Magnetoelastic stresses in a soft ferromagnetic solid with a hole of arbitrary shape subject to uniform magnetic induction

An analytical solution for the magnetoelastic problem of an infinite soft ferromagnetic material with a hole of arbitrary shape is provided in this paper. Using the method of complex variable, such as conformal mapping technique and the analytic continuation, both the magnetic fields and magnetoelastic stresses can be obtained. Explicit solutions of several examples are also provided. Comparison with the degenerate case, such as a crack of which the analytic solutions were provided in the literature. is made to assure that the solution of the present work is general and exact. Numerical results for the tangential mac,netoelastic stresses on the surface of an elliptic hole or a hypotrochoidal hole are displayed in graphic form to elucidate the effect of geometry parameters. Moreover, the stress intensity factors with r(-1/2) singularity on the crack tip are also derived.