Skip to main content
SpringerLink
Log in

Consistent Loading in Structural Reduction Procedures for Thin Plate Models

  • Chapter
  • First Online:
Advances in Mathematical Modeling and Experimental Methods for Materials and Structures

Part of the book series: Solid Mechanics and Its Applications ((SMIA,volume 168))

  • 1547 Accesses

Abstract

We distinguish between a plate which is a flat structure that has thickness much smaller than the other dimensions and between a plate model or theory which is the collection of assumptions that is used to dimensionally reduce the three-dimensional formulation and approximate its solution.

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

Access this chapter

Log in via an institution
eBook
USD 16.99
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

Institutional subscriptions

Notes

  1. 1.

    We distinguish between a plate which is a flat structure that has thickness much smaller than the other dimensions and between a plate model or theory which is the collection of assumptions that is used to dimensionally reduce the three-dimensional formulation and approximate its solution.

References

  1. Actis RL, Szabo BA, Schwab C (1999) Hierarchic models for laminated plates and shells. Comput Methods Appl Mech Eng 172:79–107

    Article  Google Scholar 

  2. Antman SS (1991) Nonlinear problems of elasticity. Applied Mathematical Science, vol 107. Springer, Berlin

    Google Scholar 

  3. Bisegna P, Sacco E (1997) A layer-wise laminate theory rationally deduced from the three-dimensional elasticity. J Appl Mech Trans ASME 64:538–545

    Article  Google Scholar 

  4. Bogner FK, Fox RL, Schmit LA (1966) The generation of interelement-compatible stiffness and mass matrices by the use of interpolation formulae. In: Proc First Conf Matrix Methods Struct Mech AFFDL-TR-66-80:397–443

    Google Scholar 

  5. Calcote LR (1969) The analysis of laminated composite structures. Van Nostrand, New York

    Google Scholar 

  6. Ciarlet PG (1997) Mathematical elasticity, vol. II: Theory of plates. North-Holland, Amsterdam

    Google Scholar 

  7. Hughes TJR, (1987) The finite element method. Prentice Hall, Englewood Cliffs, NJ

    Google Scholar 

  8. Kirchhoff G (1850) Über das gleichgewicht und die bewegung einer elastischen scheibe. J Reine Angew Math 40:51–58

    Article  Google Scholar 

  9. Krylov S, Harari I, Gadasi D (2006) Consistent loading in structural reduction procedures for beam models. Int J Multiscale Comput Eng 4:559–584

    Article  Google Scholar 

  10. O’Leary JR, Harari I (1985) Finite element analysis of stiffened plates. Comput Struct 21(5):973–985

    Article  Google Scholar 

  11. Libai A, Simmonds JG (1998) The nonlinear theory of elastic shells, 2nd edn. Cambridge Univ Press, Cambridge

    Book  Google Scholar 

  12. Madureira AL (2002) An improved biharmonic model – Incorporating higher order responses of the plate bending phenomena. Anal Appl 149:215–225

    Google Scholar 

  13. Podio-Guidugli P (2000) Recent results in the theory of elastic plates. Transp Theory Stat Phys 29(1, 2):217–224

    Google Scholar 

  14. Poisson SD (1829) Mémoire sur l’équilibre et le mouvement des corps élastiques. Memoires l’Acad Sci Paris 8:357–570

    Google Scholar 

  15. Reddy JN (1999) Theory and analysis of elastic plates. Taylor and Francis, London

    Google Scholar 

  16. Reissner E (1969) On generalized two-dimensional plate theory. II. Int J Solids Struct 5(6):629–637

    Article  Google Scholar 

  17. Rubin MB (2000) Cosserat theories: Shells, rods and points. Kluwer, Dordrecht

    Google Scholar 

  18. Sayir M, Mitropoulos C (1980) On elementary theories of linear elastic beams, plates and shells. (review paper). Zeitschrift fur Angewandte Mathematik und Physik 31:1–55

    Article  Google Scholar 

  19. Sutyrin VG, Hodges DH (1996) On asymptotically correct linear laminated plate theory. Int J Solids Struct 33:3649–3671

    Article  Google Scholar 

  20. Taylor RL, Beresford PJ, Wilson EL (1976) A non-conforming element for stress analysis. Int J Numer Methods Eng 10(6):1211–1219

    Article  Google Scholar 

  21. Vasil’ev VV, Lur’e SA (1992) On refined theories of beams, plates, and shells. J Compos Mater 26:546–557 Removed 5.03.09

    Google Scholar 

  22. Vogelius M, Babuska I (1981) On a dimensional reducion method I. The optimal selection of basis functions. Math Comput 37(55):31–46

    Google Scholar 

  23. Zienkiewicz OC, Taylor RL (2000) The finite element method, vol II. McGraw-Hill, New York

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Mechanical Engineering, Tel Aviv University, 69978, Ramat-Aviv, Tel Aviv, Israel

    I. Harari

Authors
  1. I. Harari
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. I. Sokolov
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. Krylov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. Harari .

Editor information

Editors and Affiliations

  1. Center of Samaria, Ariel University, Ariel, 44837, Israel

    Rivka Gilat

  2. Fac. Engineering, Tel Aviv University, Ramat Aviv, Tel-Aviv, 69978, Israel

    Leslie Banks-Sills

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Harari, I., Sokolov, I., Krylov, S. (2009). Consistent Loading in Structural Reduction Procedures for Thin Plate Models. In: Gilat, R., Banks-Sills, L. (eds) Advances in Mathematical Modeling and Experimental Methods for Materials and Structures. Solid Mechanics and Its Applications, vol 168. Springer, Dordrecht. https://doi.org/10.1007/978-90-481-3467-0_22

Download citation

  • DOI: https://doi.org/10.1007/978-90-481-3467-0_22

  • Published:

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-3466-3

  • Online ISBN: 978-90-481-3467-0

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation