# thermoelasticity

## Modeling the influence of the shape of the local heat flow intensity distribution on the surface of a semi-infinite body on the stress state in the vicinity of a subsurface crack

Purpose. A mathematical model to determine the two-dimensional thermoelastic state in a semi-infinite solid weakened by an internal crack under conditions of local heating is examined. 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 practical interest.

## Quasi-static problem of thermoelasticity for layered shallow cylindrical shells of irregular structure

For rectangular layered shallow cylindrical shells of irregular structure, the quasi-static problem of unbound thermoelasticity is formulated.  As a mathematical model, the equations of the shear theory of shallow shells of Timoshenko type are used.  The closed solution for the formulated problem is found by the methods of integral transformations.  The distribution of temperature, displacements, forces and moments in a two-layer cylindrical shell under local convective heating is analyzed numerically.

## Mathematical modeling of thermoelastic state in a tree-component piecewise-homogeneous plate containing a crack

Purpose. A two-dimensional mathematical model of the problem of thermoelasticity for three-component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks.

## Stressed and strained state of layered cylindrical shell under local convective heating

The stress-strain state of a layered composite cylindrical shell under local heating by the environment due to convective heat exchange has been studied.  The equation of the six-modal theory of thermoelasticity and the two-dimensional equation of thermal conductivity of inhomogeneous anisotropic shells are used for this purpose.  The solution of the nonstationary heat transfer problem and the quasi-static thermoelasticity problem for a finite hinged orthogonally reinforced shell of symmetric structure is found by the methods of integral Fourier and Laplace transforms.  Numerical results ar

## 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.