Skip to main content

New Trends in Hybrid-Treffz p-Element Approach

  • Chapter
The finite element method in the 1990’s
  • 639 Accesses

Abstract

The Hybrid-Trefftz (HT) finite element model, initiated in 1977–78 [1,2] and based on enforcing the conformity on an assumed element displacement field chosen so as to a priori satisfy the governing differential equations of the problem has now become a powerful and well established tool [3]. The paper shortly overviews and assesses the past an recent developments and outlines some new promising directions of the research under way.

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

Access this chapter

eBook
USD 16.99
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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Jirousek, J. and Leon, N. — A Powerful Finite Element for Plate Bending, Comp. Meth. Appl. Mech. Eng., 12, 77–96 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  2. Jirousek, J. — Basis for Development of Large Finite Elements Locally Satisfying All Field Equations, Comp. Meth. Appl. Mech. Eng., 14, 65–92 (1978).

    Article  MATH  Google Scholar 

  3. Zienkiewicz, O.C. and Taylor, R.L. — The Finite Element Method. Vol. 1, McGraw-Hill, London, 1989.

    Google Scholar 

  4. Trefftz, E. — ‘Ein Gegenstück zum Ritzschen Verfahren’, Proc. 2nd Int. Congr. Appl. Mech., Zürich, 1926, p. 131.

    Google Scholar 

  5. Zielinski, A.P. and Zienkiewicz, O.C. — Generalized Finite Element Analysis with T-complete Solution Functions, Int. Journal for Num. Meth. in Eng., 21, 509–528 (1985).

    Article  MATH  Google Scholar 

  6. Jirousek, J. and Teodorescu, P. — Large Finite Element Method for the Solution of Problems in the Theory of Elasticity, Computers and Structures, 15, 575–587 (1982).

    Article  MathSciNet  MATH  Google Scholar 

  7. Jirousek, J. — Hybrid-Trefftz Plate Bending Elements with p-method Capabilities, Int. Journal for Num. Meth. in Eng., 21, 1367–1393 (1987).

    Article  Google Scholar 

  8. Jirousek, J., Venkatesh, A., Zielinski, A.P. and Rabemanantsoa, H., — Comparative Study of p-extensions Based on Conventional Assumed Displacement and Hybrid-Trefftz FE Models, Internal Report LSC 91/10, Swiss Federal Institute of Technology, Lausanne, 1991.

    Google Scholar 

  9. Jirousek, J. and Venkatesh, A. — A Simple Stress Estimator for Hybrid-Trefftz p-version Elements, Int. Journal for Num. Meth. Eng., 28, 211–236 (1989).

    Article  MathSciNet  MATH  Google Scholar 

  10. Jirousek, J. and Venkatesh, A. — Adaptivity in Hybrid-Trefftz Finite Element Formulation, Int. Journal for Num. Meth. in Eng., 29, 391–405 (1990).

    Article  Google Scholar 

  11. Jirousek, J. and Venkatesh, A. — A New FE Approach for Adaptive Reliability Assurance, Computers and Structures, 37, 217–230 (1990).

    Article  MATH  Google Scholar 

  12. Jirousek, J. and Guex, L. — The Hybrid-Trefftz Finite Element Model and its Application to Plate Bending, Int. Journal for Num. Meth. Eng., 23, 651–693 (1986).

    Article  MathSciNet  MATH  Google Scholar 

  13. Jirousek, J. and N’Diaye, M. — Solution of Orthotropic Plates Based on p extension of the Hybrid-Trefftz Finite Element Model, Computers and Structures, 34, 51–62 (1990).

    Article  MATH  Google Scholar 

  14. Petrolito, J. — Hybrid-Trefftz Quadrilateral Elements for Thick Plate Analysis, TICOM Report 89–08, Texas Inst, for Comput. Mech., The University of Texas in Austin, 1989.

    Google Scholar 

  15. Jirousek, J. and N’Diaye, M. — Hybrid-Trefftz p-method Elements for Analysis of Rat Slabs with Drops, Computers and Structures (to appear).

    Google Scholar 

  16. Vörös, G.M. and Jirousek, J. — ‘Application of the Hybrid-Trefftz Finite Element Model to Thin Shell Analysis’, European Conf. on Advances in Comp. Struct. Mech., Giens, France, 1991, p. 547.

    Google Scholar 

  17. Venkatesh, A. and Jirousek, J. — ‘Accurate FE Analysis of Thin Plates Under Concentrated Loading’, IREM Internal Report 89/6, Swiss Federal Institute of Technology, Lausanne, 1989.

    Google Scholar 

  18. Piltner, R. — Special Finite Elements with Holes and Internal Cracks, Int. Journal for Num. Meth. in Eng., 21, 1471–1485 (1985).

    Article  MathSciNet  MATH  Google Scholar 

  19. Zienkiewicz, O.C, Kelly, D.W. and Bettess, P. — The Coupling of the Finite Element Method and Boundary Solution Procedures, Int. Journal for Num. Meth. in Eng., 11, 355–375 (1977).

    Article  MathSciNet  MATH  Google Scholar 

  20. Zienkiewicz, O.C, Kelly, D.W. and Bettess, P. — ‘Marriage à la Mode — the Best of Both Worlds (finite elements and boundary integrals)’, Engineering Methods in Finite Element Analysis, Eds. R. Glowinksi, E.Y. Rodin and O.C. Zienkiewicz, Wiley, 1979, p. 81.

    Google Scholar 

  21. Jin, W.G., Cheung, Y.K. and Zienkiewicz, O.C. — Application of the Trefftz Method in Plane Elasticity Problems, Int. Journal for Num. Meth. in Eng., 30, 1147–1161(1990).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

E. Oñate J. Periaux A. Samuelsson

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag Berlin Heidelberg

About this chapter

Cite this chapter

Jirousek, J. (1991). New Trends in Hybrid-Treffz p-Element Approach. In: Oñate, E., Periaux, J., Samuelsson, A. (eds) The finite element method in the 1990’s. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-10326-5_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-662-10326-5_6

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-10328-9

  • Online ISBN: 978-3-662-10326-5

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics