Thermoelastic State of a Half Space with Fixed Boundary Under the Conditions of Heat Generation in a Circular Domain Par
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THERMOELASTIC STATE OF A HALF SPACE WITH FIXED BOUNDARY UNDER THE CONDITIONS OF HEAT GENERATION IN A CIRCULAR DOMAIN PARALLEL TO THE BOUNDARY H. S. Kit1 and R. M. Andriichuk1,2
UDC 539.3
Green’s functions in some problems of thermoelasticity for a semiinfinite body are constructed with the help of the potentials of thermoelastic displacements and Boussinesq functions. The boundaries of the body are rigidly fixed either at temperature zero or under the conditions of heat insulation. We determine the temperature and stresses caused by the heat generation in a circular domain parallel to the boundary and analyze their values for some distributions of heat sources in the domain of heat generation on the boundary of the body and in its center located at a certain distance from the boundary. Keywords: half space with fixed boundary, problem of thermoelasticity, Green’s function, heat generation in a circular domain.
The three-dimensional problems of stationary heat conduction and thermoelasticity for cracked bodies can be solved by the method of two-dimensional boundary integral equations with the use of the theory of Newton potential [1]. This method was also used to solve the problems of heat conduction and thermoelasticity for bodies with heat generation in a circular domain [2]. The methods for the solution of axisymmetric problems of heat conduction and thermoelasticity for unbounded bodies with the heat generation in circular domains are well known [3–5].
In the solution of the problems of thermoelasticity for semiinfinite bodies, it is reasonable to use Green’s functions. For a half space with conditions of temperature equal to zero or heat insulation imposed on the loadfree boundary, these functions were constructed with the help of the Love biharmonic functions in [6]. Later, they were used to determine the thermoelastic state of the half spaces with a thermally active crack parallel or perpendicular to their boundary and the temperature or heat flux specified on the crack [7–9]. An intermediate stage in the analysis of the stressed state of bodies with thermally active cracks is connected with the determination of stresses at the sites of location of the cracks. The next stage includes the relaxation of these stresses on their surfaces. In what follows, we construct the Boussinesq and Green functions in the explicit form for some problems of thermoelasticity in a half space whose boundary is rigidly fixed either at temperature equal to zero or under the conditions of heat insulation. These Green functions are applied to the investigation of the stressed state of the body with heat generation in a circular domain parallel to the boundary.
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Pidstryhach Institute for Applied Problems in Mechanics and Mathematics, Ukrainian National Academy of Sciences, Lviv, Ukraine. Corresponding author; e-mail: [email protected].
Translated from Fizyko-Khimichna Mekhanika Materialiv, Vol. 53, No. 3, pp. 98–104, May–June, 2017. Original article submitted September 9, 2016. 398
1068-820X/17/5303–0398
© 2017
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