Shporta A. Perturbation method application to solving contact problems and its generalization for electroelastic materials

The dissertation is devoted to the generalization of the perturbation method and its application for the study of the stress-strain state in two-dimensional problems of the theory of elasticity and electroelasticity. The contact problem of the theory of elasticity about the action of a rigid stamp on an elastic orthotropic plate with cylindrical anisotropy is solved. The solution takes into account the friction force that occurs during the interaction. The stress distribution under the stamp is obtained. The relationship between the size of the interaction area, the angle of opening of the sector and the coefficient of friction is obtained. The influence of plate sizes on the distribution of normal stresses under the stamp for individual values of material stiffness parameters was investigated. The solution of contact problem of the theory of elasticity about the action of a rigid stamp on an elastic orthotropic curvilinear semi-infinite or finite sector with cylindrical anisotropy is given. It is taken into account that in the area of the contacts of the stamp with the plate there are two areas of slip, which are adjacent to the end points of the area of contacts, and the area of adhesion located between them. The laws of stress distribution under the stamp and the size of the coupling section area determined. A more complex case for a circular plate of finite dimensions is also considered. Similarly, the existence of areas of slip and adhesion in the area of contact of the stamp with the plate is taken into account. For the problem the value of the settling of the stamp at different values of the stiffness characteristics of the material is calculated. The generalization of the small parameter method to two-dimensional problems of electroelasticity is carried out. It is shown that it is quite possible to formulate the corresponding boundary value problems of the theory of elasticity for the basic equations and in the future, they are reduced to simpler boundary value problems. A number of model problems have been solved. Keywords: elasticity theory, contact problems, stamp indentation, curvilinear anisotropy, friction and adhesion, sliding, asymptotic method, stress-strain state, electroelasticity and electromagnetic elasticity.