Solving the problem of electromagnetic elastic bending of a multiply connected plate

The problem of bending of a plate with arbitrary holes and cracks is solved with the use of complex potentials of the theory of bending of thin electromagnetic elastic plates. Moreover, with the help of comformal mapping, expansion of holomorphic functions into the Laurent series or Faber polynomials owing to satisfaction of boundary conditions by the least squares method, the problem is reduced to an overdetermined system of linear algebraic equations, which is then solved by the method of singular expansions. Results of numerical investigations for a plate with two elliptical holes or cracks and for a plate with a hole and a crack (including an edge crack) are reported. The influence of physical and mechanical properties of the plate material and geometric characteristics of holes and cracks on the basic characteristics of the electromagnetic elastic state is studied.