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Research Papers: Design and Analysis

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

[+] Author and Article Information
M. Jabbari

Mechanical Engineering Department,
South Tehran Branch,
P.O. Box 145 781 5751,
Tehran, Iran

S. M. Mousavi

Mechanical Engineering Department,
South Tehran Branch, Islamic Azad University,
P.O. Box 146 963 6136,
Tehran, Iran

M. A. Kiani

Mechanical Engineering Department,
South Tehran Branch, Islamic Azad University,
P.O. Box 615 563 5893,
Ahvaz, Iran

Contributed by the Pressure Vessel and Piping Division of ASME for publication in the JOURNAL OF PRESSURE VESSEL TECHNOLOGY. Manuscript received July 2, 2016; final manuscript received June 21, 2017; published online August 31, 2017. Assoc. Editor: Albert E. Segall.

J. Pressure Vessel Technol 139(5), 051207 (Aug 31, 2017) (20 pages) Paper No: PVT-16-1101; doi: 10.1115/1.4037444 History: Received July 02, 2016; Revised June 21, 2017

## Abstract

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.

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## References

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## Figures

Fig. 1

Geometry of the problem studied

Fig. 2

Transient temperature distribution in the outer piezo layer hollow sphere

Fig. 3

Transient temperature distribution in FGM hollow sphere

Fig. 4

Transient temperature distribution in the inner piezo layer hollow sphere

Fig. 5

Radial displacement in the FGM layer

Fig. 6

Circumferential displacement in the FGM layer

Fig. 7

Radial stress in the FGM layer

Fig. 8

Circumferential stress in the FGM layer

Fig. 9

Radial electrical displacement in the sensor layer

Fig. 10

Electric potential in the sensor layer

Fig. 11

Electric potential in the actuator layer

Fig. 12

Radial stress in the piezo FGM hollow sphere along the thickness

Fig. 13

Circumferential stress in the piezo FGM hollow sphere along the thickness

Fig. 14

Radial electrical displacement in the sensor layer along the thickness

Fig. 15

Electric potential in the actuator along the thickness

Fig. 16

Electric potential in the sensor layer along the thickness

Fig. 17

The comparison of Radial stress in the FGM hollow sphere along the thickness by present and the finite element method

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