Solution representations for Trefftz-type finite elements
Keywords:
Trefftz functions, Trefftz-type finite elementsAbstract
Solution representations are available for several differential equations. For elasticity problems some of the solution representations are considered in this paper. The solution representations can be used for a systematic construction of Trefftz functions for the derivation of Trefftz-type finite elements. For the example of a thick plate a set of Trefftz functions is presented.
References
[l] E. Trefftz . Ein Gegenstück zum Ritzschen Verfahren. In: 2. Int. Kongr. für Techn. Mech., pages 131- 137, Zurich, 1926.
[2] E. Stein. Die Kombination des modifizierten Trefftzschen Verfahrens mit der Methode der finiten Elemente. In: Finite Elemente in der Statik, pages 172- 185. Verlag Ernst & Sohn, Berlin, 1973.
[3] G. Ruoff. Die praktische Berechnung der Kopplungsmatrizen bei der Kombination der Trefftzschen Methode und der Methode der finiten Elemente. In: Finite Elemente in der Statik, pages 242- 259. Verlag Ernst & Sohn, Berlin, 1973.
[4] O. C. Zienkiewicz, D. W. Kelly, P. Bettess. The coupling of finite element and boundary solution procedures. Int. J. Numer. Meth. Eng. , 11: 355- 376, 1977.
[5] J .P.B .M. Almeida, O.J.B .A. Pereira. A set of hybrid equilibrium finite element models for the analysis of hreedimensional solids. Int. J. Numer. Meth. Eng., 39: 2789- 2802, 1996.
[2] E. Stein. Die Kombination des modifizierten Trefftzschen Verfahrens mit der Methode der finiten Elemente. In: Finite Elemente in der Statik, pages 172- 185. Verlag Ernst & Sohn, Berlin, 1973.
[3] G. Ruoff. Die praktische Berechnung der Kopplungsmatrizen bei der Kombination der Trefftzschen Methode und der Methode der finiten Elemente. In: Finite Elemente in der Statik, pages 242- 259. Verlag Ernst & Sohn, Berlin, 1973.
[4] O. C. Zienkiewicz, D. W. Kelly, P. Bettess. The coupling of finite element and boundary solution procedures. Int. J. Numer. Meth. Eng. , 11: 355- 376, 1977.
[5] J .P.B .M. Almeida, O.J.B .A. Pereira. A set of hybrid equilibrium finite element models for the analysis of hreedimensional solids. Int. J. Numer. Meth. Eng., 39: 2789- 2802, 1996.
Published
2023-01-26
Issue
pp. 587-596
Section
Articles
License
Copyright © The Author(s).
This work is licensed under the Creative Commons Attribution 4.0 International CC BY 4.0.
How to Cite
Piltner, R. (2023). Solution representations for Trefftz-type finite elements. Computer Assisted Methods in Engineering and Science, 10(4), 587-596. https://cames3.ippt.pan.pl/index.php/cames/article/view/1067
