A Finite Element Formulation for the Analysis of Local Effects

  • A. Venkatesh
  • J. Jirousek
Conference paper
Part of the International Union of Theoretical and Applied Mechanics book series (IUTAM)


The paper reviews the progress achieved in the analysis of geometry and load dependent local effects, based on an alternative FE formulation known as the hybrid-Trefftz (HT) FE model. A brief description with examples presents the developments which have lead to a simple p-adaptive analysis of structures with stress-raisers (e.g., holes, cracks and corners) in presence of multiple load cases, including local concentrated loads.


Load Case Finite Element Formulation Line Load Frame Field Hierarchic Mode 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    E. Trefftz. Ein Gegenstück zum Ritzschen Verfahren. Proc. 2nd Intl. Cong. Appl. Mech., Zürich, pp. 131–137 (1926).Google Scholar
  2. 2.
    J. Jirousek and N. Leon. A powerful finite element for plate bending. Comp. Meths. Appl. Mech. Engrg. 12, 1, pp. 77–96 (1977).MathSciNetMATHGoogle Scholar
  3. 3.
    J. Jirousek. Basis for development of large finite elements locally satisfying all field equations. Comp. Meth. Appl. Mech. Engrg. 14, 1, pp. 65–92 (1978).MathSciNetADSMATHCrossRefGoogle Scholar
  4. 4.
    I. Babuska, J.T. Oden and J.K. Lee. Mixed hybrid finite element approximations of second-order elliptic boundary value problems, Part 2–Weak-hybrid methods. Comp. Meth. Appl. Mech. Engrg. 14, 1, pp. 1–22 (1978).MathSciNetMATHGoogle Scholar
  5. 5.
    A.P. Zielinski and O.C. Zienkiewicz. Generalized finite element analysis with T-complete boundary solution functions. Int. J. Num. Meth. Engrg. 21, pp. 509–528 (1985).Google Scholar
  6. 6.
    J. Jirousek and P. Teodorescu. Large finite element method for the solution of problems in the theory of elasticity. Comp. Struc. 15, pp. 575–587 (1982).Google Scholar
  7. 7.
    J. Jirousek and Lan Guex. Hybrid-Trefftz finite element model and its application to plate bending. Int. J. Num. Meth. Engrg. 23, pp. 651–693 (1986).MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    J. Jirousek and A. Venkatesh. Adaptivity in hybrid-Trefftz finite element formulation. Int. J. Num. Meth. Engrg. 29, pp. 391–405 (1990).CrossRefGoogle Scholar
  9. 9.
    J. Jirousek and A. Venkatesh. A simple stress error estimator for hybrid-Trefftz Aversion elements. Int. J. Num. Meth. Engrg. 28, pp. 211–236 (1989).MathSciNetMATHCrossRefGoogle Scholar
  10. 10.
    J. Jirousek. Hybrid-Trefftz plate bending elements with p-method capabilities. Int. J. Num. Meth. Engrg. 24, pp. 1367–1393 (1987).MATHCrossRefGoogle Scholar
  11. 11.
    J. Jirousek and A. Venkatesh. Hybrid-Trefftz plane elasticity elements with p-method capabilities. Int. J. Num. Meth. Engrg. To appear.Google Scholar
  12. 12.
    A.K. Rao, I.S. Raju and A.V.K. Murthy. A powerful hybrid method in finite element analysis. Int. J. Num. Meth. Engrg. 3, 3, pp. 389–403 (1971).MATHCrossRefGoogle Scholar
  13. 13.
    K.Y. Lin and P. Tong. Singular finite elements for the fracture analysis of v-notched plate. Int. J. Num. Meth. Engrg. 15, pp. 1343–1354 (1980).MATHCrossRefGoogle Scholar
  14. 14.
    R. Piltner. Spezielle finite Elemente mit Löchern, Ecken and Rissen unter Verwendung von analytischen Teillösungen. Fortschritt-Berichte der VDI Zeitschriften 1, 96, VDI-Verlag GmbH, Düsseldorf (1982).Google Scholar
  15. 15.
    T. D. Gerhardt. A hybrid/finite element approach for stress analysis of notched anisotropic materials. J. Appl. Meth. Trans. ASME 51, pp. 804–810 (1984).ADSMATHCrossRefGoogle Scholar
  16. 16.
    A. Venkatesh and J. Jirousek. Accurate FE analysis of thin plates under concentrated loading. IREM Internal Report 89/6, Dept. of Civil Engineering, Swiss Federal Institute of Technology, Lausanne, June 1989.Google Scholar
  17. 17.
    J. Jirousek. Implementation of local effects into conventional and non-conventional finite element formulations. Local Effects in the Analysis of Structures. Ed. P. Ladevèze. Elsevier, pp. 279–298 (1985).Google Scholar
  18. 18.
    B.A.Szabo. Estimation and control of error based on p-convergence. Accuracy Estimates and Adaptive Refinements in Finite Element Computations. Ed. I. Babuska, O.C. Zienkiewicz, J. Gado and E.R. de A. Oliveira. Wiley, pp. 61–78 (1986).Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1992

Authors and Affiliations

  • A. Venkatesh
    • 1
  • J. Jirousek
    • 1
  1. 1.LSC, Department of Civil EngineeringSwiss Federal Institute of TechnologyLausanneSwitzerland

Personalised recommendations