SOLUTION OF THE ELECTROMAGNETOELASTICITY PROBLEM FOR A HALF-PLANE WITH HOLES AND CRACKS

The problem of electromagnetic elasticity for a piezoelectric half-plane with arbitrarily located internal elliptical holes and rectilinear cracks is solved. In this case, functions holomorphic outside the ellipses (cracks) are expanded in Laurent series in negative powers of the corresponding variables, and functions holomorphic in the lower half-planes are expressed by the Cauchy integral method through functions obtained from the specified ones when satisfying the boundary conditions on the rectilinear boundary. With this approach, the boundary conditions on the rectilinear boundary of the half-plane are satisfied exactly. As for the boundary conditions on the contours of the holes, a generalized least squares method is used to satisfy them, reducing the problem to solving an overdetermined system of linear algebraic equations with respect to the coefficients of the Laurent series. Solutions to problems of electroelasticity, magnetoelasticity and elasticity theory are obtained as special cases, as well as analytical solutions to problems of a continuous half-plane under the action of forces on the boundary or concentrated effects at individual points. The results of numerical studies for a half-plane with holes and cracks are described, with the establishment of patterns of change in the stress-strain state of the half-plane depending on its materials, geometric characteristics of holes and cracks. Keywords: electromagnetoelastic plate, half-plane, holes, complex potentials, Cauchy-type integrals, generalized least squares method.