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The Quarterly Journal of Mechanics and Applied Mathematics Advance Access originally published online on September 18, 2007
The Quarterly Journal of Mechanics and Applied Mathematics 2007 60(4):423-442; doi:10.1093/qjmam/hbm018
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Q. Jl Mech. Appl. Math, Vol. 60. No. 4 © The author 2007. Published by Oxford University Press; all rights reserved. For Permissions, please email: journals.permissions@oxfordjournals.org

On magnetoelastic problems of a plane with an arbitrarily shaped hole under stress and displacement boundary conditions

N. Hasebe, X. F. Wang{dagger} and H. Nakanishi

( Department of Civil Engineering, Omohi College, Nagoya Institute of Technology, Gokiso-cho, Showa-ku, Nagoya 466-8555, Japan )

{dagger} < w{at}nitech.ac.jp>

Received 17 August 2006. Revise 28 June 2007.
  Abstract

An analytical method for the static plane problem of magnetoelasticity is developed for an infinite plane containing a hole of arbitrary shape under stress and displacement boundary conditions in a primary uniform magnetic field. The magnetic field influences the elastic field by introducing a body force called the Lorentz ponderomotive force in the equilibrium equations. The body force can be further described in a form relating with the electromagnetic stress tensor. The complex variable method in conjunction with the rational mapping function technique is used in the analysis for both magnetic field and mechanical field. Governing equations and boundary conditions are expressed in terms of complex functions. Complex magnetic potential and stress functions are obtained using Cauchy integrals for the paramagnetic and soft ferromagnetic materials, respectively. The distributions of magnetic field and the stress components are shown for certain directions of primary magnetic fields in an infinite plane with a square hole, as an example. It is found that the stress distributions for the two types of materials are identical despite the difference of magnetic fields. The extreme cases of a free and a fixed hole reduced to a crack and a rigid fibre, respectively, are also investigated. The stress intensity factors at the tips of crack and rigid fibre are computed, and their variation for certain directions of primary magnetic field is shown.


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