×

Toward a hybrid-Trefftz element with a hole for elasto-plasticity? (English) Zbl 1139.74048

Summary: The paper deals with the modelling of riveted assemblies for full-scale complete aircraft crashworthiness. Many comparisons between experiments and FE computations of bird impacts onto aluminium riveted panels have shown that macroscopic plastic strains were not sufficiently developed (and localised) in the riveted shell FE in the impact area. Consequently, FE models never succeed in initialising and propagating the rupture in the sheet metal plates and along rivet rows as shown by experiments, without calibrating the input data (especially the damage and failure properties of the riveted shell FE). To model the assembly correctly, it appears necessary to investigate on FE techniques such as hybrid-Trefftz finite element method. Indeed, perforated FE plates developed for elastic problems, based on a hybrid-Trefftz formulation, have been found in the literature. Our purpose is to find a way to extend this formulation so that the super-element can be used for crashworthiness. To reach this aim, the main features of an elastic hybrid-Trefftz plate are presented and are then followed by a discussion on the possible extensions. Finally, the interpolation functions of the element are evaluated numerically.

MSC:

74S05 Finite element methods applied to problems in solid mechanics
74R15 High-velocity fracture
74K20 Plates
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] A.-S. Bayart, B. Langrand, P. Drazétic, Multiscale modelling for non-linear behaviour of perforated plates in riveted airframe crashworthiness, in: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Jyväskylä, Finland, 2004.; A.-S. Bayart, B. Langrand, P. Drazétic, Multiscale modelling for non-linear behaviour of perforated plates in riveted airframe crashworthiness, in: Proceedings of the European Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS), Jyväskylä, Finland, 2004.
[2] H.C. Chen, A special finite element with an elliptical hole for laminated structures, AIAA-94-1337-CP (1994) 253-263.; H.C. Chen, A special finite element with an elliptical hole for laminated structures, AIAA-94-1337-CP (1994) 253-263.
[3] E. Deletombe, D. Delsart, J. Fabis, B. Langrand, R. Ortiz, Recent developments in modelling and experimentation fields with respect to crashworthiness and impact of aerospace structures, ECCOMAS, 2004.; E. Deletombe, D. Delsart, J. Fabis, B. Langrand, R. Ortiz, Recent developments in modelling and experimentation fields with respect to crashworthiness and impact of aerospace structures, ECCOMAS, 2004.
[4] Dhanasekar, M.; Han, J.; Qin, Q.-H., A hybrid-Trefftz element containing an elliptic hole, Finite Elements in Anal. Design, 42, 1314-1323 (2006)
[5] Dinca, G., Sur la déformation plane du corps élastique parfait (utilisation des variables complexes), Rev. Roumaine Math. Pures Appl., X, 5, 645-651 (1965), (in French or Rumanian) · Zbl 0139.18803
[6] C.A. Felippa, Three-dimensional linear elastostatics, in: Advanced Finite Element Method, University of Colorado courses, Spring 2003 (Chapter 5).; C.A. Felippa, Three-dimensional linear elastostatics, in: Advanced Finite Element Method, University of Colorado courses, Spring 2003 (Chapter 5).
[7] T. Heubrandtner, G. Rangger, D. Scherjau, Advanced spotweld failure modelling based on Trefftz formulation, in: 4th LS-DYNA Anwenderforum, Bamberg, 2005.; T. Heubrandtner, G. Rangger, D. Scherjau, Advanced spotweld failure modelling based on Trefftz formulation, in: 4th LS-DYNA Anwenderforum, Bamberg, 2005.
[8] Kita, E.; Kamiya, N., Trefftz method: an overview, Adv. Engrg. Software, 24, 3-12 (1995) · Zbl 0984.65502
[9] Langrand, B.; Bayart, A.-S.; Chauveau, Y.; Deletombe, E., Assessment of multi-physics FE methods for bird impact modelling—application to a metallic riveted airframe, Internat. J. Crashworthiness, 7, 4, 415-428 (2002)
[10] B. Langrand, E. Deletombe, A model of structural embrittlement: from plastic location to failure—theoretical basis and experimental characterisation on perforated plates, in: Proceedings of the 12th International Symposium on Plasticity, Halifax, Nova Scotia, Canada, 2006.; B. Langrand, E. Deletombe, A model of structural embrittlement: from plastic location to failure—theoretical basis and experimental characterisation on perforated plates, in: Proceedings of the 12th International Symposium on Plasticity, Halifax, Nova Scotia, Canada, 2006.
[11] N. Leconte, Mixed and hybrid finite element formulations, ONERA Report No. RA 1/11377 DMSE, March 2006 (in French).; N. Leconte, Mixed and hybrid finite element formulations, ONERA Report No. RA 1/11377 DMSE, March 2006 (in French).
[12] N. Leconte. Hybrid-Trefftz finite elements featuring holes, ONERA Report No. RA 4/11377 DMSE, December 2006 (in French).; N. Leconte. Hybrid-Trefftz finite elements featuring holes, ONERA Report No. RA 4/11377 DMSE, December 2006 (in French).
[13] Muskelishvili, N. I., Some Basic Problems of the Mathematical Theory of Elasticity (1953), Noordhoff: Noordhoff Groningen, Holland
