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Finite Element Method for 3D Solids

  • Maria Augusta Neto
  • Ana Amaro
  • Luis Roseiro
  • José Cirne
  • Rogério Leal

Abstract

A three-dimensional (3D) solid element is the most general finite element because all the displacement variables are dependent in x1, x2 and x3 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.

Keywords

Shape Function Strain Matrix Nodal Displacement Vector Tetrahedron Element Natural Coordinate System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

References

  1. 1.
    Liu GR, Quek SS (2003) The finite element method: a practical course. Butterworth-Heinemann, OxfordGoogle Scholar
  2. 2.
    Bathe K-J (1996) Finite element procedures. Hall Prentice, Englewood CliffsGoogle Scholar
  3. 3.
    Oñate E (1995) Cálculo de Estructuras por el Método de los Elementos Finitos. Ed. CIMNEGoogle Scholar
  4. 4.
    Zienkiewicz OC, Taylor RL (2000) The finite element method. Butterworth-Heinemann, OxfordzbMATHGoogle Scholar
  5. 5.
    Eisenberg MA, Malvern LE (1973) On finite element integration in natural coordinates. Int J Numer Method Eng 7:574–575CrossRefzbMATHGoogle Scholar
  6. 6.
    Love AEH (1927) A treatise on the mathematical theory of elasticity. Cambridge University Press, LondonzbMATHGoogle Scholar
  7. 7.
  8. 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):61–67CrossRefGoogle Scholar
  9. 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):289–295CrossRefGoogle Scholar
  10. 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 CrossRefGoogle Scholar
  11. 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):67–74Google Scholar
  12. 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 CrossRefGoogle Scholar
  13. 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):196–203Google Scholar
  14. 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 CrossRefGoogle Scholar
  15. 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):1398–1404CrossRefGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Maria Augusta Neto
    • 1
  • Ana Amaro
    • 1
  • Luis Roseiro
    • 2
  • José Cirne
    • 3
  • Rogério Leal
    • 3
  1. 1.CEMUC - Centre for Mechanical EngineeringUniversity of CoimbraCoimbraPortugal
  2. 2.Department of Mechanical EngineeringPolytechnic Institute of CoimbraCoimbraPortugal
  3. 3.Department of Mechanical EngineeringUniversity of CoimbraCoimbraPortugal

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