# Mathematical modeling of stationary thermoelastic state in a half plane containing an inclusion and a crack due to local heating by a heat flux

2020;
: pp. 88–95

Revised: January 20, 2020
Accepted: January 25, 2020
Authors:
1
Lviv Polytechnic National University

The two-dimensional stationary problems of heat conduction and  thermoelasticity for a semi-infinite elastic body containing an inclusion and a crack  are  considered.  For this purpose, mathematical models of these  two-dimensional problems in the form of a system of singular integral equations (SIEs) of the first and the second kinds are constructed.  The numerical solution of the system of integral equations in the case of a half plane  containing an inclusion and thermally insulated crack due to local heating by a heat flux is obtained using the method of mechanical quadratures.  We present graphical dependencies of stress intensity factors (SIFs), which characterize the distribution of intensity of stresses on the tops of a crack, on the  elastic and thermoelastic characteristics of an inclusion and a matrix, as well as on a relative position of a crack and an inclusion.  The obtained results are subsequently used to determine the critical values of a heat flux at which a crack starts to grow.  This model is the development of  known models of  two-dimensional stationary problems of heat conduction and  thermoelasticity  for piecewise-homogeneous bodies with cracks.

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Mathematical Modeling and Computing, Vol. 7, No. 1, pp. 88–95 (2020)