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Finite Element Method

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Book cover Application of the Finite Element Method in Implant Dentistry

Part of the book series: Advanced Topics in Science and Technology in China ((ATSTC))

Abstract

The finite element method may be applied to all kinds of materials in many kinds of situations: solids, fluids, gases, and combinations thereof; static or dynamic, and, elastic, inelastic, or plastic behaviour. In this book, however, we shall restrict the treatment to the deformation and stress analysis of solids, with particular reference to dental implants.

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References

  1. Argyris JH (1995) Energy Theorems and Structural Analysis. Aircraft Engineering 27

    Google Scholar 

  2. Bendixen A (1914) Die Methode der Alpha Gleichungen zur Bererchnung von Rahmenkonstruktionen, Berlin

    Google Scholar 

  3. Castigliano A (1875) Nuova Teoria Intorno dell Equilibrio dei Sistemi Elastici. Atti Acc Sci Torino

    Google Scholar 

  4. Clapeyron (1857) Theorem of Three Moments. Comptes Rendus 45:1076

    Google Scholar 

  5. Clough RW (1960) The Finite Element Method in Plane Stress Analysis. J Struc Div, ASCE, Proc. 2nd Conf. on Electronic Computation 345–378

    Google Scholar 

  6. Cook RD, Malcus DS, Plesha ME (1989) Concepts and Applications of Finite Element Analysis, Third Ed. New York, USA: John Wiley & Sons

    MATH  Google Scholar 

  7. Corum JM, N Krishnamurthy (1969) A Three-dimensional Finite Element Analysis of a Prestressed Concrete Reactor Vessel Model, Proc. of Symposium on Application of Finite Element Methods in Civil Engineering. Vanderbilt University, Nashville, Tennessee, USA 63–94

    Google Scholar 

  8. Courant R (1943) Variational Methods for the Solution of Problems of Equilibrium and Vibration. Bull Am Math Soc 49:1–23

    Article  MATH  MathSciNet  Google Scholar 

  9. Cross H (1932) Analysis of Continuous Frames by Distributing Fixed-End Moments. Trans ASCE 96:1–10

    Google Scholar 

  10. Desai CS, JF Abel (1972) Introduction to the Finite Element Method. New York, USA:van Nostrand Reinhold Co.

    MATH  Google Scholar 

  11. Euler L (1774) Methods Inveniendi Lineas Curvas Maximi Minimine Proprietate Gaudentes. Lausanne and Geneva: M. Bousquet

    Google Scholar 

  12. Galerkin BG (1915) Series Solution of Some Problems of Elastic Equilibrium of Rods and Plates (Russian). Vestn Inzh Tech 19:897–908

