Research Papers

Magnetoelastic Field of a Multilayered and Functionally Graded Cylinder With a Dynamic Polynomial Eigenstrain

[+] Author and Article Information
A. H. Akbarzadeh

Postdoctoral Fellow
Department of Mechanical Engineering,
McGill University,
Montreal, QC, H3A 0C3, Canada
Department of Mechanical Engineering,
University of New Brunswick,
Fredericton, NB, E3B 5A3, Canada
e-mail: hamid.akbarzadeh@mcgill.ca, h.akbarzadeh@unb.ca

Z. T. Chen

Department of Mechanical Engineering,
University of New Brunswick,
Fredericton, NB, E3B 5A3, Canada
e-mail: ztchen@unb.ca

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received January 25, 2013; final manuscript received March 25, 2013; accepted manuscript posted May 7, 2013; published online September 16, 2013. Assoc. Editor: Pradeep Sharma.

J. Appl. Mech 81(2), 021009 (Sep 16, 2013) (13 pages) Paper No: JAM-13-1048; doi: 10.1115/1.4024412 History: Received January 25, 2013; Revised March 25, 2013; Accepted May 07, 2013

In this paper, an analytical solution is obtained for the magnetoelastic response of a multilayered and functionally graded cylinder with an embedded dynamic polynomial eigenstrain. The internal core of the cylinder endures a harmonic eigenstrain of cubic polynomial distribution along the radial direction. Both plane strain and plane stress conditions are assumed for the axisymmetric cylinder. The composite cylinder is placed in a constant magnetic field parallel to its axis. The magnetoelastic governing equations are solved exactly and the displacement and stress components are obtained in terms of Bessel, Struve, and Lommel functions. Using the analytical solution for the multilayered, composite cylinder, the magnetoelastic response of a functionally graded cylinder with exponential and power law distribution of material properties is investigated. Finally, the numerical results reveal the effects of external magnetic field, eigenstrain, and nonhomogeneity indices on the magnetoelastic response of the heterogeneous cylinders.

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Fig. 1

Multilayered composites: (a) infinitely long cylinder with plane strain condition and (b) thin circular disk with plane stress condition

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Fig. 2

FGM cylinder with embedded eigenstrain in internal homogeneous core

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Fig. 3

Modeling of the FGM layer with artificial homogeneous layers

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Fig. 4

Effect of eigenstrain on: (a) radial displacement, (b) radial stress, (c) hoop stress, and (d) axial stress distributions in a three-layer infinitely-long cylinder

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Fig. 5

Effect of external magnetic field on: (a) radial displacement, (b) radial stress, (c) hoop stress, and (d) axial stress distributions in a three-layer infinitely-long cylinder

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Fig. 6

Effect of geometrical configuration of thin circular three-layer disk on: (a) radial displacement, (b) radial stress, and (c) hoop stress distributions

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Fig. 7

Effect of angular velocity on the distribution of: (a) radial displacement, (b) radial stress, (c) hoop stress, and (d) axial stress in an infinitely-long, FG cylinder with embedded eigenstrain

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Fig. 8

Effect of nonhomogeneity indices of power-law formulation on: (a) radial displacement, (b) radial stress, and (c) hoop stress distributions in a composite circular disk

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Fig. 9

Effect of nonhomogeneity indices of exponential formulation on: (a) radial displacement, (b) radial stress, and (c) hoop stress distributions in a composite circular disk



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