Chernyak M. Thermoelastic state of bodies with cylindrical or spherical inclusions and cracks

Founded solutions of the problems of stationary heat conduction and thermoelasticity for two-component cylinder and sphere, infinite and semi-infinite bodies with inclusions and cracks during the heating to steady temperature, heat generation or under the action of heat flow. Investigated stressed state of two-component cylinder or sphere, heated to steady temperature or during the heat generation in the internal region, with the various mechanical and thermophysical characteristics of internal and external regions. Conducted analysis of the received results and identified influence of shear modulus and linear temperature expansion coefficients on temperature distribution, displacements and stresses in two-component body. For infinite bodies with system of cylindrical and spherical inclusions solution was founded with the help of thermoelastic potential of displacements. In the case of semi-infinite body with the thermic cylindrical inclusions conditions on the bounds of the body were get with the help of Eri's stress finction. Stressed state of semi-infinite body with the axially symmetric system thermic spherical inclusions, heated to steady temperature, founded with the help of Love's biharmonic function. Investigated flat deformation of a body with the circular cylindrical inclusion and the crack placed on the continuation of its diameter under the influence of the homogenous heat flow and tension stresses (mechanical and thermophysical characteristics of inclusion and body are different), and also infinity body with two thermic cylindrical inclusions and tunnel or elliptic crack and semi-infinite body with cylindrical inclusion and crack that is on the border of the body. Defined stress intensity factors on the cracks. On the basis of solved problems investigated influence on the temperature distribution, displacements and stresses physico-mechanical features of materials and geometrical characteristic of bodies and inclusions.