Skip to main content

Dynamic Contact Problems for Shells with Moderately Large Deflections

  • Conference paper
  • 939 Accesses

Part of the book series: IUTAM Bookseries ((IUTAMBOOK,volume 30))

Abstract

We deal with an initial-boundary value problem describing the perpendicular vibrations of Kármán-Donnell shells with a rigid inner obstacle. The elastic as well the viscoelastic materials are considered. A weak formulation of the problems are in the form of the hyperbolic variational inequalities.We solve the problem using the penalization method.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bock, I.: On the semidiscretization and linearization of a pseudoparabolic von Kármán system for viscoelastic plates. Math. Meth. Appl. Sci. 29, 557–573 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bock, I.: On a pseudoparabolic system for a viscoelastic shallow shell. PAMM Proc. Appl. Math. Mech. 6, 621–622 (2006)

    Article  Google Scholar 

  3. Bock, I., Jarušek, J.: Unilateral dynamic contact of viscoelastic von Kármán plates. Advances in Math. Sci. and Appl. 16, 175–187 (2006)

    MATH  Google Scholar 

  4. Bock, I., Jarušek, J.: Solvability of dynamic contact problems for elastic von Kármán plates. SIAM J. Math. Anal. 41, 37–45 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  5. Eck, C., Jarušek, J., Krbec, M.: Unilateral Contact Problems in Mechanics. Variational Methods and Existence Theorems. In: Monographs & Textbooks in Pure & Appl. Math., vol. 270. Taylor & Francis Group, Boca Raton (2005)

    Google Scholar 

  6. Voľmir, A.G.: Gibkije plastinky i oboločky, Gosizdat, Moskva (1956) (in Russian)

    Google Scholar 

  7. Vorovič, I.I., Lebedev, I.P.: Existence of solutions in nonlinear theory of shallow shells. Applied Mathematics and Mechanics 36(4), 691–704 (1972)

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Dordrecht Heidelberg London New York

About this paper

Cite this paper

Bock, I. (2011). Dynamic Contact Problems for Shells with Moderately Large Deflections. In: Stépán, G., Kovács, L.L., Tóth, A. (eds) IUTAM Symposium on Dynamics Modeling and Interaction Control in Virtual and Real Environments. IUTAM Bookseries, vol 30. Springer, Dordrecht. https://doi.org/10.1007/978-94-007-1643-8_33

Download citation

  • DOI: https://doi.org/10.1007/978-94-007-1643-8_33

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-007-1642-1

  • Online ISBN: 978-94-007-1643-8

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics