Zaletov V. Problems of viscoelasticity and thermal viscoelasticity for multilinked plates with elastic and rigid in-clusions

The thesis is devoted to building the numerical-analytical solutions of three-dimensional mixed problems of elasticity of the action concentrated and distributed normal efforts to isotropic elastic half-space with attached boundary survey and based on their patterns of distribution of elastic stresses and displacements in varying physical and mechanical constants, and type of external loading area and shape his actions. It consistently implemented by the construction of integral transforms exact analytical solution of axisymmetric problem about the normal concentrated force applied at the center of a cylindrical coordinate system on the surface of elastic half-space when in points there is the condition of proportionality normal stresses and displacements and no tangential stress; analytic representation is build in rectangular coordinates for the components of the stressed-strain state in the case of arbitrary point of application of concentrated force on the surface of the half-space by the considering boundary conditions, building of integral Fredholm equation, which determines the solution to the problem about the boundary of half the normal load, distributed in any form domain, without which the condition of proportionality normal stresses and displacements is carried and no tangential stress, study the properties of its nucleus; implemented the algorithm of applying the method of successive approximations for the construction of the Neumann series solution of integral equations in problems of the action of distributed loads. On the basis of the approach proposed in the study examined class of mixed problems by the solution construction problem about the normal to the half-space efforts, uniformly distributed in a rectangular area, and axisymmetric solution to the problem about the normal half-space efforts, uniformly distributed in a circular area. The algorithms of numerical realization of solutions for the calculation component of the stress tensor and displacement vector at interior points and on the boundary of elastic half-space are supposed. The research and summarize of the main patterns of distribution of stresses and displacements in an isotropic half-space with varying physical, mechanical and geometrical parameters of the problem in the case of concentrated force or uniformly distributed normal load are made. The results have practical applications in mining and engineering industries. Key words: isotropic elastic medium, mixed boundary conditions of elastic fixed edjes, the action of concentrated and distributed normal load, analytical and numerical-analytical solutions, distribution of stresses and displacements, effects of influence of fixing stiffness characteristics on stressed-strain state.