CONCENTRATION OF NORMAL STRESSES IN TURN BY THE ACTION OF A LINEAR TEMPERATURE FIELD

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Visnyk LNAU: Architecture and Farm Building 2018 №19: 46-48

## CONCENTRATION OF NORMAL STRESSES IN TURN BY THE ACTION OF A LINEAR TEMPERATURE FIELD

### T. Bubniak , Candidate of Physical and Mathematical Sciences Lviv National Agrarian University

https://doi.org/10.31734/architecture2018.19.046

#### Annotation

In the mechanics of deformed solids, the spatial problems of the theory of elasticity and thermoelasticity, which relate to the distribution of stresses in the vicinity of inhomogeneities containing constructive composites, occupy an important place. The emergence of heterogeneities in some cases is due to the production technology, in others - heterogeneity is introduced to achieve optimal structural strength.

Important is the problem of obtaining reliable and complete information on the distribution of stresses in materials or structural elements, taking into account the real picture of interphase interaction, which is due to the use of effective methods for solving spatial problems of the theory of elasticity.

One of the effective methods for solving the problems of the theory of elasticity is the Fourier method, which is based on the representation of general solutions of equations of equilibrium through potential functions. A feature of the Fourier method is the use of various representations of the solution of the Lyme equations through harmonic functions, which allows us to search for a solution in the form of series.

The problem of the distribution of the thermal stresses of an unbound transversal isotropic medium, which contains anisotropic, with respect to mechanical and thermal properties, inclusion in the form of a compressed spheroid for linear uniaxial heating is considered. At the interface of the phases are offered the conditions of non-ideal mechanical and thermal contacts.

The calculation of the thermo-stressed state in a transversally isotropic medium with a spheroidal inclusion for the action of a linear temperature field under nonideal thermal and mechanical contacts was carried out for materials: magnesium - medium, cobalt - inclusion.

The analysis of the obtained results shows that the maximum concentration of stresses is reached in the corner, the minimum - at the inclusion pole.

#### Key words

potential functions, transversally isotropic medium, nonideal contact, spheroid, stress field