Determination of quasi-static thermoelastic state of layered thermosensitive plates


  • B. V. Protsiuk Pidstryhach Institute of Applied Probleme of Mechanics and Mathematiecs of NAS of Ukraine, 79060, Lviv, Naukova str., 3-b



The technique of determining the quasistatic thermoelastic state of the layered thermosensitive plates free of load is illustrated. Much attention is paid to finding analytical-numerical solutions of one-dimensional non-stationary heat conduction problems taking into account the temperature dependences of the thermal and temperature conductivity coefficients. Their finding involves use of the Kirchhoff transformation, generalized functions, Green's functions of the corresponding linear heat conduction problem, exact sums of the series, in particular those for which the Gibbs effect takes place, linear splines and solving the received recurrent systems of nonlinear algebraic equations relative to the values in the nodes of the spline of the Kirchhoff variable on the layer division surfaces and the derivative in time on inner flat-parallel surfaces of layers. The results of numerical calculations of temperature fields in two-layer plates with different thicknesses of layers and the external surface heated by a constant heat flux are presented. The accuracy of the found solution is investigated. The comparison of the temperature fields, which are determined assuming simple nonlinearity, stable thermophysical characteristics with the ones based on the exact solution of the corresponding nonlinear stationary heat conduction problem is fulfilled.

Key words: layered thermosensitive plate, thermoelastic state, nonlinear heat conduction problem, Green's function, linear splines.

Pages of the article in the issue: 162-165

Language of the article: Ukrainian


PROTSIUK, B.V. (2003) Kvazystatycheskye temperaturnye napryazhenyya v mnohosloynoy plastyne pry nahreve teplovym potokom. Teoretycheskaya y prykladnaya mekhanyka. 38. pp. 63-69.

PROTSIUK, B. (2009) Metod intehral'nykh rivnyan' u nestatsionarnykh zadachakh teploprovidnosti termochutlyvykh til. Fizyko-matematychne modelyuvannya ta informatsiyni tekhnolohiyi. 10. pp. 96-105.


How to Cite

Protsiuk, B. V. (2019). Determination of quasi-static thermoelastic state of layered thermosensitive plates. Bulletin of Taras Shevchenko National University of Kyiv. Physics and Mathematics, (1), 162–165.



Differential equations, mathematical physics and mechanics