Skip to main content
SpringerLink
Log in
Book cover

Mixed Finite Element Method pp 15–73Cite as

Fundamentals of the Finite Element Method

  • Chapter

Part of the book series: Lecture Notes in Engineering ((LNENG,volume 72))

Abstract

The finite element method (FEM) appeared as a need for analysis of complex structural systems, for which there is no simple solution. In the application of the method the structural system is subdivided into elements of finite dimensions, i.e. finite elements. An approximate solution is found for such a small element, and then, by assembling all the elements of the system, a system of algebraic equations is derived. The solution of these equations gives an approximate solution of the complete structural system. In that way a very complex problem is reduced to a solution of simple algebraic equations.

This is a preview of subscription content, 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   84.99
Price excludes VAT (USA)
  • Available as 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

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adini A., Clough R., “Analysis plate bending by the finite element method”, Rept. to National Sci. Foundation, 1961.

    Google Scholar 

  2. Adini A., “Analysis of shell structures by the finite element method”, ph. D. Dis. Dept. Civil Eng. Univ. of California, Berkeley 1961.

    Google Scholar 

  3. Atluri S., Tong P., Murakava H., “Recent studies in hybrid and mixed finite element methods in mechanics”, Conf. Hybrid and Mixed M, John Wiley, 1983, 51–71.

    Google Scholar 

  4. Argiris J., “Triangular elements with linearly varying strain for the matrix displacement method”, J.Royal Aero. Sci. Tech. Note, 69. 711–13.

    Google Scholar 

  5. Argiris J., “Matrix analysis of three-dimensional elastic media–small and large displacements”, AIAA J. 3, 1965, 45–51.

    Article  Google Scholar 

  6. Ashwell D., Sabir A., “A new cylindrical finite element based on simple independent functions”, Dept. Civil Eng. Univ. Wales, Cardiff 1971.

    Google Scholar 

  7. Backlund J., “Limit analysis of reinforced concrete slabs by a finite element method”, Chalmers Tech. Hog Sc. Goteborg, 1972.

    Google Scholar 

  8. Backlund J., “Mixed finite element analysis of plates in bending”, Chalmers Tech. Hog Sc.Goteborg, 1972.

    Google Scholar 

  9. Bogner F., Fox R., Schmit L., “A cylindrical shell discrete element”, AIAA J. 5, No. 4, 1967.

    Article  Google Scholar 

  10. Cantin G., Clough R., “A curved cylindrical shell discrete element”, AIAA J. 6, No. 5, 1968

    Google Scholar 

  11. Clough R., “The finite element method after twenty-five years, a personal,view”. Eng. Appication of the FEM, Vol. 1., A.S.Computas, Novik, Norway 1981, 1–31.

    Google Scholar 

  12. Clough R., “The finite element method in plane stress analysis”, Proc. 2nd ASCE Conf. Electronic Comp., Pitsburg 1960.

    Google Scholar 

  13. Clough R., Tocher J., “Finite eiement stiffness matrices for analysis of plate bending”, Conf.Matrix Meth. Str. Mechanics, Wright Patterson AFB, Ohio, 1965.

    Google Scholar 

  14. Clough R., Felipe C., “A refined quadrilateral element for analysis of plate bending”, AFF-TR-68–150, 1968.

    Google Scholar 

  15. Clough R., “Comparision of three-dimensional finite elements” Symp. Application of FEM in Civil Eng. Nashville, Ten. 1969.

    Google Scholar 

  16. Cook R., “Some elements for analysis of plate bending”, Proc.ASCE 98, No. EMS, 1972, 1453–70.

    Google Scholar 

  17. Connor J., Will D., “A mixed finite element shallow shell

    Google Scholar 

  18. Connor J., Will D., “A mixed finite element shallow shell formulation”, Matrix Meth. Str. Anal. Design, Univ. Alabama, 1971, 105–137.

    Google Scholar 

  19. Cowper G., Lindberg G., Olson M., “A shallow shell finite element of thriangular shape”, Int. J.Solids Str. 6, 1970, 1133.

