Denysova T. Application of addition theorems to the solution of the problems of Elasticity Theory

The new contact tasks for elastic halfspace with multiply-connected contact domain and tasks of Elasticity Theory for bodies, which contain some stress concentrators are investigated. The purpose of this research is to develop efficient methods of solution and construction the solutions themselves of these problems on basis of known and received by the author addition theorems of solutions for Laplace's equation and for Lame's system of equations. Methods have been proposed and solutions of following problems: 1) problem on influence of additional load on the contact tensions under concentric ring stamp; 2) problem on pressure of eccentric ring stamp without friction; 3) problem for some, two in particular, circular stamps, which are pressed without friction; 4) the problem on equilibrium of a plane with circular hole and with one or two hyperbolic cuts; 5) problem on torsion of elastic halfspace with paraboloid elastic core by circular stamp; 6) problem on deformation of elastic space with spherical and paraboloid cavities have been received. Research methods are based on the generalised Fourier's method, infinite systems of linear algebraic equations, addition theorems of solutions for Laplace's equation and for Lame's system of equations, integral equations. The application sphere may be as follows: potensial theory, thermal conductivity theory, fluid and gas mechanics, destruction theory, composite theory, industrial and civil engineering.