Edge stress state of a circular plate of variable thickness under thermo-mechanical loading on the basic of refined theory

Аuthors

Firsanov V. V.^*, Doan Q. H.^**

Moscow Aviation Institute (National Research University), 4, Volokolamskoe shosse, Moscow, А-80, GSP-3, 125993, Russia

*e-mail: k906@mai.ru
**e-mail: dqhieu57@gmail.com

Abstract

The development of aviation and space technology requires solving complex problems of determining the strength and durability of structural elements. Actual is the problem of increa- sing the reliability of methods for calculating the stress-deformed state (SDS) of round plates under the action of mechanical loads and external temperature influences. One of the aspects of these problems is the construction of more reliable methods for determining the stress-deformed state near stress distortion zones. Round and annular plates of variable thickness were conside- red, which were under the combined action of axisymmetric force loading and temperature hea- ting. The required displacements of the plate along the coordinate normal to its median plane were approximated by polynomials two degrees higher compared to the classical theory of

Kirchhoff-Love type. Based on the three-dimensional equations of the elasticity theory and the variation Lagrange principle, a refined mathematical model of the stress-deformed state in the boundary zone of the plates under consideration was constructed. The mathematical model was a system of two-dimensional differential equations in displacements with variable coefficients and natural boundary conditions at the edges of the plate. As an example, an annular plate with a linearly varying thickness was considered provided that the load and temperature were evenly distributed. The solution of the boundary-value problem was solved by reducing the system of two-dimensional differential equations to ordinary differential equations using trigonometric series in the circumferential coordinate. The finite difference method was applied to the resulting system of equations. An analysis of stresses corresponding to the refined theory with a change in temperature was given. It was shown that, when calculating a round plate according to a revised theory, there were additional rapidly decaying edge stress states of the «boundary layer» type. The corresponding transverse normal stresses, which were neglected in classical theory, were obtained on the same order with the maximum values of the main bending stress. Taking into account the effect of temperature on the stress-deformed state of a round plate according to a revised theory allows us to obtain significantly more accurate values of thermoelastic stresses. This result is of great importance, since it makes it possible to more reliably assess the strength and fracture toughness in the zones of distortion of the stress state of structural elements of aircraft, as well as other engineering objects.

Keywords:

round plate, variable thickness, temperature, thermoelasticity, Lagrange variation principle, expansion into trigonometric series, finite difference method, matrix sweep method, stress layer «boundary layer».

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