Vakulenko S. The basic problems of the theory of an elasticity for a half-plane with holes and cracks

Have received the further development methods of the decision of regional problems of the theory of elasticity isotropic bodies and their appendices to a problem of studying it is stress-deformed status of a multiconnected plate and half-plane with holes, inclusions and cracks. On the basis of a problem closed decision for a plate with an elliptic hole received in work, the new specified representations of complex potentials for a plate with holes, inclusions and the cracks containing in case of cracks the selected features of functions are found. By using these representations of complex potentials and a method of integrals such as Cauchy on an infinite straight line are received containing singularities in case of presence of cracks the general representations of complex potentials for the multiconnected half-plane, precisely satisfying conditions on the loaded or rigidly supported border of half-plane. For the first time the effective method of the mixed problem decision of the elasticity theory about action stamps rigidly linked with border the multiconnected half-plane, which is based on use of analytic continuation through unloaded sites of rectilinear border and restriction of boundary conditions on the other part to the Riman-Gilbert problems (linear conjugate) for cuts in the multiconnected expanded plane is developed. The decision of these problems receives the general representations of complex potentials precisely satisfying boundary conditions on rectilinear border, containing selected singularities at the end of cracks and the bases of stamps. The series of the new problems are solved. The stress-deformed status changing is investigated depending upon the geometrical sizes and amount of holes and cracks, the ways of loading and reinforcements of rectilinear border and holes contours, as well as actions of stamps; the series of the new mechanical regularities are detected.