Mathematical Modelling of Stationary Thermoelastic State for a Plate with Periodic System of Inclusions and Cracks

Two-dimensional stationary problem of heat conduction and thermoelasticity for infinite elastic body containing periodic system of inclusions and cracks is considered. Solution of the problem is constructed using the method of singular integral equations (SIEs). The numerical solution of the system integral equations are obtained by the method of mechanical quadrature for a plate heated by a heat flow, containing periodic system elliptic inclusions and thermally insulated cracks. There are obtained graphic dependences of stress intensity factors (SIFs), which characterise the distribution of intensity of stresses at the tops of a crack, depending on the length of crack, elastic and thermoelastic characteristics inclusion, relative position of crack and inclusion.