[14] R. Piltner, Spezielle finite elemente mit Lochern, Ecken und Rissen unter Verwendung von analytischen Teillosungen, Doctoral Thesis, Ruhr-Universitat Bochum, Fortschr.- Ber. VDI-Z. Reihe 1 Nr 96, VDI-Verlag, Dusseldorf, 1982 (in German).; R. Piltner, Spezielle finite elemente mit Lochern, Ecken und Rissen unter Verwendung von analytischen Teillosungen, Doctoral Thesis, Ruhr-Universitat Bochum, Fortschr.- Ber. VDI-Z. Reihe 1 Nr 96, VDI-Verlag, Dusseldorf, 1982 (in German). · Zbl 0555.73074
[15] Piltner, R., Special finite elements with holes and internal cracks, Internat. J. Numer. Methods Engrg., 21, 1471-1485 (1985) · Zbl 0572.73109
[16] R. Piltner, Comments on “A high precision element with a central circular hole” [Int. J. Solids Struct. 36 (1999) 5485-5497], Internat. J. Solids and Structures 38 (2001) 6265-6266.; R. Piltner, Comments on “A high precision element with a central circular hole” [Int. J. Solids Struct. 36 (1999) 5485-5497], Internat. J. Solids and Structures 38 (2001) 6265-6266. · Zbl 0929.74109
[17] R. Piltner, Comments on “Development of two-dimensional elements with a central circular hole”, A.K. Soh, Z.F. Long [Comput. Meth. Appl. Mech. Engrg. 188 (2000) 431-440], Comput. Methods Appl. Mech. Engrg. 191 (2001) 503-504.; R. Piltner, Comments on “Development of two-dimensional elements with a central circular hole”, A.K. Soh, Z.F. Long [Comput. Meth. Appl. Mech. Engrg. 188 (2000) 431-440], Comput. Methods Appl. Mech. Engrg. 191 (2001) 503-504. · Zbl 0963.74066
[18] R. Piltner, Mixed finite elements with voids and inclusions, in: 15th Engineering Mechanics Conference, New York, 2002.; R. Piltner, Mixed finite elements with voids and inclusions, in: 15th Engineering Mechanics Conference, New York, 2002.
[19] Tong, P.; Pian, T. H.H.; Lasry, S. J., A hybrid-element approach to crack problems in plane elasticity, Internat. J. Numer. Methods Engrg., 7, 297-308 (1973) · Zbl 0264.73113
[20] Qin, Q.-H., The Trefftz Finite and Boundary Element Method (2000), WIT Press: WIT Press Southampton
[21] Qin, Q.-H., Formulation of hybrid Trefftz finite element method for elastoplasticity, Appl. Math. Modelling, 29, 235-252 (2005) · Zbl 1081.74043
[22] Soh, A. K.; Long, Z. F., A high precision element with a central circular hole, Internat. J. Solids and Structures, 36, 5485-5497 (1999) · Zbl 0929.74109
[23] Soh, A. K.; Long, Z. F., Development of two-dimensional elements with a central circular hole, Comput. Methods Appl. Mech. Engrg., 188, 431-440 (2000) · Zbl 0963.74066
[24] A.K. Soh, Z.F. Long, Reply to comments on “A high precision element with a central circular hole” [Int. J. Solids Struct. 36 (1999) 5485-5497], Internat. J. Solids and Structures 38 (2001) 6267.; A.K. Soh, Z.F. Long, Reply to comments on “A high precision element with a central circular hole” [Int. J. Solids Struct. 36 (1999) 5485-5497], Internat. J. Solids and Structures 38 (2001) 6267. · Zbl 0929.74109
[25] A.K. Soh, Z.F. Long, Reply to Comments by R. Piltner on “Development of two-dimensional elements with a central circular hole”, [Comput. Methods Appl. Mech. Engrg. 188 (2000) 431-440], Comput. Methods Appl. Mech. Engrg. 191 (2001) 505-507.; A.K. Soh, Z.F. Long, Reply to Comments by R. Piltner on “Development of two-dimensional elements with a central circular hole”, [Comput. Methods Appl. Mech. Engrg. 188 (2000) 431-440], Comput. Methods Appl. Mech. Engrg. 191 (2001) 505-507. · Zbl 0963.74066
[26] Teixeira De Freitas, J. A.; Wang, Z. M., Hybrid-Trefftz stress elements for elastoplasticity, Internat. J. Numer. Methods Engrg., 43, 655-683 (1998) · Zbl 0951.74072
[27] E. Trefftz, Ein Gegenstuck zum Ritzschen Verfahren. 2. Internationale Kongress fur Technische Mechanik, Zurich, 1926, pp. 131-137 (in German).; E. Trefftz, Ein Gegenstuck zum Ritzschen Verfahren. 2. Internationale Kongress fur Technische Mechanik, Zurich, 1926, pp. 131-137 (in German).
[28] Wang, X.; Zhou, Y.; Zhou, W., A novel hybrid finite element with a hole for analysis of plane piezoelectric medium with defects, Internat. J. Solids and Structures, 41, 7111-7128 (2004) · Zbl 1181.74142
[29] Zienkiewicz, O. C.; Kelly, D. W.; Bettess, P., The coupling of the finite element method and boundary solution procedures, Internat. J. Numer. Methods Engrg., 11, 355-375 (1977) · Zbl 0347.65048
[30] O.C. Zienkiewicz, D.W. Kelly, P. Betess, Marriage a la mode: the best of both worlds (finite elements and boundary integrals), in: Proceedings of the International Symposium on Innovative Numerical Analysis in Applied Engineering Science, Versailles, May 1977, pp. 19-26.; O.C. Zienkiewicz, D.W. Kelly, P. Betess, Marriage a la mode: the best of both worlds (finite elements and boundary integrals), in: Proceedings of the International Symposium on Innovative Numerical Analysis in Applied Engineering Science, Versailles, May 1977, pp. 19-26.
[31] Zienkiewicz, O. C.; Taylor, R. L., The Finite Element Method (1989), McGraw-Hill: McGraw-Hill London · Zbl 0991.74002
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.