539.3

нелінійна задача теплопровідності
термопружний стан
термочутливі півпростори
тепловиділення
метод лінеаризувальних параметрів
аналітично-числова методика
nonlinear heat conduction problem
thermoelastic state
thermosensitive half-space
heat release
linearizing parameters method
analytic-numerical method

Побудовано розв’язок квазістатичної задачі термопружності для двох контактуючих термочутливих півпросторів з миттєвими або постійними тепловиділеннями на межі дотику та досліджено їх термопружний стан.
Modern scientific-technological development in determination of the stress-strain state of structural elements imposes increased demands to their mathematical models in order to represent more completely real physical processes. This, in turn, anticipates accounting of such important factors as thermosensitivity of materials, complex heat exchange, presence of internal heat sources, power loads, contact interaction, etc. When neglecting mechanical energy transformation into heat energy we arrive at the solution of the quasi-static uncoupled thermoelasticity problem, which is divided into separate problems: determination of the temperature field of the body and determination of its thermoelastic state caused by this field and other possible power factors. Complexity of such models lies in the necessity to solve nonlinear boundary- value problems of mathematical physics and boundary-value problems for the systems of differential equations with variable coefficients. Beside numerical methods, analytical-numerical approaches are widely used to solve such class of problems. They make it possible to verify the reliability of purely numerical solutions and to widen the possibilities of engineering practice as to choice of efficient and available means of solution actual problems. One of such approach, based on utilization of the linearizing parameters method, which was widely approved on non-stationary heat conduction problems for thermosensitive bodies of simple geometric shape under complex heat exchange with the surroundings, was approved as to solution of the heat conduction problems for contacting thermosensitive bodies for heat sources acting on the contact boundary. The solution of quasi-static thermoelasticity problem for two contacting half-spaces, made of zirconium oxide and titanium alloy with instant or constant heat release on the contact boundary was constructed. Their thermoelastic state was studied.