The Trefftz finite elements modelling crack propagation

• Autorzy: Sanecki H. , Zieliński A.
• Języki publikacji: EN

Abstrakty

EN

Investigation of crack propagation can sometimes be a crucial stage of engineering analysis. The T-element method presented in this work is a convenient tool to deal with it. In general, T-elements are the Trefftz-type finite elements, which can model both continuous material and local cracks or inclusions. The authors propose a special T-element in a form of a pentagon with shape functions analytically modelling the vicinity of the crack tip. This relatively large finite element can be surrounded by even larger standard T-elements. This enables easy modification of the rough element grid while investigating the crack propagation. Numerical examples proved that the "moving pentagon" concept enables easy automatic generation of the T-element mesh, which facilitates observation of crack propagation even in very complicated structures with many possible crack initiators occurring for example in material fatigue phenomena.

Słowa kluczowe

EN

modelling; crack; Trefftz finite element models

PL

modelowanie; pękanie; modele elementów skończonych Trefftza

• Wydawca: Instytut Podstawowych Problemów Techniki PAN
• Czasopismo: Computer Assisted Mechanics and Engineering Sciences
• Rocznik: 2008
• Tom: Vol. 15, No. 3/4
• Strony: 353--368
• Opis fizyczny: Bibliogr. 25 poz., wykr.

Twórcy

autor

Sanecki H.

autor

Zieliński A.

• Cracow University of Technology, Krakow, Poland

Bibliografia

• [1] T. Belytschko, T. Black. Elastic crack growth in finite elements with minimal remeshing. International Journal for Numerical Methods in Engineering, 45: 601-620, 1999.
• [2] S. Bordas. Extended Finite Element and Level Set Methods with Applications to Growth of Cracks and Biofilms. PhD thesis, Northwestern University Evanston, Illinois, December 2003.
• [3] F. Erdogan, G.C. Sih. On the crack extension in plates under plane loading and transverse shear. Journal of Basic Engineering, Transactions of the ASME, 85D: 519-527, 1963.
• [4] J.A.T. Freitas, Z.Y. Ji. Hybrid-Trefftz equilibrium model for crack problems. International Journal for Numerical Methods in Engineering, 39: 569-584, 1996.
• [5] J. Jirousek, N. Leon. A powerful finite element for plate bending. Computer Methods in Applied Mechanics and Engineering, 12: 77-96, 1977.
• [6] J. Jirousek, A. Venkatesh. Hybrid-Trefftz plane elasticity elements with p-method capabilities. International Journal for Numerical Methods in Engineering, 35: 1443-1472, 1992.
• [7] J. Jirousek, A. Wroblewski. T-elements: State of the art and future trends. Archives of Computational Methods in Engineering, 3/4: 323-434, 1996.
• [8] J. Jirousek, A.P. Zieliriski. Survey of Trefftz-type element formulations. Computers and Structures, 63(2): 225-242, 1997.
• [9] D.G. Lewicki, R. Ballarini. Effect of rim thickness on gear crack propagation path. NASA Technical Memorandum 107229, Army Research Laboratory Technical Report ARL-TR-1110. Prepared for the 7th International Power Transmission and Gearing Conference, October 6-9, 1996, sponsored by the ASME, San Diego, California.Available: http://gltrs.grc.nasa.gov/reports/1996/TM-107229.pdf.
• [10] N. Moes, J. Dolbow, T. Belytschko. A Finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46: 131-150, 1999.
• [11] R. Piltner. Special finite elements with holes and internal cracks. International Journal for Numerical Methods in Engineering. 21: 1471-1485, 1985.
• [12] Q.H. Qin. The Trefftz Finite and Boundary Element Method, WITpress, Southampton, 2000.
• [13] H. Sanecki, A.P. Zielinski, S. Laczek. Application of Analytical Finite Elements to Cruel: Problems (in Polish),Grant T11F012 23 of KBN (Polish State Committee for Scientific Research), Report, Pari I. Cracow, 2003,
• [14] H. Sanecki, A.P. Zielinski. Crack propagation modelled by T-element.s. Engineering Computations. 23(2): 100-123, 2006.
• [15] H. Sanecki, A.P. Zielinski. Application of T-elements to crack path prediction in 2D engineering structures CMM2005 Częsstochowa 21-24 June 2005, pp. 27. ISBN 83-921605-7-6/CD.
• [16] G.C. Sih. Energy-density concept in fracture mechanics. Engineering Fracture Mechanics, 5: 1037 1040, 1973.
• [17] G.C. Sih. Some basic problems in fracture mechanics and new concepts. Engineering Fracture Mechanics, 5: 365-377, 1973.
• [18] G.C. Sih. Strain energy-density factor applied to mixed-mode crack problems. International Journal of Fracture, 10: 305-321, 1974.
• [19] B.A. Szabo, .J. Babuska. Computation of the Amplitude of Stress Singular Terms for Cracks and Reentrant Corners. Report WU/CCM-86/1, Washington Univ. In St. Louis. February 1986.
• [20] P. Tong, P.H. Pian, S.L. Lasry. A hybrid-element approach to crack problems in plane elasticity International Journal for Numerical Methods in Engineering, 7: 297 308, 1973.
• [21] G. N. Wells. Discontinuous Modelling of Strain Localisation and Failure. PhD thesis (Proefsehrift ter verkrijging van de graad van doctor aan de Technische Universiteit Delft), 2001.
• [22] M. L. Williams. Stress singularities resulting from various boundary conditions in angular corners ol plater in extension. Journal of Applied Mechanics, 19: 526-528, 1952.
• [23] A. P. Zielinski, O.C. Zienkiewicz. Generalized finite element analysis with T-complete boundary solution functions. International Journal for Numerical Methods in Engineering, 21: 509-528, 1985.
• [24] A. P. Zielinski, I. Herrera. Trefftz method: fitting boundary conditions. International Journal for Numerical Methods in Engineering, 24: 871-891, 1987.
• [25] A. P. Zieliński. On trial functions applied in the generalized Trefftz method. Advances in Engineering Software, 24: 147-155, 1995.