Thermoelasticity of the reinforced plate under influence of quick change for coordinate of thermal and force factors on the boundary

Аuthors

Myltcina O. A.^*, Belostochny G. N.^**

Saratov State University named after N. G. Chernyshevsky, 83, Astrakhanskaya str., Saratov, 410012, Russia

*e-mail: omyltcina@yandex.ru
**e-mail: belostochny@mail.ru

Abstract

On the base of the Love model and the classical Fourier thermoconductivity theory the analysis of the thermoelastic behaviour of the geometrically irregular plate is carried out. Two opposite edges of the plate are exposed to quick change in temperature fields and force stress on space coordinate. Such temperature fields and force stress are described as multiplication of suitable functions by the Heaviside function. These functions at force stress points, when the Heaviside function is not defined, become zero along with their derivatives until the required order.
The temperature field, in conditions of convective heat exchange via surfaces and boundaries exposed to quick change in temperature, is defined in the plate beforehand. One temperature jump over one of the surface caused by partial destruction of thermal shield is supposed. The solution of the boundary problem of thermoconductivity has been obtained in a closed form suitable for quantitative analysis and sequential solution of incoherent thermoelasticity.
The solution of the thermoelacticity problem is reduced to integration of inhomogeneous irregular differential equation with variable coefficients in a form of the generalized Dirac function and its derivatives. By the method of the sum single trigonometric series with variable coefficients and different functions for satisfying boundary conditions the solutions are reduced to the integration of inhomogeneous ordinary differential equation with irregular coefficients. The fundamental system functions are obtained for an irregular equation. The solution is written in a closed form. The conditions of fixing two edges of thermoelastic system at rest can be any of the known in the theory of the plate.
On the basis of exact solutions the 3D figures of thermal surfaces and bending surfaces are obtained for different values of physical, mechanical and geometrical parameters. The configuration of surfaces greatly depends on the directions of quickly changing forces and a temperature stress.
The regions of largest bending coincide with the regions of largest temperature difference in thickness. The bends are less sensitive to the intensity forces stress on the boundaries. It is worthwhile noting that practically in all considered cases the increase of parameter of the relative height of the confirmatory rib decreases the value of bending if the heat insulation of the surfaces is not broken.
In the paper the given solutions of the incoherent thermoelasticity of the geometrical irregular plates exposed to the quickly changing loading are aimed to the analysis of thermoelasticity behaviour of the thick constructions required in the various technological areas.

Keywords:

temperature, convective heat exchange, incoherent thermoelasticity, plate, geometrical irregularity, singular equation, closed integral, bending

References

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