Scherbakova Y. The Axysymmetrical Problems of Theory of Elasticity for Transversally Isotropic Multiply Connected Bodies with Spheroidal and Paraboloidal bounds

In the offered thesis the generalized Fourier's method of elastic boundary value problem research is developed for multiply connected transversally isotropic bodies. The new basic vector solutions of equilibrium equations are obtained for transversally iso-tropic paraboloid. The additional theorems are got for transversally isotropic spheroids with the displaced centers, half-space and paraboloid, paraboloid and spheroid. Basic and mixed problems are solved for a spheroid with a spheroidal cavity and circular crack, space with two spheroidal cavities, half-space with paraboloidal foundation, paraboloid with a spheroidal cavity and circular crack. The detailed research for property of the got resolvent systems is made for all indicated problems. The parametric analysis of the tension between boundary surfaces for these indicated problems based on numerical results is executed. Asymptotic decisions are resulted as small-parameter expansion in a problem about the concentrated force which operates on transversally isotropic half-space.