Skip to main content

Abstract

A three-dimensional (3D) solid element is the most general finite element because all the displacement variables are dependent in x 1, x 2 and x 3 coordinates. The formulation of 3D solids elements is straightforward, because it is basically an extension of 2D solids elements. All the techniques described in 2D solids can be utilized, except that all the variables are now functions of special coordinate.

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 EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 129.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 159.99
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

References

  1. Liu GR, Quek SS (2003) The finite element method: a practical course. Butterworth-Heinemann, Oxford

    Google Scholar 

  2. Bathe K-J (1996) Finite element procedures. Hall Prentice, Englewood Cliffs

    Google Scholar 

  3. Oñate E (1995) Cálculo de Estructuras por el Método de los Elementos Finitos. Ed. CIMNE

    Google Scholar 

  4. Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth-Heinemann, Oxford

    MATH  Google Scholar 

  5. Eisenberg MA, Malvern LE (1973) On finite element integration in natural coordinates. Int J Numer Method Eng 7:574–575

    Article  MATH  Google Scholar 

  6. Love AEH (1927) A treatise on the mathematical theory of elasticity. Cambridge University Press, London

    MATH  Google Scholar 

  7. (2015) http://lakeforestdentalarts.com/northshore/chicago-partial-dentures.html

  8. Onodera K, Sato T, Nomoto S, Miho O, Yotsuya M (2011) Effect of connector design on fracture resistance of zirconia all-ceramic fixed partial dentures. Bull Tokyo Dent Coll 52(2):61–67

    Article  Google Scholar 

  9. Nemoto R, Nozaki K, Fukui Y, Yamashita K, Miura H (2013) Effect of framework design on the surface strain of zirconia fixed partial dentures. Dent Mater J 32(2):289–295

    Article  Google Scholar 

  10. Kou W, Kou S, Liu H, Sjögren G (2007) Numerical modeling of the fracture process in a three-unit all-ceramic fixed partial denture. Dent Mater 23(8):1042–1049. doi:10.1016/j.dental.2006.06.039

    Article  Google Scholar 

  11. Rezaei SMM, Heidarifar H, Arezodar FF, Azary A, Mokhtarykhoee S (2011) Influence of connector width on the stress distribution of posterior bridges under loading. J Dent (Tehran, Iran) 8(2):67–74

    Google Scholar 

  12. Romeed SA, Dunne SM (2013) Stress analysis of different post-luting systems: a three-dimensional finite element analysis. Aust Dent J 58(1):82–88. doi:10.1111/adj.12030

    Article  Google Scholar 

  13. Kermanshah H, Bitaraf T, Geramy A (2012) Finite element analysis of IPS Empress II ceramic bridge reinforced by Zirconia Bar. J Dent (Tehran, Iran) 9(4):196–203

    Google Scholar 

  14. Lin J, Shinya A, Gomi H, Shinya A (2012) Finite element analysis to compare stress distribution of connector of Lithia disilicate-reinforced glass-ceramic and zirconia-based fixed partial denture. Odontol/Soc Nippon Dent Uni 100(1):96–99. doi:10.1007/s10266-011-0025-2

    Article  Google Scholar 

  15. Wakabayashi N, Anusavice KJ (2000) Crack initiation modes in bilayered alumina/porcelain disks as a function of core/veneer thickness ratio and supporting substrate stiffness. J Dent Res 79(6):1398–1404

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this chapter

Cite this chapter

Neto, M.A., Amaro, A., Roseiro, L., Cirne, J., Leal, R. (2015). Finite Element Method for 3D Solids. In: Engineering Computation of Structures: The Finite Element Method. Springer, Cham. https://doi.org/10.1007/978-3-319-17710-6_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-17710-6_7

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-17709-0

  • Online ISBN: 978-3-319-17710-6

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics