SOLVING THE PROBLEM OF BENDING AN ELECTRO-MAGNETO-ELASTIC MULTICONNECTED THIN PLATE WITH RIGIDLY REINFORCED HOLES

Using the complex potentials of the theory of bending of thin electro-magneto-elastic plates, a solution is given to the problem of bending plates with holes and cuts with rigidly reinforced contours. In this case, using the conformal mappings, expansion of holomorphic functions in Laurent series and satisfaction of boundary conditions by the generalized least squares method, the problem is reduced to an overdetermined system of linear algebraic equations solved by the singular value decomposition method. For the case of one hole or cut, an exact analytical solution to the problem is constructed. The results of numerical studies for a plate with one or two elliptical holes or rectilinear cuts are described. The patterns of influence of the physical and mechanical properties of the plate material and the geometric characteristics of holes and cuts on the values of the main characteristics of the electro-magneto-elastic state are investigated.