Revenko V. Stress-strain state of locally loaded elastic bodies with cylindrical and plane-parallel surfaces

This thesis is devoted to the development of efficient analytical and numerical methods for the solution of two- and three-dimensional boundary-value problems of the elasticity theory for homogeneous and multilayer cylindrical bodies, plates and rectangular prisms with concern to the analysis of their stress-strain states. It is proved that the general solution to the Lame equations contains three independent harmonic functions. Two representations for the general solution are constructed in the cylindrical coordinate system those contain either the axial or radial coordinate as a multiplier at the harmonic function. The analytical-numerical algorithm has been developed in order to satisfy all the contact (on the interfaces) and boundary (on the surface) conditions for a multilayer cylinder by making use of the generalized quadratic forms. The convergence and existence conditions for the numerical solutions to the boundary-value problems are established. The distribution of the stress-strain state of locally loaded plate-like and cylindrical bodies according to their geometrical characteristics, location of the loading area, as well as the steepness and maximum value, are found.