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Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2021, Volume 21, Issue 1, Pages 60–75
DOI: https://doi.org/10.18500/1816-9791-2021-21-1-60-75
(Mi isu875)
 

This article is cited in 2 scientific papers (total in 2 papers)

Scientific Part
Mechanics

Repeated alternating loading of a elastoplastic three-layer plate in a temperature field

E. I. Starovoitov, D. V. Leonenko

Belarusian State University of Transport, 34 Kirova St., Gomel 246653, Belarus
Full-text PDF (415 kB) Citations (2)
References:
Abstract: Axisymmetric deformation of a three-layer circular plate under repeated alternating loading from the plastic region by a local load is considered. To describe kinematics of asymmetrical on the thickness of the plate pack is adopted the hypothesis of a broken line. In a thin elastic-plastic load-bearing layers are used the hypothesis of Kirchhoff. A non-linearly elastic relatively thick filler is incompressible in thickness. It is taken to be a hypothesis of Tymoshenko regarding the straightness and the incompressibility of the deformed normals with linear approximation of the displacements through the thickness layer. The work of the filler in the tangential direction is taken into account. The physical relations of stress-strain relations correspond to the theory of small elastic-plastic deformations. The effect of heat flow is taken into account. The temperature field in the plate was calculated by the formula obtained by averaging the thermophysical parameters over the thickness of the package. The system of differential equations of equilibrium under loading of the plate from the natural state is obtained by the Lagrange variational method. Boundary conditions on the plate contour are formulated. The solution of the corresponding boundary value problem is reduced to finding the three desired functions: deflection, shear and radial displacement of the shear surface of the filler. A non-uniform system of ordinary nonlinear differential equations is written for these functions. Its analytical iterative solution is obtained in Bessel functions by the method of elastic solutions of Ilyushin. In case of repeated alternating loading of the plate, the solution of the boundary value problem is constructed using the theory of variable loading of Moskvitin. In this case, the hypothesis of similarity of plasticity functions at each loading step is used. Their analytical form is taken independent of the point of unloading. However, the material constants included in the approximation formulas will be different. The cyclic hardening of the material of the bearing layers is taken into account. The parametric analysis of the obtained solutions under different boundary conditions in the case of a local load distributed in a circle is carried out. The influence of temperature and nonlinearity of layer materials on the displacements in the plate is numerically investigated.
Key words: three-layer circular plate, plasticity, repeated alternating local loading, temperature field, numerical analysis SSS.
Funding agency Grant number
Belarusian Republican Foundation for Fundamental Research Т20Р-047
This work was supported by the Belarusian Republican Foundation for Fundamental Research (projects No.~T20R-047).
Received: 12.09.2019
Revised: 26.11.2019
Bibliographic databases:
Document Type: Article
UDC: 539.374
Language: Russian
Citation: E. I. Starovoitov, D. V. Leonenko, “Repeated alternating loading of a elastoplastic three-layer plate in a temperature field”, Izv. Saratov Univ. Math. Mech. Inform., 21:1 (2021), 60–75
Citation in format AMSBIB
\Bibitem{StaLeo21}
\by E.~I.~Starovoitov, D.~V.~Leonenko
\paper Repeated alternating loading of a elastoplastic three-layer plate in~a~temperature field
\jour Izv. Saratov Univ. Math. Mech. Inform.
\yr 2021
\vol 21
\issue 1
\pages 60--75
\mathnet{http://mi.mathnet.ru/isu875}
\crossref{https://doi.org/10.18500/1816-9791-2021-21-1-60-75}
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  • This publication is cited in the following 2 articles:
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    Известия Саратовского университета. Новая серия. Серия Математика. Механика. Информатика
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