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Research Papers: Design and Analysis

Nonaxisymmetric Mechanical and Thermal Stresses in FGPPM Hollow Cylinder

[+] Author and Article Information
M. Jabbari

Assistant Professor
e-mail: m_ jabbari@azad.ac.ir

M. Meshkini

Postgraduate Student
e-mail: mohsenmeshkini@gmail.com
South Tehran Branch
Islamic Azad University, Iran

M. R. Eslami

Professor
Fellow ASME
Fellow of the Academy of Sciences
Department of Mechanical Engineering,
Amirkabir University of Technology,
15875-4413 Iran
e-mail: eslami@aut.ac.ir

1Corresponding author.

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 3, 2011; final manuscript received March 6, 2012; published online November 21, 2012. Assoc. Editor: Spyros A. Karamanos.

J. Pressure Vessel Technol 134(6), 061212 (Nov 21, 2012) (25 pages) doi:10.1115/1.4007034 History: Received July 03, 2011; Revised March 06, 2012

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.

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Figures

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Fig. 2

(a) Radial displacement in the cross section of cylindrical; (b) radial displacement versus r/a at θ = π/3

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Fig. 3

(a) Circumferential displacement in the cross section of cylindrical; (b) circumferential displacement versus radius at θ = π/3

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Fig. 4

(a) Electric potential in the cross section of cylindrical; (b) electric potential versus radius at θ = π/3

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Fig. 5

(a) Radial thermal stress in the cross section of cylindrical; (b) radial distribution of radial thermal stress σrr at θ = π/3

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Fig. 6

(a) Hoop thermal stress in the cross section of cylindrical; (b) radial distribution of hoop thermal stress σθθ at θ = π/3

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Fig. 9

(a) Circumferential electrical displacement in the cross section of cylinder; (b) circumferential electrical displacement Dθθ at θ = π/3

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Fig. 19

(a) Circumferential displacement in the cross section of cylinder; (b) circumferential displacement versus radius at θ = π/3

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Fig. 20

(a) Electric potential in the cross section of cylinder; (b) electric potential versus radius at θ = π/3

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Fig. 21

(a) Radial thermal stress in the cross section of cylinder; (b) radial distribution of radial thermal stress σrr at θ = π/3

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Fig. 22

(a) Hoop thermal stress in the cross section of cylinder; (b) distribution of hoop thermal stress σθθ at θ = π/3

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Fig. 23

(a) Shear thermal stress in the cross section of cylinder; (b) distribution shear thermal stress σrθ at θ = π/3

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Fig. 24

(a) Radial electrical displacement in the cross section of cylinder; (b) radial electrical displacement Drr at θ = π/3

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Fig. 25

(a) Circumferential electrical displacement in the cross section of cylinder; (b) circumferential electrical displacement Dθθ at θ = π/3

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Fig. 26

(a) Radial thermal stress in the cross section of cylinder for different values of the compressibility coefficient (B); (b) radial thermal stress in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 27

(a) Hoop thermal stress in the cross section of cylinder for different values of the compressibility coefficient (B); (b) hoop thermal stress in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 28

(a) Shear thermal stress in the cross section of cylinder for different values of the compressibility coefficient (B); (b) shear thermal stress in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 29

(a) Radial electrical displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) radial electrical displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 30

(a) Circumferential electrical displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) circumferential electrical displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 31

(a) Radial displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) radial displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 32

(a) Circumferential displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) circumferential displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 33

(a) Electric potential in the cross section of cylinder for different values of the compressibility coefficient (B); (b) electric potential in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 34

(a) Temperature distributions in the cross section of cylinder of θ=90 deg. Analytical result of this paper and the finite-volume result presented in Ref. [58]. (b) Radial stress distributions in the cross section of cylinder of θ=90 deg. Analytical result of this paper and the finite-volume result presented in Ref. [58]. (c) Circumferential stress distributions in the cross section of cylinder of θ=90 deg. Analytical result of this paper and the finite-volume result presented in Ref. [58].

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Fig. 1

(a) Temperature distribution in the cross section of cylindrical; (b) temperature distribution along radius at θ = π/3

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Fig. 7

(a) Shear thermal stress in the cross section of cylindrical; (b) radial distribution of shear thermal stress σrθ at θ = π/3

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Fig. 8

(a) Radial electrical displacement in the cross section of cylindrical; (b) variation of electrical displacement Drr at θ = π/3

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Fig. 13

(a) Radial electrical displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) radial electrical displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 14

(a) Circumferential electrical displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) circumferential electrical displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 15

(a) Radial displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) radial displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 16

(a) Circumferential displacement in the cross section of cylinder for different values of the compressibility coefficient (B); (b) circumferential displacement in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 17

(a) Electric potential in the cross section of cylinder for different values of the compressibility coefficient (B); (b) electric potential in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 18

(a) Radial displacement in the cross section of cylinder; (b) radial displacement versus r/a at θ = π/3

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Fig. 10

(a) Radial thermal stress in the cross section of cylinder for different values of the compressibility coefficient (B); (b) radial thermal stress in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 11

(a) Hoop thermal stress in the cross section of cylinder for different values of the compressibility coefficient (B); (b) hoop thermal stress in the cross section of cylinder for different values of the pore volume fraction (φ)

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Fig. 12

(a) Shear thermal stress in the cross section of cylinder for different values of the compressibility coefficient (B); (b) shear thermal stress in the cross section of cylinder for different values of the pore volume fraction (φ)

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