The non-axisymmetric loading of an elastoplastic three-layer plate in its plane

  • Eduard I. Starovoitov Belarusian State University of Transport, 34 Kirava Street, Homieĺ 246653, Belarus
  • Alina V. Nesterovich Belarusian State University of Transport, 34 Kirava Street, Homieĺ 246653, Belarus
DOI: https://doi.org/10.33581/2520-6508-2022-2-57-69

Abstract

The statement of the boundary value problem on the deformation of a circular three-layer plate in its plane under the action of a non-axisymmetric load is herein presented. The materials of thin carrier layers obey the hypotheses of the theory of small elastoplastic deformations. The relatively thick filler is physically non-linearly elastic. A system of non-linear differential equilibrium equations in partial derivatives is obtained. A general technique for solving the problem in displacements based on the Fourier method and Ilyushin’s method of elastic solutions is proposed. The case of an external cosine load is considered. An iterative solution of a boundary value problem for a physically non-linear plate is obtained. The corresponding solution of the elastic problem is written out in the final form. The obtained solution is numerically tested.

Author Biographies

Eduard I. Starovoitov, Belarusian State University of Transport, 34 Kirava Street, Homieĺ 246653, Belarus

doctor of science (physics and mathematics), full professor; head of the department of structural mechanics, faculty of industrial and civil engineering

Alina V. Nesterovich, Belarusian State University of Transport, 34 Kirava Street, Homieĺ 246653, Belarus

PhD (physics and mathematics); associate professor at the department of structural mechanics, faculty of industrial and civil engineering

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Published
2022-08-01
Keywords: circular three-layer plate, non-axisymmetric load, movement, plastic
Supporting Agencies This work was supported by the Belarusian Republican Foundation for Fundamental Research (project T20R-047).
How to Cite
Starovoitov, E. I., & Nesterovich, A. V. (2022). The non-axisymmetric loading of an elastoplastic three-layer plate in its plane. Journal of the Belarusian State University. Mathematics and Informatics, 2, 57-69. https://doi.org/10.33581/2520-6508-2022-2-57-69
Issue
No 2 (2022): Journal of the Belarusian State University. Mathematics and Informatics
Section
Theoretical and Applied Mechanics

Copyright (c) 2022 Journal of the Belarusian State University. Mathematics and Informatics

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