Skip to main content
SpringerLink
Log in
Book cover

Innovative Approaches and Solutions in Advanced Intelligent Systems pp 17–27Cite as

Finite Element Method for Nonlinear Vibration Analysis of Plates

  • Chapter
  • First Online:

Part of the book series: Studies in Computational Intelligence ((SCI,volume 648))

Abstract

Plates are structures which have wide applications among engineering constructions. The knowledge of the dynamical behavior of the plates is important for their design and maintenance. The dynamical response of the plate can change significantly due to the nonlinear terms at the equation of motion which become essential in the presence of large displacements. The current work presents numerical methods for investigating the dynamical behavior of plates with complex geometry. The equation of motion of the plate is derived by the classical plate theory and geometrical nonlinear terms are included. It is discretized by the finite element method and periodic responses are obtained by shooting method. Next point from the frequency-response curve is obtained by the sequential continuation method. The potential of the methods is demonstrated on rectangular plate with hole. The main branch along the fundamental mode is presented and the corresponding time responses and shapes of vibration are shown.

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

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 EPUB and 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

References

  1. Blackford, L.S., Choi, J., Cleary, A., D’Azevedo, E., Demmel, J., Dhillon, I., Dongarra, J., Hammarling, S., Henry, G., Petitet, A., Stanley, K., Walker, D. Whaley, R.C.: ScaLAPACK users’ guide. Soc. Ind. Appl. Math. (1997)

    Google Scholar 

  2. Davis, T.: Algorithm 832: Umfpack, an unsymmetric-pattern multifrontal method. ACM Trans. Math. Softw. 30(2), 196–199 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  3. Fix, G., Strang, G.: An Analysis of the Finite Element Method. Wellesley-Cambridge Press (2008)

    Google Scholar 

  4. Nayfeh, A., Pai, P.: Linear and Nonlinear Structural Mechanics. Wiley (2004)

    Google Scholar 

  5. Reddy, J.N.: Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. CRC Press (2004)

    Google Scholar 

  6. Stoykov, S., Margenov, S.: Scalable parallel implementation of shooting method for large-scale dynamical systems. application to bridge components. J. Comput. Appl. Math. 293, 223–231 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  7. Zienkiewicz, O., Taylor, R. Zhu, J.: The Finite Element Method: Its Basis and Fundamentals. Elsevier (2005)

    Google Scholar 

Download references

Acknowledgments

This work was supported by the project AComIn “Advanced Computing for Innovations”, grant 316087, funded by the FP7 Capacity Programme.

Author information

Authors and Affiliations

  1. Institute of Information and Communication Technologies, Bulgarian Academy of Sciences, Acad. G. Bonchev Str., bl. 25A, 1113, Sofia, Bulgaria

    Stanislav Stoykov & Svetozar Margenov

Authors
  1. Stanislav Stoykov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Svetozar Margenov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Stanislav Stoykov .

Editor information

Editors and Affiliations

  1. Inst. of Info. & comm. Tech., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Svetozar Margenov

  2. INst. of Info. & Comm. Tech., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Galia Angelova

  3. Inst. of Info. & Comm. Tech., Bulgarian Academy of Sciences, Sofia, Bulgaria

    Gennady Agre

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Stoykov, S., Margenov, S. (2016). Finite Element Method for Nonlinear Vibration Analysis of Plates. In: Margenov, S., Angelova, G., Agre, G. (eds) Innovative Approaches and Solutions in Advanced Intelligent Systems . Studies in Computational Intelligence, vol 648. Springer, Cham. https://doi.org/10.1007/978-3-319-32207-0_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-32207-0_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-32206-3

  • Online ISBN: 978-3-319-32207-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation