Issue 48

A. Fesenko et alii, Frattura ed Integrità Strutturale, 48 (2019) 768-792; DOI: 10.3221/IGF-ESIS.48.70 770 elastic layer is considered in [36]. The contact stresses concentrations between the plates and the layer was studied, as it can induce destruction of the engineering structure. The advances in the use of thermoelastic stress analysis for fracture mechanics assessment were reviewed in [37]. The development of techniques to determine stress intensity factor was presented, followed by the application of these techniques to fatigue crack growth. The work [38] investigates the behavior of a Transvers Crack Tensile specimen undergoing fatigue loading, by means of a Thermoelastic Stress Analysis experimental setup. The information on the stress distribution settling near the crack tips and its evolution with crack growth under fatigue is provided. A review of the above papers shows that the problem of constructing an exact solution for problems of an elastic layer remains open, despite the variety of methods and in particular numerical solutions. The results obtained, based on the exact solution of the spatial problem can be used as the basis for solving problems by approximate numerical methods. This dictates an increasing interest in the development of analytical methods to solve three-dimensional elasticity problems and in particular for a layer as the most important model object. The purpose of this paper is to establish the changes in the fields of displacements and stress of the semi-infinite elastic layer for the effects of different types of loading, in particular temperature, mechanical loads and proper weight. Earlier in paper [16], the problem of stationary heat conduction and the elasticity problem for a layer were solved separately. It was stated that using this technique makes it is possible to solve the problem of uncoupled thermoelasticity, which was accomplished in this work. Solving this task requires use of the Green function apparatus, moreover, the Green matrix function, which has not been used for the problems of this type. The proposed work consists of a new approach that makes it possible to obtain an exact solution of mixed uncoupled thermoelasticity, which can be also applied to solve analogical problems with much more complicated boundary conditions. T HE STATEMENT OF THE MIXED UNCOUPLED THERMOELASTICITY PROBLEM et’s consider the elastic semi-infinite layer (Fig. 1) occupying the area           0 , , 0 x y z h (1) , , x y z are the Cartesian’s coordinate system Figure 1 : Geometric model of the problem The conditions of an ideal contact are given at the layer’s edge  0 x and at the lower face  0 z - by this, the authors mean frictionless contact conditions. At the same time, these faces are thermo-isolated. The known temperature ( , , ) T x y z , found earlier from the corresponding thermoconductivity problem, and pressure load ( , ) p x y both L