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Hybrid displacement FE formulations including a hole

  • Leconte, Nicolas (Department of Aeroelasticity and Structural Dynamics, The French Aerospace Lab (ONERA)) ;
  • Langrand, Bertrand (Department of Aeroelasticity and Structural Dynamics, The French Aerospace Lab (ONERA)) ;
  • Markiewicz, Eric (Laboratory of Industrial and Human Automation Control, Mechanical Engineering and Computer Science (LAMIH UMR CNRS 8530), University of Valenciennes)
  • Received : 2008.08.26
  • Accepted : 2008.11.07
  • Published : 2009.03.10

Abstract

The paper deals with the problem related to the modelling of riveted assemblies for crashworthiness analysis of full-scale complete aircraft structures. Comparisons between experiments and standard FE computations on high-energy accidental situations onto aluminium riveted panels show that macroscopic plastic strains are not sufficiently localised in the FE shells connected to rivet elements. The main reason is related to the structural embrittlement caused by holes, which are currently not modelled. Consequently, standard displacement FE models do not succeed in initialising and propagating the rupture in sheet metal plates and along rivet rows as observed in the experiments. However, the literature survey show that it is possible to formulate super-elements featuring defects that both give accurate singular strain fields and are compatible with standard displacement finite elements. These super-elements can be related to the displacement model of the hybrid-Trefftz principle of the finite element method, which is a kind of domain decomposition method. A feature of hybrid-Trefftz finite elements is that they are mainly used for elastic computations. It is thus proposed to investigate the possibility of formulating a hybrid displacement finite element, including the effects of a hole, dedicated to crashworthiness analysis of full-scale aeronautic structures.

Keywords

References

  1. Chen, H.C. (1994), "A special finite element with an elliptical hole for laminated structures", AIAA-94-1337-CP, 253-263
  2. Darilmaz, K. and Kumbasar, N. (2006), "An 8-node assumed stress hybrid element for analysis of shells", Comput. Struct., 84, 1990-2000 https://doi.org/10.1016/j.compstruc.2006.08.003
  3. Dhanasekar, M., Han, J. and Qin, Q.H. (2006), “A hybrid-Trefftz element containing an elliptic hole”, Finite Elem. Anal. Des., 42, 1314-1323 https://doi.org/10.1016/j.finel.2006.06.008
  4. Felippa, C.A. (2006), Advanced Finite Element Method, University of Colorado Courses. http://www.colorado. edu/engineering/CAS/courses.d/AFEM.d/
  5. Freitas, J.A.T. (1999), "Hybrid finite element formulations for elastodynamic analysis in the frequency domain", Int. J. Solids Struct., 36, 1883-1923 https://doi.org/10.1016/S0020-7683(98)00064-X
  6. Grimaldi, R., Addessi, D. and Ciampi, V. (2004), "Mixed finite elements for non-linear material problems", Proceedings of ECCOMAS 2004, Jyväskylä, Finland
  7. Horrigmoe, G. and Bergan, P.G. (1976), "Incremental variational principles and finite element models for nonlinear problems", Comput. Meth. Appl. Mech. Eng., 7, 201-217 https://doi.org/10.1016/0045-7825(76)90013-X
  8. Kita, E. and Kamiya, N. (1995), "Trefftz method: An overview", Adv. Eng.Software, 24, 3-12 https://doi.org/10.1016/0965-9978(95)00067-4
  9. Langrand, B., Bayart, A.-S., Chauveau, Y. and Deletombe, E.(2002), “Assessment of multi-physics FE methods for bird impact modelling – Application to a metallic riveted airframe”, Int. J. Crashworthines, 7, 415-428
  10. Leconte, N. (2006), "Hybrid-Trefftz finite elements featuring holes", ONERA report n° RA 4/11377 DMSE (inFrench)
  11. Leconte, N. and Di Paola, F. (2007), "Establishment and analyse of perforated plate analytical solutions", ONERA report n° RA 5/12514 DMSE (in French)
  12. Leconte, N., Langrand, B. and Markiewicz, E. (2008a), "Toward a Hybrid-Trefftz element with a hole for elastoplasticity?",J. Comput. Appl. Math., 218, 88-95 https://doi.org/10.1016/j.cam.2007.04.034
  13. Leconte, N., Langrand, B. and Markiewicz, E. (2008b), "On some features of a plate hybrid-Trefftz displacement element containing a hole", Finite Elements in Analysis and Design, in press, submitted paper
  14. Liu, M.L. and To, C.W.S. (1995), "Hybrid strain based three node flat triangular shell elements – I Nonlinear theory and incremental formulation", Comput. Struct., 54, 1031-1056 https://doi.org/10.1016/0045-7949(94)00395-J
  15. Muskhelishvili, N.I. (1953), Some Basic Problems of the Mathematical Theory of Elasticity, Noordhoff,Groningen, Holland
  16. Piltner, R. (1985), "Special finite elements with holes and internal cracks", Int. J. Numer. Meth. Engng., 21,1471-1485 https://doi.org/10.1002/nme.1620210809
  17. Trefftz, E. (1926), "Ein Gegenstuck zum Ritzschen Verfahren", 2nd. Int. Kongr. Fur Tech. Mech., Zurich, (inGerman)

Cited by

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  2. On some features of a plate hybrid-Trefftz displacement element containing a hole vol.46, pp.10, 2010, https://doi.org/10.1016/j.finel.2010.05.001
  3. Comparative study of the resistance of bonded, riveted and hybrid assemblies; Experimental and numerical analyses vol.70, pp.4, 2009, https://doi.org/10.12989/sem.2019.70.4.467