Adaptive p-refinement of hybrid-Trefftz finite element solutions

Finite Elements in Analysis and Design

Volumn 39, Issue 11, 2003, Pages 1095-1121

  Teixeira de Freitas, J A ^a   Cismasiu C ^b  

^a INSTITUTO SUPERIOR TÉCNICO   (Portugal)

^b UNIVERSIDADE NOVA DE LISBOA   (Portugal)

Author keywords

Hybrid finite elements; P adaptivity; Trefftz method

Indexed keywords

ADAPTIVE SYSTEMS; BOUNDARY CONDITIONS; DEGREES OF FREEDOM (MECHANICS); FINITE ELEMENT METHOD; STRAIN;

TREFFTZ METHOD;

MATHEMATICAL TECHNIQUES;

EID: 0041669382     PISSN: 0168874X     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0168-874X(02)00159-2     Document Type: Article

References (23)

1. E. Trefftz, Ein Gegenstück zum Ritzschen Verfahren, in: Proceedings of the Second International Congress of Applied Mechanics, Zürich, 1926, pp. 131-137.
2. J.A.T. Freitas, J.P.M. Almeida (Eds. special issue), Trefftz Method, Computer Assisted Mechanics and Engineering Sciences, 8 (2/3) (2001).
3. Jiroušek J., Wróblewski A. T-elements. state of the art and future trends Arch. Comput. Methods Eng. 3:1996;323-434.
4. A.P. Zielinski (Ed. special issue), Trefftz Method, Computer Assisted Mechanics and Engineering Sciences 4 (3/4) 1997.
5. T.H.H. Pian, Derivation of element stiffness matrices by assumed stress distributions, AIAA J. (3) (1967) 1333-1335.
6. T.H.H. Pian, P. Tong, Basis of finite element methods for solid continua, Internat. J. Numer. Methods Eng. (1) (1969) 3-28.
7. S. Idelsohn, E. Oñate, E. Dvorkin (Eds.), hp-Adaptive Procedures in Hybrid-Trefftz Finite Element Approach, Computational Mechanics, New Trends and Applications, CIMNE, Barcelona, 1998.
8. Jiroušek J., Venkatesh A. A simple stress error estimator for hybrid-Trefftz p-version elements. Internat. J. Numer. Methods Eng. 28(1):1989;211-236.
9. Jiroušek J., Venkatesh A. Adaptivity in hybrid-Trefftz finite element formulation. Internat. J. Numer. Methods Eng. 29(2):1990;391-405.
10. Freitas J.A.T., Almeida J.P.B.M., Pereira E.M.B.R. Non-conventional formulations for the finite element method. Comput. Mech. 5/6(23):1999;488-501.
11. I. Cismaşiu, An implementation of a parallel model for the post processing of hybrid-Trefftz finite element solutions, Technical Report DT 7/96, IC/IST, DECivil, Lisboa, 1996.
12. Freitas J.A.T., Cismaşiu C. Numerical implementation of hybrid-Trefftz displacement elements. Comput. & Structures. 73:1999;207-225.
13. Freitas J.A.T., Cismaşiu I. Shape optimization with hybrid-Trefftz displacement elements. Internat. J. Numer. Methods Eng. 53:2002;473-498.
14. Freitas J.A.T., Ji Z.-Y. Hybrid-Trefftz equilibrium model for crack problems. Internat. J. Numer. Methods Eng. 39(4):1996;569-584.
15. Freitas J.A.T., Ji Z.-Y. Hybrid-Trefftz finite element formulation for simulation of singular stress fields. Internat. J. Numer. Methods Eng. 39(2):1996;281-308.
16. Almeida J.P.B.M., Freitas J.A.T. On the parallel implementation of non-conventional finite element formulations. Papadrakakis M. Advanced Finite Element Solution Techniques. 1995;CIMNE, Barcelona.
17. Freitas J.A.T., Bussamra F.L.S. Three-dimensional hybrid-Trefftz stress elements. Internat. J. Numer. Methods Eng. 47:2000;927-950.
18. Hager W.W. Updating the inverse of a matrix. SIAM Rev. 2:1989;221-239.
19. O.J.B.A. Pereira, J.P.B.M. Almeida, Elimination of spurious static modes in meshes of hybrid compatible triangular and tetrahedral finite elements, Internat. J. Numer. Methods Eng. (1999), 50 (2001) 885-898.
20. Freitas J.A.T., Cismaşiu C., Wang Z.M. Comparative analysis of hybrid-Trefftz stress and displacement elements. Arch. Comput. Methods Eng. State Art Rev. 6(1):1999;35-59.
21. Freitas J.A.T., Cismaşiu C., Wang Z.M. Numerical applications with hybrid-Trefftz stress and displacement elements. Strojnícky Časopis. 50(č. 2):1999;73-95.
22. Freitas J.A.T. Formulation of elastostatic hybrid-Trefftz stress elements. Comput. Methods Appl. Mech. Eng. 153(1/2):1998;127-151.
23. Y.F. Dong, P. Parreira, H-adaptive BEM based on linear hierarchical functions, in: C. Brebbia (Ed.), Boundary Elements XIV, Field Problems and Applications, WIT Press, Vol. 1, 1992, pp. 653-665.