Special Trefftz elements and improvement of their conditioning

Communications in Numerical Methods in Engineering

Volumn 13, Issue 10, 1997, Pages 765-775

  Zielinski A P ^a  

^a CRACOW UNIVERSITY OF TECHNOLOGY   (Poland)

Author keywords

T elements; Tikhonov procedure; Trefftz method

Indexed keywords

BOUNDARY CONDITIONS; LEAST SQUARES APPROXIMATIONS;

TIKHONOV PROCEDURE; TREFFTZ ELEMENT METHOD;

FINITE ELEMENT METHOD;

EID: 0031244717     PISSN: 10698299     EISSN: None     Source Type: Journal    
DOI: 10.1002/(SICI)1099-0887(199710)13:10<765::AID-CNM93>3.0.CO;2-L     Document Type: Article

References (20)

1. I. Herrera, 'Boundary methods: an algebraic theory', Pitman Adv. Publ. Program, London 1984.
2. I. Herrera, 'Trefftz method' in Topics in Boundary Element Research, Vol. 1, C. A. Brebbia (Ed.), Springer-Verlag, 1984.
3. A. P. Zieliński and O. C. Zienkiewicz, 'Generalized finite element analysis with T-complete boundary solution functions', Int. j. numer. methods eng., 21, 509-528 (1985).
4. A. P. Zieliński, 'On trial functions applied in the generalized Trefftz method'. Adv. Eng. Softw., 24, 147-155 (1995).
5. J. Jirousek and A. P. Zieliński, 'Survey of Trefftz-type element formulations', Comput. Struct., 63, 225-242 (1997).
6. J. Jirousek, 'Basis for development of large finite elements locally satisfying all field equations', Comput. Methods Appl. Mech. Eng., 14. 65-92 (1978).
7. J. Jirousek, 'New trends in hybrid-Trefftz p-element approach', in The Finite Element Method in the 1990's (dedicated to O. C. Zienkiewicz), E. Onate, J. Periaux and A. Samuelson (Eds.), Springer-Verlag, Barcelone, 1991.
8. K. Lin and P. Tong, 'Singular finite elements for the fracture analysis of V-notched plates', Int. j. numer. methods eng., 15, 1343-1354 (1980).
9. R. Piltner, 'Special finite elements with holes and internal cracks', Int. J. numer. methods eng., 21, 1471-1485 (1985).
10. J. Jirousek and A. Venkatesh, 'Hybrid-Trefftz plane elasticity elements with p-method capabilities', Int. j. numer. methods eng., 35, 1443-1472 (1992).
11. H. Sanecki and A. P. Zieliński, 'Special analytical finite elements and their application to optimal design', Proc. Conf. on Numerical Methods in Continuum Mechanics, Slovakia, Sept. 1996.
12. J. Jirousek and A. P. Zieliński, 'Dual hybrid-Trefftz element formulation based on independent boundary traction frame', Int. j. numer. methods eng., 36, 2955-2980 (1993).
13. R. Mathon and R. L. Johnston, 'The approximate solution of elliptic boundary value problems by fundamental solutions', SIAM J. numer. Anal., 14, 638-650 (1977).
14. A. P. Zieliński and I. Herrera, 'Trefftz method: fitting boundary conditions', Int. j. numer. methods eng., 24, 871-891 (1987).
15. A. Tikhonov, 'On certain problems of linear algebra and a stable method of their solution' (in Russian), Dokl. AN SSSR, 163(3), 591-594 (1965).
16. L. Chmielewski, 'The Use of Collocation Method in Solving Planar Elastostatics Problem with Arbitrary Boundary Conditions', Ph.D. Thesis, Warsaw Univ. Tech., Warszawa 1984 (in Polish).
17. B. Szybiński and A. P. Zieliński, 'Alternative T-complete systems of shape functions applied in analytical Trefftz finite elements', Numer. Methods for Part. Diff. Eq., 11 (1995).
18. A. K. Louis, Inverse und schlecht gestellte Probleme, Teubner, Stuttgart, 1989.
19. J. M. Melenk, 'Finite Element Methods with Harmonic Shape Functions for Solving Laplace's Equation', M.Sc. Thesis, Univ. Maryland, 1992 (directed by I. Babuška).
20. K. Andersen, S. Dannemeyer, H. Friebe, R. Mahnken, R. Ritter and E. Stein, 'Parameteridentifikation für ein plastisches Stoffgesetz mit FE-Methoden und Rasterverfahren', Bauingenieur, 71, 21-31 (1996).