Influence of boundary constraints on the appearance of asymmetrical equilibrium states in circular plates under normal pressure

Authors

  • Svetlana M. Bauer Saint Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russia; Research and Education Center «Materials», Don State Technical University, 1 Gagarina Square, Rostov-on-Don 344000, Russia
  • Eva B. Voronkova Saint Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russia; Research and Education Center «Materials», Don State Technical University, 1 Gagarina Square, Rostov-on-Don 344000, Russia https://orcid.org/0000-0002-3065-4473

Keywords:

circular plate, buckling, heterogeneity
Supporting Agencies
This research was supported by the Government of Russia (grant No. 14.Z50.31.0046).

Abstract

Unsymmetrical buckling of nonuniform circular plates with elastically restrained edge and subjected to normal pressure is studied in this paper. The unsymmetric part of the solution is sought in terms of multiples of the harmonics of the angular coordinate. A numerical method is employed to obtain the lowest load value, which leads to the appearance of waves in the circumferential direction. The effect of material heterogeneity and boundary on the buckling load is examined. It is shown that if the outer edge of a plate is elastically restrained against radial deflection, the buckling load for unsymmetrical buckling is larger than for a plate with a movable edge. The elasticity modulus decrease away from the center of a plate leads to sufficient lowering of the buckling pressure if the outer edge can move freely in the radial direction.

Author Biographies

  • Svetlana M. Bauer, Saint Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russia; Research and Education Center «Materials», Don State Technical University, 1 Gagarina Square, Rostov-on-Don 344000, Russia

    doctor of science (physics and mathematics), full professor; professor at the department of theoretical  and applied mechanics, faculty of mathematics and mechanics, Saint Petersburg State University, and leading researcher at the laboratory of mechanics of biomaterials, Research and Education Center «Materials», Don State Technical University

  • Eva B. Voronkova, Saint Petersburg State University, 7/9 Universitetskaya Embankment, Saint Petersburg 199034, Russia; Research and Education Center «Materials», Don State Technical University, 1 Gagarina Square, Rostov-on-Don 344000, Russia

    PhD (physics and mathematics); associate professor at the department of mathematical modeling of power  systems, faculty of applied mathematics and control processes, Saint Petersburg State University, and junior researcher at the laboratory of mechanics of biomaterials, Research and Education Center «Materials», Don State Technical University

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Published

2020-03-29

Issue

No. 1 (2020): Journal of the Belarusian State University. Mathematics and Informatics

Section

Theoretical and Applied Mechanics

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How to Cite

[1]
Bauer, S.M. and Voronkova, E.B. 2020. Influence of boundary constraints on the appearance of asymmetrical equilibrium states in circular plates under normal pressure. Journal of the Belarusian State University. Mathematics and Informatics. 1 (Mar. 2020), 38–46. DOI:https://doi.org/10.33581/2520-6508-2020-1-38-46.