Analytical Solution of the Problem About Bending of Annular Plates Subject to the Action of the Lateral Load

Authors

  • A. N. Tyurekhojayev K.I. Satpayev Kazakh National Technical University, Almaty, Kazakhsta
  • G. K. Kalzhanova Ilyas Zhansugurov Zhetysu State University, Taldykorgan, Kazakhstan
  • A. G. Ibrayev L.N.Gumilev Eurasian National University, Astana, Kazakhstan

Keywords:

Thin round plate, compound bending, lateral load, radial force, deflection of the median plane of the plate, system of linear differential equations with variable coefficients, method of partial discretization of differential equations

Abstract

The paper considers the problem of compound bending of non-uniform round flexible
plate subjected to lateral load under temperature changes through the thickness of the plate with
the influence of tension on bending. The problem is reduced to the study of an unrelated system of
differential equations, analytical solution of which has not been possible using existing mathematical
apparatus. The paper managed to decompose the related system of equations into two unrelated
equations and to find a solution using the method of partial discretization of differential equations.
Results are represented as formulae and graphs

References

1. Kovalenko A.D. Fundamentals of thermoelasticity. Kiev: "Naukova Dumka" , (1970) [in Russian]
2. Tyurekhodzhaev A.N., Kalzhanova G.K. The problem of axisymmetric nonlinear bending of inhomogeneous
flexible circular plate in the inhomogeneous temperature field. "Reports of the National Academy of Sciences
of Kazakhstan" . №3. pp.23-33. (in Russian) (2005)

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Published

2018-09-28

Issue

Vol. 86 No. 3 (2015): Journal of Mathematics, Mechanics and Computer Science

Section

Mathematical modeling of technological processes