Bayeva A. The two-dimensional problem of electroelesticity for multiconnected mediums with holes and cracks

The methods of solution of boundary problems of the theory of elasticity and their applications to the problem of study of electroelastic state of multiconnected piezoelectric body with holes and cracks are developed more in this work. These methods are based on the solution of the problems of linear coupling for cuts in multiconnected sphere or on the using of classic complex potentials with the separated peculiarities at the ends of plane concentrators of stresses and the least squares method. The problems for bodies with the concentrators of stresses along a plane (straight line) have been led to the systems of the problems of linear coupling, by solving of which the general presentations of the complex potentials are got, which satisfy the boundary conditions on the surfaces of the plane concentrators exactly and contain the unknown functions, determining from the conditions on the closed contours and the conditions of the solution of the problem. The general solution of the two-dimensional problemfor multiconnected body with arbitrary placed holes and cracks is built. This solution is based on the using of the complex potentials with separated singularities at the ends of cracks, on obtaining of the formulae for definition of the coefficient of intensity of stresses, induction and tenseness of the field, on working out the methods of using of the discrete least squares method for defining the unknown constants, which enter the complex potentials. New problems for multiconnected piezoelectric body and plate are solved. The row of the new appropriateness of the influence of geometric forms and sizes of holes and cracks, their quantity, mutual positions and combinations, piezoelectric properties of materials of considering bodies and plates on electroelastic state are discovered. Presented in the thesis results of researches have both theoretical and practical interests. The proposed methods can be used for solution of various engineering problems.