# thermoelasticity

## Mathematical modeling of stationary thermoelastic state in a half plane containing a periodic system of cracks due to periodic local heating by a heat flux

Purpose. To determine the two-dimensional thermoelastic state in a semi-infinite solid (half-plane), weakened by a system of periodic internal cracks under conditions of local heating on the edge of the half plane. Heat flux due to frictional heating on the local area of the body, causes changes in temperature and stresses in the body, which significantly affects its strength, as it can lead to crack growth and local destruction. Therefore, the study of the problem of frictional heat is of a practical interest.

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

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 pre

## Functionally gradient isotropic cylindrical shell locally heated by heat sources

The stress-strain state of a functionally gradient isotropic thin circular cylindrical shell under local heating by a flat heat source has been investigated.  For this purpose, a mathematical model of the classical theory of inhomogeneous shells has been used.  A two-dimensional heat equation is derived under the condition of a linear dependence of the temperature on the transverse coordinate.  The solutions of the non-stationary heat conduction problem and the quasi-static thermoelasticity problem for a finite closed cylindrical pivotally supported shell have been obtained by means of meth

## On the calculation of thermoelastic processes in a cylindrical shell with local heat sources

A quasistatic problem of thermoelasticity for a yielding cylindrical finite-length shell under the action of axially symmetric heat sources in a wide range of heating modes is solved. The numerical calculation of the temperature fields, the ring forces and the bending moments for the values of the time at which they reach the maximal levels is carried out. The influence of the shear degree is studied.