Trefftz in translation

• Autorzy: Maunder E. A. W.
• Konferencja: International Workshop on the Trefftz Method (3 ; 16-18.09. 2002 ; Exeter, England)
• Języki publikacji: EN

Abstrakty

EN

This paper reviews the important concepts presented by Trefftz in 1926 regarding bounds to solutions, error estimation, and hybrid fields for use with domain decomposition. Observations are offered from the perspective of today's relatively mature state of the art in finite element methods. The numerical examples presented by Trefftz are also reviewed with the benefit of `exact' solutions made available from current commercial finite element methods. The accuracies of the solutions given by Trefftz are quantified and compared, and the effectivity indices of Trefftz's proposed error estimates are also quantified. An English translation of the original German version of Trefftz's paper is included for reference in an Appendix.

Słowa kluczowe

EN

Trefftz method; Ritz method

PL

metoda Trefftza

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2003
• Tom: Vol. 10, No. 4
• Strony: 545--563
• Opis fizyczny: Bibliogr. 14 poz., rys.

Twórcy

autor

Maunder E. A. W.

• Department of Engineering, School of Engineering and Computer Science, University of Exeter, Exeter, EX4 4QF, England

Bibliografia

• [1] E. Trefftz. Ein gegenstuck zum ritzschen verfahren. In: Proceedings of the 2nd International Congress of Applied Mechanics, Grell Fussli Verlag., pages 131-137, Zurich, 1926.
• [2] E. Stein. An appreciation of Erich Trefftz. Camp. Ass. Mech. and Eng. Sci., 4: 301-304, 1997.
• [3] B.M. Fraeijs de Veubeke. Stress Analysis, chapter 9: Displacement and equilibrium models in the finite element method. Wiley, New York, 1965.
• [4] M. Ainsworth, J.T. Oden. A posteriori error estimation in finite element analysis. Wiley, New York, 2000.
• [5] O.J.B.A. Pereira, J.P.M. Almeida. Adaptive refinement for a local error bound based on duality. In: 3rd International Workshop/ EuroConference on Trejjtz Methods, Exeter, 2002.
• [6] B. Szabo, I. Babuska. Finite Element Analysis. Wiley, New York, 1991.
• [7] O.C. Zienkiewicz, R.L. Taylor. The Finite Element Method, volume 1. Butterworth-Heinemann, Oxford, 5th edition, 2000.
• [8] J. Jirousek, A. Wroblewski. T-elements: state of the art and future trends. Arch. Camp. Meth. Engrg., 3/4: 323-434, 1996.
• [9] J.P.M. Almeida, J.A.T. Freitas. Continuity conditions for finite element analysis of solids. Int. J. Num. Meth. in Eng., 33: 845-853, 1992.
• [10] J.P.M. Almeida, J.A.T. Freitas. Alternative approach to the formulation of hybrid equilibrium finite elements. Computers & Structures, 40(4): 1043-1047, 1991.
• [11] J.A.T. Freitas. Formulation of elastostatic hybrid-Trefftz stress elements. Comp. Meth. Appl. Mech Eng., 153: 127-151, 1998.
• [12] J. Jirousek, A.P. Zielinski. Dual hybrid-Trefftz element formulation based on independent boundary traction frame. Int. J. Numer. Meth. Eng., 36: 2955-2980, 1993.
• [13] E.E. Sechler. Elasticity in engineering. Dover, New York, 1968.
• [14] P. Ladeveze, J.-P. Pelle. La maitrise du calculen mecanique lineaire et non lineaire. Hermes Science Publications, Paris, 2001.