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Warianty tytułu
Konferencja
International Workshop on the Trefftz Method (2 ; 1999 ; Lisbon, Portugal
Języki publikacji
Abstrakty
Variational formulations that can be employed in the approximation of boundary value problems involving essential and natural boundary conditions are presented in this paper. They are based on trial functions so chosen as to satisfy a priori the governing differential equations of the problem. The essential boundary conditions are used to construct the displacement approximation basis at finite element level. The natural boundary conditions are enforced on average and their integral forms constitute the variational expression of the finite element approach. The shape functions contain both homogeneous and particular terms, which are related through the interpolation technique used. The application in the framework of the finite element method of the approach proposed here is not trouble free, particularly in what concerns the inter-element continuity condition. The Gauss divergence theorem is used to enforce the essential boundary conditions and the continuity conditions at the element boundary. An alternative but equivalent boundary technique developed for the same purpose is presented also. It is shown that the variational statement of the Trefftz approach is recovered when the Trefftz trial functions are so chosen as to satisfy the essential boundary conditions of the problem.
Słowa kluczowe
Rocznik
Tom
Strony
213--226
Opis fizyczny
Bibliogr. 27 poz., rys., tab.
Twórcy
autor
- Faculty of Civil Engineering, Tishreen University, Lattakia, Syria
Bibliografia
- [1] S. Abo Diab, Entwicklung und Einsatz Gemischt-Hybrider Finiter Elemente Fuer Aufgaben Der Linearen Kinetik von Faltwerken - Ein Beitrag zu FALT-FEM 5, Ph.D. Thesis, Technical University Dresden, (1989).
- [2] S. Abo Diab, Entwicklung und Einsatz hybrider finiter Stabelemente fuer Aufgaben der linearen Kinetik und Statik von rauemlichen Stabtragwerke - kompakte gerade Staebe, Bauingenieur, 66:437-440, (1991).
- [3] S. Abo Diab, Direkte Zuordnung des Verschiebungs - und Schnittkraftzustand zum Belastungszustand bei der FEM, Festschrift Prof. Dr.-Ing Habil. Heinz Mueller 65 Jahre ehemalige Doktoranden gratulieren, Technical University Dresden, (1994).
- [4] S. Abo Diab, New aspects in the application of the finite element displacement model, Basel Al Assad J. Engng. Sciences, Damascus (in Arabic), 3, (1995).
- [5] S. Abo Diab, A suggestion for a finite element approach, 1st Int. Workshop on Treftz Method - Recent Development and Perspectives, Summaries and Final Programme, Cracow, Poland, (1996).
- [6] S. Abo Diab, Energy methods in linear structural mechanics finite element methods, Dar Al-Hasad Dar Al-Kalimah, Damascus, 1998(in Arabic).
- [7] J. Jirousek, Basis for development of large finite elements locally satisfying all field equations, Comp. Meth. Appl. Mech. Engng., 14:65-92, (1978).
- [8] J. Jirousek, L. Guex, The hybrid Trefftz finite element model and it is application to plate bending, Int. J. Numer. Meth. Eng., 13:651-693 (1986).
- [9] J. Jirousek, P. Teodorescu, Large finite elements for the solution of problems in the theory of elasticity, Computers & Structures, 15:575-587, (1982).
- [10] J. Jirousek, A. Venkatesh, A new finite element approach for adaptive reliability assurance, Computers & Structures, 37:217-230, (1992).
- [11] J. Jirousek, A.P. Zielinski, Dual hybrid-Trefftz element formulation based on independent boundary traction frame, Int. J. Numer. Meth. Engng., 28:431-443, (1993).
- [12] J. Jirousek, A.P. Zielinski, Survey of Trefftz-type element formulations, 1st Int.Workshop Trefftz Method - Recent Developments and Perspectives, Cracow, Poland, (1996).
- [13] H. Mueller, S. Abo Diab, Lineare Kinetik von stabversteiften Faltwerken mit FALT-FEM, 62. Seminar „Finite Elemente V", Technical University Dresden, Johanngeorgenstadt, (1988).
- [14] H. Mueller, S. Abo Diab, Lineare Kinetik stabversteifter Faltwerke mit FALT-FEM5, 6th Inf. Conf. Theoretical and Experimental Mechanics, Technical University Dresden, (1989).
- [15] H. Mueller, S. Abo Diab, W. Graf, A. Hoffmann, A., Linear Kinetic of folded structures with hybrid-mixed elements, IKM-Weimar, Weimar (1994).
- [16] H. Mueller, A. Hoffmann, B. Moeller, J. Olden, A. Abo Diab, S., Some examples for the application of the hybrid-mixed elements in FALT-FEM, Finite Elements - Anwendung in der Baupraxis - Karlsruhe, (1991).
- [17] T.H.H. Pian, Finite element methods by variational principles with relaxed continuity requirement in engineering, Southampton Univ. Press, (1973).
- [18] T.H.H. Pian, P. Tong, Basis of finite element method for solid continua, Int. J. Numer. Meth. Engng., 1:3-38, (1969).
- [19] D.W. Pilkey, W. Wunderlich, Mechanics of structures variational and computational methods, CRC Press, (1994).
- [20] R. Piltner, Special finite elements with holes and internal cracks, Int. J. Numer. Meth. Engng., 21:1471- 1485, (1985).
- [21] R. Piltner, Recent developments in the Trefftz method for finite element and boundary element applications, Adv. Engng. Software, 24:107-115, (1995).
- [22] J.N. Reddy, Energy and variational methods in applied mechanics with an introduction to the finite element method, John Wiley & Sons, (1984).
- [23] B. Szybinski, A.P. Zielinski, Alternative T-complete systems of shape functions applied in analytical Trefftz finite elements, Numer. Meth. Partial Differential Equations, 11:375-388, (1995).
- [24] S. Timoshenko, Theory of plates and shells, McGraw Hill, (1940).
- [25] R.A. Toupin, A variational principle for mesh-type analysis of mechanical systems, Trans. ASME, J. Appl. Mech., 74:151-152, (1952).
- [26] E. Trefftz, Ein Gegenstueck zum Ritzchen Verfahren, Proc. 2nd Int. Cong. Applied Mechanics, Zurich, (1926).
- [27] W. Wunderlich, Mixed models for plates and shells: Principles-elements-examples, in Hybrid and Mixed Finite Element Methods, S. N. ATLURI, R. H. GALLAGHER, O. C. ZIENKIEWICZ (eds.), John Wiley & Sons, (1983).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BPB1-0006-0039