    Article  Google Scholar 

  20. Felipa C., “Refined finite element analysis of linear and non-linear two-dimensional structures”, Univ. of California, Berkeley, Str. Eng. Lab., Rep. SESM 66–22, 1966.

    Google Scholar 

  21. Herrmann L., “A bending analysis of plates, Proc. Conf. Matrix. Meth. Str. Mech., Wright Patterson AFB, Ohio 1965.

    Google Scholar 

  22. Herrmann L., “Finite element bending analysis of plates”, ASCE 93, No. EMS, 1967.

    Google Scholar 

  23. Roland I., Bergan P., “Higher order finite element for plane stress”, ASCE 94, No. EM2, 1968.

    Google Scholar 

  24. Irons B., Zienkiewicz 0., “The isoparametric element system, - a new concept in finite element analysis”, Conf. Recent Advances in Stress Anal., J.B.C..A., Royal Aero, Soc. London 1968.

    Google Scholar 

  25. Irons B., “Engineering application of numerical integration in stiffness method” AIAA J. 4, 1966.

    Google Scholar 

  26. Irons B., Ahmad S., “Techniques of finite elements”, Ellis Horwood, John Wiley, New York 1980.

    Google Scholar 

  27. Kantorovié L., Krilov V., “Pribli2ennie metodi vi§ego analiza”, Gos.Izd.Teh. Lit., Moskva 1950.

    Google Scholar 

  28. Kokalanov G., Poceski A., “Proraëun stabilnosti plo6a primenom me§ovitog metoda kona6nih elemenata”, II Jug. Simp. MKE, Maribor 1979.

    Google Scholar 

  29. Kokalanov G., “Mesoviti izoparametrijski elementi za analiza na ploèi”, Dokt. Dis., Grade2en Fakultet, Skopje 1983.

    Google Scholar 

  30. Kokalanov G., “Mesoviti konaLni elementi za analizu plo-a”, 16 Jug. Kon. Teor. Prim. Mehanike, Becici 1984, C7, 361–68.

    Google Scholar 

  31. Melosh R., “Basis for derivation of matrices by the direct stiffness method”, AIAA J. 1, 1963, 1931.

    Article  Google Scholar 

  32. Oden J., Reddy J., “Some observations on properties of certain mixed finite element approximations”, Int. J.Num. Meth. Eng. Vol. 9. No4., 1975, 933–38.

    Google Scholar 

  33. Pian T., Tong P., Basis for finite element methods for solid continua“, Int.J. Num. Meth. Eng. Vol. 1 1969, 3–28.

    Article  MATH  Google Scholar 

  34. Poceski A., “From deformation to mixed and hybrid formulation of the finite element method”, J. Theor. Appl. Mechanics, No. 5, Belgrade 1979.

    Google Scholar 

  35. Poceski A., Simonôe V., “Metodot na koneôni elementi i negovata primena”, Grade2en fakultet, Skopje 1972.

    Google Scholar 

  36. Poceski A., “A mixed finite element method for bending of plates”, Int. J.Num. Meth. Eng. Vol. 9,No. 1, 1975, 3–15.

    Article  MATH  Google Scholar 

  37. Poceski A., “Meovit metod na kone-ni elementi (III)”, 12 Jug.Kon. Teor. Prim. Mehanike, Ohrid 1974.

    Google Scholar 

  38. Poceski A., “Teorija na konstrukciite”, Grade2en fakultet, 1986.

    Google Scholar 

  39. Poceski A., “A new approach for development of finite elements”, J. Theor. App. Mechanics, No.8, Belgrade 1982, 111–18.

    MATH  Google Scholar 

  40. Poceski A., “KritiLki osvrt na osnovne postavke metoda konaLnih elemenata”, 16 Jug.Kon. Teor.Prim.Mehanike, BeLiéi 1984 (pozvani referat).

    Google Scholar 

  41. Poceski A., Kokalanov G., “Meovit element za analiza na debeli plo-i”, 16 Jug. Kongres Teor.Prim.Meha.iika, Be6idi, 1984, C7, 369–376.

