Electromagnetic twisting of a mindlin plate with a through crack

This paper deals with the electromagneto-elastic problem of a fixed ended conducting plate of finite width with a through crack under a uniform electric current flow and a constant magnetic field. The study is based on Mindlin's theory of plate bending. The current flow is disturbed by the presence of the crack and the twisting moment is caused by the interaction between the magnetic field and the disturbed current. Fourier transforms are used to reduce the electromagneto-elastic problem to one involving the numerical solution of a system of simultaneous Fredholm integral equations. The problem concerning the electric current density field is also solved and reduced to a Fredholm integral equation of the second kind. The singular character and the detailed structure of the electric current densities and the stresses near the ends of the crack are determined in closed forms. Numerical results are given for the twisting moment intensity factor and the shear force intensity factor for several values of the geometrical parameters.