    Google Scholar 

  13. Gallagher RH (1975) Finite Element Analysis Fundamentals. New Jersey, USA: Prentice Hall, Inc.

    Google Scholar 

  14. Hrenikoff A (1941) Solution of Problems in Elasticity by the Framework Method. J Appl Mech 8:A169–A175

    Google Scholar 

  15. Huebner KH (1975) The Finite Element Method for Engineers. New York, USA: John Wiley & Sons 9–13

    Google Scholar 

  16. Krishnamurthy N (1983) Finite Elements for the Practicing Engineer. Singapore: J Inst Engrs 23(1)

    Google Scholar 

  17. Levy S (1953) Structural Analysis and influence Coefficients for Delta Wings. J Aero Sci 20(7): 449–454

    MATH  Google Scholar 

  18. Livesley RK (1964) Matrix Methods in Structural Analysis. Pergamon Press

    Google Scholar 

  19. Maney GB (1915) Studies in Engineering (No. 1). Minneapolis, Minnesota: University of Minnesota

    Google Scholar 

  20. Maxwell JC (1864) On the Calculations of the Equilibrium and Stiffness of Frames. Phil Mag 4(27): 294

    Google Scholar 

  21. McHenry D (1944) A Lattice Analogy for The Solution of Plane Stress Problems. Proc Inst Civ Engrs 21(2):59–82

    Google Scholar 

  22. Melosh RJ (1963) Basis for Derivation of Matrices for the Direct Stiffness Method. AIAA J 1(7):1631–1637

    Article  Google Scholar 

  23. Morice PB (1959) Linear Structural Analysis. New York, USA: The Ronald press Co.

    MATH  Google Scholar 

  24. Newmark NM (1943) Numerical Procedure for Computing Deflections, Moments, and Buckling Loads. Trans ASCE 68–69

    Google Scholar 

  25. Oden JT (1972) Finite Elements of Nonlinear Continua. New York, USA: McGraw-Hill Book Co.

    MATH  Google Scholar 

  26. Przemieniecki JS (1968) Theory of Matrix Structural Analysis, New York, USA: McGraw-Hill Book Co.

    MATH  Google Scholar 

  27. Rubin Carol, N Krishnamurthy, E Capilouto, H Yi (1983) Stress Analysis of the Human Tooth Using a Three-dimensional Finite Element Model. J Dent Res 62(2):82–86

    Google Scholar 

  28. Southwell RV (1940) Relaxation Methods in Engineering Science. Oxford, UK: Clarendon Press

    Google Scholar 

  29. Turner MJ, Clough RW, Martin HC, Topp LJ (1956) Stiffness and Deflection Analysis of Complex Structures. J Aero Sci 23(9):805–823

    Google Scholar 

  30. Von Karman, T MA Biot (1940) Mathematical Methods in Engineering. New York, USA: McGraw-Hill Book Co.

    Google Scholar 

  31. Wieghardt K (1906) Ber einen Grenz Bergang der Elastizit Tslehre und Seine Andwendung auf die Statik Hochgradig Statisch Unbestimmter Fachwerke. Verhandlungen des Vereins z. Bef rderung des Gewerbefleisses. Abhandlungen 85:139–176

    Google Scholar 

  32. Wilson EL (1963) Finite Element Analysis of Two-dimensional Structures, Report No. 63. Dept of Civil Eng, Univ of California, Berkeley

    Google Scholar 

  33. Zienkiewicz OC, Cheung YK (1967) The Finite Element Method in Structural and Continuum Mechanics, London, UK: McGraw-Hill Publishing Co.

    MATH  Google Scholar 

  34. Krishnamurthy, N (1971) Three dimensional Finite Element Analysis of Thick Walled Pipe Nozzle Junctions with Curved Transitions, Preprints of the First International Conference on Structural Mechanics In Reactor Technology, Berlin, Germany, 3. Reactor pressure vessels, Part G Steel Pressure Vessels. Organised by: Budesanstalt fur Materialprufung (BAM), Berlin, Commission of the European Communities, Brussel

    Google Scholar 

  35. Task Committee on Automated Analysis and Design, Committee on Electronic Computation, Guidelines for Finite Element Idealization, Meeting Preprint 2504 (1975) ASCE National Structural Engineering Convention, New Orleans, Louisiana, USA

    Google Scholar 

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Author information

Authors and Affiliations

  1. Consultant, Structures, Safety, and Computer Applications, Singapore

    N. Krishnamurthy

Authors
  1. N. Krishnamurthy
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Editor information

Editors and Affiliations

  1. Clinical Research Institute, Second Affiliated Hospital, Zhejiang Universyty School of Medicine, 88 Jiefang Road, Hangzhou, 310009, China

    Jianping Geng  & Weiqi Yan  & 

  2. School of Engineering (H5), University of Surrey, Surrey, GU2 7XH, UK

    Wei Xu

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© 2008 Zhejiang University Press, Hangzhou and Springer-Verlag GbmH Berlin Heidelberg

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Krishnamurthy, N. (2008). Finite Element Method. In: Geng, J., Yan, W., Xu, W. (eds) Application of the Finite Element Method in Implant Dentistry. Advanced Topics in Science and Technology in China. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73764-3_1

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  • DOI: https://doi.org/10.1007/978-3-540-73764-3_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-73763-6

  • Online ISBN: 978-3-540-73764-3

  • eBook Packages: EngineeringEngineering (R0)

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