    Google Scholar 

  42. Poceski A., Kokalanov G., “Meoviti ravninski kona-ni elementi”, 16 Jug. Kongres Teor.Prim.Mehanika, Be-ii 1984, C7, 353–360.

    Google Scholar 

  43. Poceski A., Kokalanov G., “Plo-i - ravninska sostojba na napreganjata”, Grade’en fakultet, Skopje 1982, izv. 2. 4.

    Google Scholar 

  44. Poceski A., Kokalanov G., “Mixed plate bending elements”, Int. Conf.Computer aided anal. Design Concrete Str.part I, Split 1984, Pineridge press, 721–34.

    Google Scholar 

  45. Poceski A., Kokalanov G., “Mixed plane stress finite elements”, Int.Conf.Comp. Aided Anal. Design Concrete Str. Split 194, part I, Pineridge press, 707–19.

    Google Scholar 

  46. Poceski A., Kokalanov G., “Lupi-primena na me3ovitiot metod na kone’-ni elementi”, Grade2en fakultet, Skopje 1986, izv. 2. 5.

    Google Scholar 

  47. Prato C., “A mixed finite element method for thin shell analysis”, ph. D. Th. Dept. Civil Eng. MIT, 1968.

    Google Scholar 

  48. Prato C., “Shell finite element method via Reissner’s principle”, Int.J.Solids Str. 5, 1969. 1119.

    Article  MATH  Google Scholar 

  49. Przemieniecki J., “Theory of matrix structural analysis”, Mcraw-Hill, 1968.

    Google Scholar 

  50. Sekulovié M., “Metod konaLnih elemenata”, Gradjevinska knjiga, Beograd 21984.

    Google Scholar 

  51. Sekulovid M., “Osnovi metode konaftih elemenata”, drugi seminar, MKE i prora-unu in’. konstrukcija, Gradjevinski Fakultet, Beograd, 1982, 208.

    Google Scholar 

  52. Stankovié D., “Metod konadnih elemenata ploàa”, Dr.Dis., Gradjevinski fakultet Ni, 1980.

    Google Scholar 

  53. Stankovi D., Poceski A., “Neka poboljanja u meovitom metodu kona-nih elemenata za analizu ploda”, 15. Jug. Kongres Teor. Prim. Mehanike, Kupari 1981.

    Google Scholar 

  54. Timoshenko S., Voinovski-Kriger S., “Theory of plates and shells”, McGraw-Hill, 1959.

    Google Scholar 

  55. Tocher J., Hartz B., “High-order finite element for plane stress”, ASCE 93, No.EM4, 1967.

    Google Scholar 

  56. Turner M., Clough R., Matrin H., Topp L., “Stiffness and deflection analysis of complex structures”, J.Aeronaut, Sci. 23, No. 9, 1956, 805–23.

    MATH  Google Scholar 

  57. Wunderlich W., “Mixed models for plates and shells: Principles-elements-examples”, Int.conf. Hybrid and Mixed Methods, John Wiley, 1983, 215–41.

    Google Scholar 

  58. Zienkiewicz O,., Taylor R., Too J., “Reduced integration technique in general analysis of plates and shells”, Int. J. Num. Meth. Eng. Vol. 3, 1971, 275–90.

    Article  MATH  Google Scholar 

  59. Zienkiewicz 0., Irons B., Ergatoudis J., Ahmad S., Scott F., “Isoparametric and associated element family for two-and three-dimensional analysis”, FEM in Stress Analysis, Tapir 1969.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Gradežen Fakultet, 91000, Skopje, Yugoslavia

    Prof. Apostol Poceski

Authors
  1. Prof. Apostol Poceski
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

Copyright information

© 1992 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Poceski, A. (1992). Fundamentals of the Finite Element Method. In: Mixed Finite Element Method. Lecture Notes in Engineering, vol 72. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-84676-2_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-84676-2_2

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54916-1

  • Online ISBN: 978-3-642-84676-2

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation