Petrenko A. The two-dimensional problems of magnetoelectroelasticity for bodies with cavities and cracks

The methods of two-dimensional and plane elastic electroelastic, and magnetoelastic problems solving and their applications for the magnetoelectroelastic state of multi-connected finite and infinite magneto-electric solids, half-space and layer investigation are developed further. The methods are based on the constitutive equations obtaining for the two-dimensional and plane magnetoelectroelastic problems, on the generalized complex potentials introduction and investigation for the mag-netoelectroelasticity, on the boundary conditions deriving for their determination and the relations receiving for the basic magnetoelectroelastic state (MEES) characteristics calculation through them, for stress, inductions and tensions intensity fac-tors (SITIF). For the complex potentials determination from the mechanical, electric and magnetic boundary conditions in the case of the finite and infinite solids with arbitrarily situated cavities and cracks the methods of conformal mapping, Fou-rier series and Faber polynomials expansions and least-squares method are used. In the case of the multi-connected half-space and layer for the boundary conditions at the plain borders satisfaction the Cauchy integrals or least-squares methods are applied. The solutions for the practically important problems for the solid, half-space and layer with arbitrarily situated cavities and cracks, 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 mechanical regularities of the solids geometric characteristics and physicomechanical material properties influence on the basic MEES characteristics and SITIF. In particular, from the ob-tained results follows, that for the elastic equilibrium of the magneto-electric solids investigation the classic elastic theory problem solving with electric and magnetic material properties neglecting is not enough and the general magnetoelectroelas-tic problem has to be solved. The distance between cavities and cracks decreasing leads to the basic MEES characteristics and SITIF values increasing. The plain borders nearness significantly increases the characteristics values. The investigations results presented in the thesis have both theoretical and practical importance. The proposed methods can be used for а wide variety of engineering problems solving.