Skip to main content
SpringerLink
Log in

Shear Deformable Plates

  • Chapter
  • First Online:
Partial Differential Equations of Classical Structural Members

Part of the book series: SpringerBriefs in Applied Sciences and Technology ((BRIEFSCONTINU))

Abstract

This chapter covers the continuum mechanical description of thick plate members. Thick plates are plates where the contribution of the shear force on the deformations is considered. Based on the three basic equations of continuum mechanics, i.e., the kinematics relationship, the constitutive law, and the equilibrium equation, the partial differential equations, which describes the physical problem, is derived.

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

Access this chapter

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 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Notes

  1. 1.

    Strictly speaking, there is a small difference between the plate theory according to Reissner [4] and Mindlin [2] and only for zero Poisson’s ratio both derivations are the same.

  2. 2.

    This plate elasticity matrix should not be confused with the compliance matrix which is represented by the same symbol.

References

  1. Blaauwendraad J (2010) Plates and FEM: surprises and pitfalls. Springer, Dordrecht

    Book  Google Scholar 

  2. Mindlin RD (1951) Influence of rotary inertia and shear on flexural motions isotropic, elastic plates. J Appl Mech-T ASME 18:1031–1036

    Google Scholar 

  3. Reddy JN (2006) An introduction to the finite element method. McGraw Hill, Singapore

    Google Scholar 

  4. Reissner E (1945) The effect of transverse shear deformation on the bending of elastic plates. J Appl Mech-T ASME 12:A68–A77

    MathSciNet  Google Scholar 

  5. Ventsel E, Krauthammer T (2001) Thin plates and shells: theory, analysis, and applications. Marcel Dekker, New York

    Book  Google Scholar 

  6. Wang CM, Reddy JN, Lee KH (2000) Shear deformable beams and plates: relationships with classical solution. Elsevier, Oxford

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mechanical Engineering, Esslingen University of Applied Sciences, Esslingen, Baden-Württemberg, Germany

    Andreas Öchsner

Authors
  1. Andreas Öchsner
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andreas Öchsner .

Rights and permissions

Reprints and permissions

Copyright information

© 2020 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

Öchsner, A. (2020). Shear Deformable Plates. In: Partial Differential Equations of Classical Structural Members. SpringerBriefs in Applied Sciences and Technology(). Springer, Cham. https://doi.org/10.1007/978-3-030-35311-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-030-35311-7_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-030-35310-0

  • Online ISBN: 978-3-030-35311-7

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation