Skip to main content
SpringerLink
Log in

Efficient finite element analysis of models comprised of higher order triangular elements

  • Published:
Acta Mechanica Aims and scope Submit manuscript

Abstract

This paper introduces an efficient method for the finite element analysis of models comprised of higher order triangular elements. The presented method is based on the force method and benefits graph theoretical transformations. For this purpose, minimal subgraphs of predefined special patterns are selected. Self-equilibrating systems are then constructed on these subgraphs leading to sparse and banded null basis. Finally, well-structured flexibility matrices are formed for efficient finite element analysis.

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

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. de Henderson J.C.C.: Topological aspects of structural analysis. Aircr. Eng. 32, 137–141 (1960)

    Article  Google Scholar 

  2. Maunder, E.A.W.: Topological and Linear Analysis of Skeletal Structures, Ph.D. Thesis, London University, Imperial College (1971)

  3. de Henderson J.C.C., Maunder E.A.W.: A problem in applied topology: on the selection of cycles for the flexibility analysis of skeletal structures. J. Inst. Math. Appl. 5, 254–269 (1969)

    Article  MathSciNet  MATH  Google Scholar 

  4. Kaveh, A.: Application of Topology and Matroid Theory to the Analysis of Structures, Ph.D. Thesis, Imperial College, London University (1974)

  5. Kaveh A.: Improved cycle bases for the flexibility analysis of structures. Comput. Methods Appl. Mech. Eng. 9, 267–272 (1976)

    Article  MathSciNet  MATH  Google Scholar 

  6. Kaveh A.: Recent developments in the force method of structural analysis. Appl. Mech. Rev. 45, 401–418 (1992)

    Article  Google Scholar 

  7. Kaveh A.: Graphs and structures. Comput. Struct. 40, 893–901 (1991)

    Article  MathSciNet  MATH  Google Scholar 

  8. Kaveh A.: A combinatorial optimization problem optimal generalized cycle bases. Comput. Methods Appl. Mech. Eng. 20, 39–52 (1979)

    Article  MATH  Google Scholar 

  9. Kaveh A., Koohestani K., Taghizadieh N.: Efficient finite element analysis by graph-theoretical force method. Finite Elem. Anal. Des. 43, 543–554 (2007)

    Article  Google Scholar 

  10. Kaveh A., Koohestani K.: Efficient finite element analysis by graph-theoretical force method; triangular and rectangular plate bending elements. Finite Elem. Anal. Des. 44, 646–654 (2008)

    Article  Google Scholar 

  11. Kaveh A., Koohestani K.: Efficient graph-theoretical force method for three dimensional finite element analysis. Commun. Numer. Methods Eng. 24, 1533–1551 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  12. Kaveh A., Koohestani K.: Efficient graph-theoretical force method for two-dimensional rectangular finite element analysis. Commun. Numer. Methods Eng. 25, 951–971 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Kaveh A., Tolou Kian M.J.: Efficient finite element analysis using graph-theoretical force method with brick elements. Finite Elem. Anal. Des. 54, 1–15 (2012)

    Article  Google Scholar 

  14. Maunder, E.A.W.: On stress-based equilibrium elements and a flexibility method for the analysis of thin plated structures. In: Whitemen, J.R. (ed.) Math. Finite Elem. Appl. VI. Academic Press (1988)

  15. Ladeveze P., Maunder E.A.W.: A general methodology for recovering equilibrating finite element tractions and stress fields for plate and solid elements. Comput. Assis. Mech. Eng. Sci. 4, 533–548 (1997)

    MATH  Google Scholar 

  16. Denke, P.H.: A general digital computer analysis of statically indeterminate structures. NASA-TD-D-1666 (1962)

  17. Robinson J.: Integrated Theory of Finite Element Methods. Wiley, New York (1973)

    MATH  Google Scholar 

  18. Topçu, A.: A Contribution to the Systematic Analysis of Finite Element Structures Using the Force Method (in German). Doctoral Dissertation, Essen University, Germany (1979)

  19. Kaneko I., Lawo M., Thierauf G.: On computational procedures for the force methods. Int. J. Numer. Methods Eng. 18, 1469–1495 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  20. Soyer E., Topçu A.: Sparse self-stress matrices for the finite element force method. Int. J. Numer. Methods Eng. 50, 2175–2194 (2001)

    Article  MATH  Google Scholar 

  21. Gilbert J.R., Heath M.T.: Computing a sparse basis for the nullspace. SIAM J. Algebr. Discret. Meth. 8, 446–459 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  22. Coleman T.F., Pothen A.: The null space problem I; complexity. SIAM J. Algebr. Discret. Meth. 7, 527–537 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  23. Coleman T.F., Pothen A.: The null space problem II; algorithms. SIAM J. Algebr. Discret. Meth. 8, 544–561 (1987)

    Article  MathSciNet  Google Scholar 

  24. Pothen A.: Sparse null basis computation in structural optimization. Numer. Math. 55, 501–519 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  25. Patnaik S.N.: Integrated force method versus the standard force method. Comput. Struct. 22, 151–164 (1986)

    Article  MATH  Google Scholar 

  26. Patnaik S.N.: The variational formulation of the integrated force method. AIAA J. 24, 129–137 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  27. Przemieniecki J.S.: Theory of Matrix Structural Analysis. McGraw-Hill, New York (1968)

    MATH  Google Scholar 

  28. Kaveh A., Roosta G.R.: Comparative study of finite element nodal ordering methods. Eng. J. 20, 86–96 (1998)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Narmak, Tehran-16, Iran

    A. Kaveh

  2. Building and Housing Research Center, Tehran, Iran

    M. J. Tolou Kian

Authors
  1. A. Kaveh
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. M. J. Tolou Kian
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. Kaveh.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kaveh, A., Tolou Kian, M.J. Efficient finite element analysis of models comprised of higher order triangular elements. Acta Mech 224, 1957–1975 (2013). https://doi.org/10.1007/s00707-013-0855-9

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00707-013-0855-9

Keywords

Search

Navigation