Visnyk LNAU: Architecture and Farm Building 2017 №18: 8-11


T. Bubnjak, Physics and Mathematics Ph.D.
J.Famulak, PhD
Lviv National Agrarian University


Construction of the elements of the constructions depends on their critical states- I mean the providing of the optimal load carrying capacity, rigidity, solidity and endurance of the building. Strength of the buildings is determined by their constructive forms, which are based on a bunch of principles: usage of pre-used tensed constructions, creation of constructions that would provide the biggest concentration of the material, etc.

Spatial tasks of the theory of elasticity and plasticity occupy an important place among the tasks of the mechanics of the deformed solid body.

J.M. Podilchuck’s work has one method to build the exact solutions of the first and second critical tasks of the elasticity theory for the isotropic bodies of canonical form.

One of the effective methods of solving the elasticity theory tasks is the Fourier’s method, which is based on presenting the general equilibrium equation solving tasks with help of the potential functions.

The work surveys the transversally isotropic environment that contains the inclusion of the compressed spheroid form. At the edge of the phase division the imperfect mechanical contact conditions were made, the outer field- lineal.

An important task about the interposition of the tension concentration in the vicinity from the transversally isotropic inclusion under the influence of the linear force field during the torsion under imperfect contact conditions between the environment and the inclusion; to observe, how does the sizes of the elliptical inclusion (semiaxises relations) influence the tension concentration.

The solution of the equilibrium equation tasks under critical conditions on the surface of the inclusion of the lineal force and temperature fields leads to the development searched potential functions into the trigonometric series with help of added Legendre’s functions of the first and second generations.

Tensed condition in the environment is defined by the superposition of the main and additional caused by the presence of the inclusion.

This work points out the change of the tense concentration depending on environment shift modules and the inclusion for different geometry of spheroids. The analysis of the results shows that the higher gets the rigidity of the environment relative to inclusion the higher gets the tension concentration. Nevertheless, when going further from the spheroidal inclusion (e.g. at the distance of the spheroid axis) the influence of the environment rigidity and inclusion influence gets inconsiderable.

Key words

potential function, transversely isotropic medium, perfect and imperfect contact spheroid field stresses

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