Trefftz functions in FEM, BEM and meshless methods

• Autorzy: Kompiš V. , Štiavnicky M.
• Języki publikacji: EN

Abstrakty

EN

The paper contains three different multi-domain formulations using Trefftz (T-) displacement approximation/interpolation, namely the hybrid-displacement FEM, reciprocity based FEM (multi-domain BEM) and the Boundary Meshless Method (BMM) for a single and multi-domain (MD) formulation. All three methods can lead to compatible formulation with the isoparametric FEM, when the displacements along the common boundaries are defined by same interpolation function. All three T-formulations enable to define more complicated elements/subdomains (the T-element can be also a multiply connected region) with integration along the element boundaries, only.

Słowa kluczowe

EN

Trefftz method; FEM; BEM

PL

metoda Trefftza; FEM; BEM

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2006
• Tom: Vol. 13, No. 3
• Strony: 417--426
• Opis fizyczny: Bibliogr. 18 poz.

Twórcy

autor

Kompiš V.

autor

Štiavnicky M.

• Academy of the Armed Forces of General Milan, Demanowska 393, 031 19 Lipt. Mikulaš, Slovakia

Bibliografia

• [1] V.I. Blokh. Theory of Elasticity (in Russian). University Press, Kharkov, 1964.
• [2] .J. Boussinesq. Application des Potentiels a l'Etude I'Equilibre et du Mouvement des Solides Elastiques. Gautier-Villars, Paris, 1885.
• [3] V. Cerruti. Ricerche intorno all'equilibrio dei corpi elastici isotropi. Atti della R. Academia dei Lincei, Memoriae della Classe di Scienze Fiziche. Matematiche e Naturali, 13: 81, 1881-1882.
• [4] A.H.-D. Cheng, D.T. Cheng. Heritage and early history of the boundary element method. Eng. Anal, with Boundary Elements, 29: 268-302, 2005.
• [5] T.A. Cruse. Numerical solutions in three dimensional elastostatics. Int. J. Solids Struct., 5: 1259-1274, 1969.
• [6] J. Jirousek. Basis for the development of large finite elements locally satisfying all field equations. Comp. Meth. Appl. Mech. Eng., 14: 65-92, 1977.
• [7] J. Jirousek, A. Wróblewski. T-elements: State of the art and future trends. Archives of Comput. Meth.. in Engrg., 3(4): 323-434, 1996.
• [8] M. Kachanov, B. Shafiro, I. Tsukrov. Handbook of Elasticity Solutions. Kluwer Academic Publishers, Dordrecht, 2003.
• [9] V. Kompiš. Finite elements satisfying all governing equations inside the element. Comput. Struct., 4: 273-278, 1994.
• [10] V. Kompiš, J. Oravec, J. Búry. Reciprocity based FEM. In: Proc. Conf, on Numerical Methods in Continuum Mechanics, High Tatras, Slovak Republic, 45-51, 1998.
• [11] V. Kompiš, M. Štiavnicky. Evaluation of local fields by the boundary point method. In Computational Mechanics, WCCM VI in conjunction with APCOM'04, Beijing, China, Tsinghua University Press & Springer-Verlag, 2004.
• [12] V. Kompiš, M. Toma, M. Žmindák, M. Handrik. Use of Trefftz functions in non-linear BEM/FEM. Comput. Struct., 82(27): 2351-2360, 2004.
• [13] W.T. Kelvin. Note on integrations of the equations of equilibrium of an elastic solid. Math J., Cambridge, Dublin,1848.
• [14] R., Mathon, R.L. Johnston. The approximate solution of elliptic boundary-value problems by fundamental solutions. SIAM J. Numer. Anal, 27: 638-650, 1977.
• [15] J. Mazùr, V. Kompiš, P. Novák. FEM stress, recovery using Trefftz polynomials. In: K.-J. Bathe, ed.. Proc. Third MIT Conference, on Fluid and Solid. Mechanics, Elsevier, Boston, 361-364, 2005.
• [16] Numerical Computing with MATLAB, The MathWorks, Inc., http://www.mathworks.com/moler
• [17] C. Somigliana. Sulla teoria delle distorsioni elastiche. Note I e II Atti Accad Naz Lined Classe Sci Fis e Nat, 23: 463-472, 1914, and 24: 655-666, 1915.
• [18] E. Trefftz. Ein Gegenstűck zum Ritzschen Verfahren. Proceedings 2nd International Congress of Applied Mechanics, Zurich, 131-137, 1926.