Tokovyy Y. Elastic equilibrium of homogeneous and inhomogeneous solids with plane and cylindrical surfaces

The thesis is devoted to development of efficient methods for analysis of elastic equilibrium of homogeneous and inhomogeneous anisotropic solids with plane and cylindrical surfaces under action of complex thermal and force loadings. The primary goal of this work lies in the construction of analytical solutions to the two- and three-dimensional problems of elasticity and thermoelasticity for such solids, which are presented in the form of explicit functional dependences on the loadings and are efficient in satisfaction of the boundary conditions on the complete surface of a solid. A technique for analysis of the residual stresses in a long hollow cylinder with a butt-weld joint is proposed. By making use of the model of the elastic-plastic material, the joint has been represented by a locally-distributed field of the residual strains. The method of superposition is developed for construction of analytical solutions to the axisymmetric and non-axisymmetric problems of elasticity and thermoelasticity for solid cylinders of finite length. In particular, the algorithms for efficient application of this method in the case of non-smooth and discontinuous force and thermal loadings are presented.