Analysis of stresses in an infinite elastic conductive plate with an elliptic hole subjected to a uniform magnetic field

Stress distribution is determined in a thin conductive plate containing an elliptic hole under the external electromagnetic loads. The aim of this study is to explore the concentrating effects of both the electric current density and the stresses in the plate due to the existence of the elliptic hole. Use is made of the elliptic coordinates for the ease of treating ellipse shaped boundary, while the analytical results for the components in the Cartesian coordinates are provided for convenience of application. After the distribution of the current density is derived, an anti-plane shear problem is formulated whose solution is obtained in closed form. The mode IE stress intensity factor is deduced by considering the case in which the minor axis vanishes when the ellipse degenerates to a Griffith crack.