Skip to main content

Asymmetric Buckling of Orthortropic Plates Under Normal Pressure

  • Chapter
  • First Online:
Advances in Solid and Fracture Mechanics

Part of the book series: Advanced Structured Materials ((STRUCTMAT,volume 180))

Abstract

The work is concerned with asymmetric buckling of clamped orthotropic circular plates under normal pressure. The effect of degree of orthotropy on the buckling load and buckling modes is examined. The problem is solved analytically and using the finite element method in the ANSYS package. It is shown that the critical load increases as the ratio of the circumferential to radial elastic modulus increases. The number of waves in the circumferential direction also increases.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

eBook
USD 16.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 139.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 199.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. D.Y. Panov, and V.I. Feodos’ev. On the equilibrium and loss of stability of shallow shells in the case of large displacement (in Russ.). Prikladnaya Matematika Mekhanika, 12:389–406, 1948.

    Google Scholar 

  2. L.S. Cheo and E.L. Reiss. Unsymmetric wrinkling of circular plates. Quarterly of Applied Mathematics, 31(1):75–91, 1973.

    Google Scholar 

  3. N.F. Morozov. The uniqueness of the symmetrical solution in the problem of the large deflection of a symmetrically loaded circular plate (in Russ.). Dokl. Akad. Nauk SSSR, 123(3):417–419, 1958.

    Google Scholar 

  4. N.F. Morozov. On the existence of a non-symmetric solution in the problem of large deflections of a circular plate with a symmetric load (in Russ.). Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2:126–129, 1961.

    Google Scholar 

  5. N.F. Morozov. A qualitative investigation of a circular, symmetrically compressed plate under a large edge load (proof of the appearance of crimping) (in Russ.). Dokl. Akad. Nauk SSSR, 147(6):1318–1319, 1962.

    Google Scholar 

  6. C.D. Coman and A.P. Bassom. Asymptotic limits and wrinkling patterns in a pressurised shallow spherical cap. International Journal of Non-Linear Mechanics, 81:8–18, 2016.

    Google Scholar 

  7. C.D. Coman. On the asymptotic reduction of a bifurcation equation for edge-buckling instabilities. Acta Mech., 229, 1099–1109, 2018.

    Google Scholar 

  8. S.M. Bauer, E.B. Voronkova and N.F. Morozov. On unsymmetrical equillibrium states of circular plates under normal pressure (in Russ.). In: Chigarev, A.B. (ed.) Theoretical and Applied Mechanics: International Scientific and Technical Collection. pp. 31–35, Minsk, 2012.

    Google Scholar 

  9. S.M. Bauer and E.B. Voronkova. 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, pp. 79–89. Springer, Cham, 2019.

    Google Scholar 

  10. S.M. Bauer and E.B. Voronkova: On buckling behavior of inhomogeneous shallow spherical caps with elastically restrained edge. In: Altenbach, H., Chinchaladze, N., Kienzler, R., M¨uller, W. (eds.) Analysis of Shells, Plates, and Beams, pp. 65–74. Springer, Cham, 2020.

    Google Scholar 

  11. G.A. Manuylov, S.B. Kosytsyn and M.M. Begichev. About initial imperfection sensitivity of some thin-walled strustures (in Russ.). International Journal for Computational Civil and Structural Engineering, 10(1):111–117, 2014.

    Google Scholar 

  12. G.A. Manuylov, S.B. Kosytsyn, and M.M. Begichev. Critical and postcritical equilibria in stability problems of elastic systems (in Russ.). Structural Mechanics of Engineering Constructions and Buildings, 5:47–54, 2015.

    Google Scholar 

  13. G.A. Manuylov, S.B. Kosytsyn and M.M. Begichev. On computational differences of critical points on equilibrium curve (in Russ.). International Journal for Computational Civil and Structural Engineering, 13(2):125–135, 2017.

    Google Scholar 

  14. S.A. Ambartsumyan. The General Theory of Anisotropic Shells (in Russ.). Moscow, 1974

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Svetlana M. Bauer .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Bauer, S.M., Indeitsev, D.A., Semenov, B.N., Voronkova, E.B. (2022). Asymmetric Buckling of Orthortropic Plates Under Normal Pressure. In: Altenbach, H., Bauer, S.M., Belyaev, A.K., Indeitsev, D.A., Matveenko, V.P., Petrov, Y.V. (eds) Advances in Solid and Fracture Mechanics. Advanced Structured Materials, vol 180. Springer, Cham. https://doi.org/10.1007/978-3-031-18393-5_2

Download citation

Publish with us

Policies and ethics