Boronenko O. Тhe two-dimensional problems of magnetoelasticity for multiconnected mediums

The methods of two-dimensional and plane elastic and electroelastic problems solving and their applications for the magnetoelastic state of finite and infinite piezomagnetic solids, half-space and layer with cavities, cracks and inclusions investigation are developed further. The methods are based on the constitutive equations obtaining for the two-dimensional and plane magnetoelastic problems, on the generalized complex potentials introduction and investigation for the mag-netoelasticity, on the boundary conditions deriving for their determination and the relations receiving for the basic magnetoelastic state (MES) characteristics calculation through them, for stress, induction and tension intensity factors (SITIF) and internal energy density evaluation. For the complex potentials determination from the mechanical and magnetic boundary conditions in the case of the finite and infinite solids with arbitrarily situated cavities, cracks and inclusions the methods of conformal mapping, Fourier series andFaber polynomials expansions and least-squares method are used. In the case of the multiconnected half-space and layer for the boundary conditions at the plain borders satisfaction the Cauchy integrals or least-squares methods are applied. The developed methods effectiveness and the received results steadiness are shown by the numerical investigations. The solutions for the practically important problems for the solid, half-space and layer with arbitrarily situated cavities, cracks and inclusions, including the plain borders cross ones, are given. The detailed numerical investigations of the considered problems are carried out. By means of them, the new magnetomechanical regularities of the solids and inclusions physicomechanical material properties, geometric sizes, quantity and positioning of the cavities, cracks and inclusions influence on the basic MES characteristics, SITIF and internal energy density values are determined. The investigations re-sults presented in the thesis have both theoretical and practical importance. The proposed methods can be used for а wide variety of engineering problems solving.