Horechko N. Solving of the quasi-static thermoelasticity problems for semi-infinite inhomogeneous bodies on basis of series by the multiple probability integrals

The thesis presents the analytico-numerical procedure for the solutions construction of the one-and two-dimensional quasi-static thermoelasticity problems in fast-convergent series form by the multiple probability integrals. Using it the solutions of the new quasi-static thermoelasticity problems for piecewise-homogeneous structures, which components consists of the semi-infinite regions is obtained. Proposed procedure for the solution construction of the nonlinear axial-symmetric non-stationary thermal conductivity problem for the half-space is applied. This half-space with heat exchange is considered on basis of the thermosensitive body model. Using perturbation method the corresponding thermoelasticity problem for the thermosensitive half-space is reduced to the solving of the sequence of Poisson's equation problems using multiple probability integrals expansions for every approximation. Analysis of the inhomogeneous parameters regularities and temperature dependencies of material thermomechanical behavior on the temperature fields distribution and stresses caused by them is carried out in considered constructions.