Zenchenkov A. The stressed-strained state of anisotropic half-plane with elastic fixed boundary under the action of normal load

The thesis is devoted to construction of analytical solutions of the mixed problems of the theory of elasticity about action of normal load on isotropic and anisotropic half-planes with the elastic fixed borders and to investigation on their basis of regularities of redistribution of stresses and displacements in elastic domain at change of physico-mechanical properties of the environment and the type of external load. By means of Fourier's integral transformation in work exact analytical solutions of the mixed problems of the theory of elasticity are received for the isotropic and anisotropic half-planes on which border the concentrated force operates, normal stresses is proportional to displacements, tangential stresses are absent. Influence of elastic fixing of border on distribution of stresses and displacements in the isotropic and transversely isotropic half-planes under the action normally applied concentrated force is investigated. The quantitative assessment of stressed-strained state of the half-plane from elastic properties of anisotropic material is given. The mixed problems for the concentrated force are generalized on the case of the distributed load. Analytical solutions of problems on the deformation of the isotropic and orthotropic half-planes are received in the case, when on border tangential stresses are absent, in points of finite domain the distributed load is applied, outside domain the normal stresses and displacements are proportional. Unknown function, which simulates density of load in the domain, determined by solving the Fredholm integral equation of the second kind. Regularities of distribution of stresses and displacements inside and on the border of half-plane is numerically investigated in cases, when load is distributed uniformly or under piecewise linearly law on one site of border, is distributed uniformly on two not being crossed sites. On the basis of the constructed mathematical models and analytical solutions the cycle of problems of rock mechanics about development of layered mineral deposits is investigated. The results have practical applications in the mining and engineering industries.