in FGPPM Hollow Cylinder

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
M. Jabbari ◽  
M. Meshkini ◽  
M. R. Eslami
Keyword(s):  
Power Law ◽  
Material Properties ◽  
Heat Conduction Equation ◽  
Thermal Stresses ◽  
Direct Method ◽  
Functionally Graded ◽  
Complex Fourier Series ◽  
Thick Cylinder ◽  
A Direct Method ◽  
Radial Variable

In this paper, the general solution of steady-state 2D nonaxisymmetric mechanical and thermal stresses and electrical and mechanical displacements of a hollow thick cylinder made of fluid-saturated functionally graded porous piezoelectric material (FGPPM) is presented. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and the nonhomogenous system of partial differential Navier equations, using the complex Fourier series and the power law functions method. The material properties, except Poisson's ratio, are assumed to depend on the radial variable and they are expressed as power law functions along the radial direction.

One-Dimensional Moving Heat Source in a Hollow FGM Cylinder

2008 ◽  
Vol 131 (2) ◽  
Author(s):  
M. Jabbari ◽  
A. H. Mohazzab ◽  
A. Bahtui
Keyword(s):  
Heat Source ◽  
Hollow Cylinder ◽  
Thermal Stresses ◽  
Direct Method ◽  
Functionally Graded ◽  
Moving Heat Source ◽  
Power Functions ◽  
One Dimensional ◽  
Generalized Bessel Function ◽  
Graded Material

This paper presents the analytical solution of one-dimensional mechanical and thermal stresses for a hollow cylinder made of functionally graded material. The material properties vary continuously across the thickness, according to the power functions of radial direction. Temperature distribution is symmetric and transient. The thermal boundary conditions may include conduction, flux, and convection for inside or outside of a hollow cylinder. The thermoelasticity equation is transient, including the moving heat source. The heat conduction and Navier equations are solved analytically, using the generalized Bessel function. A direct method of solution of Navier equation is presented.

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.

Mechanical and Thermal Stresses in FGPPM Hollow Cylinder Due to Radially Symmetric Loads

2015 ◽  
Vol 138 (1) ◽  
Author(s):  
M. Jabbari ◽  
M. Meshkini ◽  
M. R. Eslami
Keyword(s):  
Power Law ◽  
Thermal Stresses ◽  
Poisson Ratio ◽  
Piezoelectric Materials ◽  
Direct Method ◽  
Functionally Graded ◽  
Complex Fourier Series ◽  
Thick Cylinder ◽  
A Direct Method ◽  
Radial Variable

In this paper, the general solution of steady-state 1D radially symmetric mechanical and thermal stresses and electrical and mechanical displacements for a hollow thick cylinder made of fluid-saturated functionally graded poro piezoelectric materials (FGPPMs) is developed. The general form of thermal and mechanical boundary conditions is considered on the inside and outside surfaces. A direct method is used to solve the heat conduction equation and nonhomogenous system of partial differential Navier equations, using complex Fourier series and power law functions method. The material properties, except the Poisson ratio, are assumed to depend on the radial variable r and they are expressed as power law functions.

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