On non-axisymmetrical buckling modes ofcircular plates under normal pressure

Authors

  • Svetlana M. Bauer St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Eva B. Voronkova St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation
  • Boris N. Semenov St Petersburg State University, 7-9, Universitetskaya nab., St Petersburg, 199034, Russian Federation

DOI:

https://doi.org/10.21638/spbu01.2022.303

Abstract

The paper presents the results of a study of the bifurcation of axisymmetric equilibrium forms of round plates under various conditions for fixing the outer edge. It is shown that for the case of sliding edge, the analytical, asymptotic and finite element approaches give close results. When the edge of the plate is hinged, the buckling to a non-axisymmetric state occurs at a much higher load and with the formation of a smaller number of waves than for a sliding boundary conditions. Difficulties in obtaining a numerical solution based on the analytical approach are apparently associated with the need for a more accurate description of the stress-strain subcritical state of the plate.

Keywords:

circular plate, buckling, finite element modelling

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References

Литература

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2. Cheo L.S., Reiss E.L. Unsymmetric wrinkling of circular plates. Quart. Appl. Math. 31 (1),75-91 (1973). https://doi.org/10.1090/qam/99710

3. Морозов Н.Ф. К вопросу о существовании несимметричного решения в задаче о большихпрогибах круглойпластинки, загруженнойсимметричнойнагрузкой. Известия высших учебныхзаведений. Математика, № 2, 126-129 (1961).

4. Piechocki W. On the nonlinear theory of thin elastic spherical shells: Nonlinear partial differentialequations solutions in theory of thin elastic spherical shells subjected to temperature fields and externalloading. Archiwum mechaniki stosowanej 21 (1), 81-102 (1969).

5. Coman C.D., Bassom A.P. Asymptotic limits and wrinkling patterns in a pressurized shallow spherical cap. International Journal of Non-LinearMechanics 81, 8-18 (2016).https://doi.org/10.1016/j.ijnonlinmec.2015.12.004

6. Coman C.D. On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mech. 229, 1099-1109 (2018). https://doi.org/10.1007/s00707-017-2036-8

7. Бауэр С.М., Воронкова Е.Б., Морозов Н.Ф. О несимметричных формах равновесия круглых пластин под действием нормального давления. В: Чигарев А.В.(ред.). Теоретическая и прикладная механика: международный научно-технический сборник. Вып. 27, 31-35. Минск (2012).

8. Bauer S.M., Voronkova E.B. Unsymmetrical wrinkling of nonuniform annular plates and spherical caps under internal pressure. In: Altenbach H., Chroscielewski J., Eremeyev V., Wisniewski K. (eds). Recent Developments in the Theory of Shells. Advanced Structured Materials. Vol. 110, 79-89. Cham,Springer (2019). https://doi.org/10.1007/978-3-030-17747-8_6

9. Bauer S.M., Voronkova E.B. On Buckling Behavior of Inhomogeneous Shallow Spherical Capswith Elastically Restrained Edge. In: Altenbach H., Chinchaladze N., Kienzler R., Muller W. (eds).Analysis of Shells, Plates, and Beams. Advanced Structured Materials. Vol. 134, 65-74. Cham, Springer(2020). https://doi.org/10.1007/978-3-030-47491-1_4

10. Мануйлов Г.А., Косицын С.Б., Бегичев М.М. Устойчивость осесимметричного равновесия круглойпластины при больших прогибах. International Journal for Computational Civil andStructural Engineering 10 (1), 111-117 (2014).

11. Мануйлов Г.А., Косицын С.Б., Бегичев М.М. О критических и послекритических равновесиях в задачах устойчивости упругих систем. Строительная механика инженерных конструкцийи сооружений, № 5, 47-54 (2015).

12. Мануйлов Г.А., Косицын С.Б., Бегичев М.М. О вычислительных признаках различиякритических точек на кривойравновесий. International Journal for Computational Civil and Structural Engineering 13 (2), 125-135 (2017). https://doi.org/10.22337/2587-9618-2017-13-2-125-13

References

1. Panov D.Y., Feodosiev V.I. On the equilibrium and loss of stability of shallow shells in the caseof large displacement Prikladnaya matematika i mehanika 12, 389-406 (1948). (In Russian)

2. Cheo L.S., Reiss E.L. Unsymmetric wrinkling of circular plates. Quart. Appl. Math. 31 (1),75-91 (1973). https://doi.org/10.1090/qam/99710

3. Morozov N.F. On the existence of a non-symmetric solution in the problem of large deflectionof a circular plate with a symmetric load. Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, no. 2,126-129 (1961). (In Russian)

4. Piechocki W. On the nonlinear theory of thin elastic spherical shells: Nonlinear partial differentialequations solutions in theory of thin elastic spherical shells subjected to temperature fields and externalloading. Archiwum mechaniki stosowanej 21 (1), 81-102 (1969).

5. Coman C.D., Bassom A.P. Asymptotic limits and wrinkling patterns in a pressurized shallow spherical cap. International Journal of Non-Linear Mechanics 81, 8-18 (2016).https://doi.org/10.1016/j.ijnonlinmec.2015.12.004

6. Coman C.D. On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mech. 229, 1099-1109 (2018). https://doi.org/10.1007/s00707-017-2036-8

7. Bauer S.M., Voronkova E.B., Morozov N.F. On unsymmetrical equillibrium states of circularplates under normal pressure. In: Chigarev A. B. (ed.). Theoretical and Applied mechanics: internationalscientific and technical collection. Iss. 27, 31-35. Minsk (2012). (In Russian)

8. Bauer S.M., Voronkova E.B. Unsymmetrical wrinkling of nonuniform annular plates and spherical caps under internal pressure. In: Altenbach H., Chroscielewski J., Eremeyev V., Wisniewski K. (eds).Recent Developments in the Theory of Shells. Advanced Structured Materials. Vol. 110, 79-89. Cham,Springer (2019). https://doi.org/10.1007/978-3-030-17747-8_6

9. Bauer S.M., Voronkova E.B. On Buckling Behavior of Inhomogeneous Shallow Spherical Capswith Elastically Restrained Edge. In: Altenbach H., Chinchaladze N., Kienzler R., Muller W. (eds).Analysis of Shells, Plates, and Beams. Advanced Structured Materials. Vol. 134, 65-74. Cham, Springer(2020). https://doi.org/10.1007/978-3-030-47491-1_4

10. Manuylov G.A., Kosytsyn S.B., Begichev M.M. About Initial Imperfection Sensitivity ofSome Thin-Walled Strustures. International Journal for Computational Civil and Structural Engineering 10 (1), 111-117 (2014). (In Russian)

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12. Manuylov G.A., Kosytsyn S.B., Begichev M.M. On Computational Differences of CriticalPoints on Equilibrium Curve. International Journal for Computational Civil and Structural Engineering 13 (2), 125-135 (2017). https://doi.org/10.22337/2587-9618-2017-13-2-125-135 (In Russian)

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Published

2022-10-10

How to Cite

Bauer, S. M., Voronkova, E. B., & Semenov, B. N. (2022). On non-axisymmetrical buckling modes ofcircular plates under normal pressure. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 9(3), 417–425. https://doi.org/10.21638/spbu01.2022.303

Issue

Vol. 9 No. 3 (2022)

Section

On the anniversary of N.F. Morozov

License

Articles of "Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy" are open access distributed under the terms of the License Agreement with Saint Petersburg State University, which permits to the authors unrestricted distribution and self-archiving free of charge.

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