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

An analytical method for the static plane problem of magnetoelasticityis developed for an infinite plane containing a hole of arbitraryshape under stress and displacement boundary conditions in aprimary uniform magnetic field. The magnetic field influencesthe elastic field by introducing a body force called the Lorentzponderomotive force in the equilibrium equations. The body forcecan be further described in a form relating with the electromagneticstress tensor. The complex variable method in conjunction withthe rational mapping function technique is used in the analysisfor both magnetic field and mechanical field. Governing equationsand boundary conditions are expressed in terms of complex functions.Complex magnetic potential and stress functions are obtainedusing Cauchy integrals for the paramagnetic and soft ferromagneticmaterials, respectively. The distributions of magnetic fieldand the stress components are shown for certain directions ofprimary magnetic fields in an infinite plane with a square hole,as an example. It is found that the stress distributions forthe two types of materials are identical despite the differenceof magnetic fields. The extreme cases of a free and a fixedhole reduced to a crack and a rigid fibre, respectively, arealso investigated. The stress intensity factors at the tipsof crack and rigid fibre are computed, and their variation forcertain directions of primary magnetic field is shown.