zbMATH — the first resource for mathematics

A meshfree thin shell method for nonlinear dynamic fracture. (English) Zbl 1194.74537
Summary: A meshfree method for thin shells with finite strains and arbitrary evolving cracks is described. The $$C^{1}$$ displacement continuity requirement is met by the approximation, so no special treatments for fulfilling the Kirchhoff condition are necessary. Membrane locking is eliminated by the use of a cubic or quartic polynomial basis. The shell is tested for several elastic and elasto-plastic examples and shows good results. The shell is subsequently extended to modelling cracks. Since no discretization of the director field is needed, the incorporation of discontinuities is easy to implement and straightforward.

MSC:
 74S30 Other numerical methods in solid mechanics (MSC2010) 74K25 Shells
Full Text:
References:
 [1] Krysl, International Journal of Solids and Structures 33 pp 3057– (1996) [2] Noguchi, International Journal for Numerical Methods in Engineering 47 pp 1215– (2000) [3] Li, Computational Mechanics 25 pp 102– (2000) [4] Kim, International Journal for Numerical Methods in Engineering 53 pp 2087– (2002) [5] Garcia, International Journal for Numerical Methods in Engineering 47 pp 1381– (2000) [6] Wang, Computer Methods in Applied Mechanics and Engineering 193 pp 1065– (2004) [7] Kanok-Nukulchai, International Journal for Numerical Methods in Engineering 52 pp 705– (2001) [8] Rabczuk, International Journal for Numerical Methods in Engineering 61 pp 2316– (2004) [9] Belytschko, International Journal for Numerical Methods in Engineering 50 pp 993– (2001) [10] Moes, International Journal for Numerical Methods in Engineering 46 pp 133– (1999) [11] Ventura, International Journal for Numerical Methods in Engineering 54 pp 923– (2002) [12] , . Nonlinear Finite Elements for Continua and Structures. Wiley: Chichester, 2000. · Zbl 0959.74001 [13] Rabczuk, Computer Methods in Applied Mechanics and Engineering [14] Rabczuk, International Journal of Fracture 137 pp 19– (2006) [15] Rabczuk, International Journal for Numerical Methods in Engineering 69 pp 993– (2007) [16] Belytschko, International Journal for Numerical Methods in Engineering 37 pp 229– (1994) [17] Belytschko, International Journal of Solids and Structures 32 pp 2547– (1995) [18] , , . Meshfree methods. Encyclopedia of Computational Mechanics. Wiley: New York, 2004. [19] Areias, International Journal for Numerical Methods in Engineering 195 pp 5343– (2006) [20] Song, International Journal for Numerical Methods in Engineering 69 pp 868– (2006) [21] Simo, Computer Methods in Applied Mechanics and Engineering 73 pp 53– (1989) [22] Parish, International Journal for Numerical Methods in Engineering 31 pp 127– (1991) [23] Bucalem, International Journal for Numerical Methods in Engineering 36 pp 3729– (1993) [24] Hauptmann, International Journal for Numerical Methods in Engineering 42 pp 49– (1998) [25] Belytschko, Computer Methods in Applied Mechanics and Engineering 51 pp 221– (1985) [26] Areias, International Journal for Numerical Methods in Engineering 64 pp 1166– (2005) [27] Sze, International Journal for Numerical Methods in Engineering 53 pp 2617– (2002) [28] Areias, Finite Elements in Analysis and Design 39 pp 1191– (2003) [29] Weissmann, International Journal for Numerical Methods in Engineering 39 pp 2337– (1996) [30] Crisfield, Engineering Computations 13 pp 110– (1996) [31] Areias, International Journal for Numerical Methods in Engineering (2005) [32] Ibrahimbegović, International Journal for Numerical Methods in Engineering 52 pp 1235– (2001) [33] Eriksson, Computer Methods in Applied Mechanics and Engineering 191 pp 3775– (2002) [34] Peng, International Journal for Numerical Methods in Engineering 35 pp 1829– (1992) [35] Sansour, Computational Mechanics 21 pp 512– (1998) [36] Masud, Computational Mechanics 26 pp 1– (2000) [37] Campello, Computational Mechanics 31 pp 505– (2003) [38] Sansour, Computational Mechanics 24 pp 435– (2000) [39] Finite Element Technology, Damage Modeling, Contact Constraints and Fracture Analysis. bibmiscDoutoramento, FEUP–Faculdade de Engenharia da Universidade do Porto, Rua Dr. Roberto Frias s/n 4200-465 Porto, Portugal, 2003. www.fe.up.pt. [40] Eberlein, Computer Methods in Applied Mechanics and Engineering 171 pp 243– (1999) [41] Wagner, Computers and Structures 80 pp 857– (2002) [42] Muscat-Fenech, International Journal of Fracture 84 pp 297– (1997) [43] Keesecker, Computers and Structures 81 pp 1633– (2003) [44] Areias, International Journal for Numerical Methods in Engineering 63 pp 760– (2005) [45] Beschuss von fluessigkeitsgefuellten Behaeltern. Ph.D. Thesis, University of Karlsruhe, Institut fuer Massivbau und Baustofftechnologie, 2002. [46] . A constitutive model and data for metals subjected to large strains, high strain rates, and high temperatures. Proceedings of 7th International Symposium on Ballistics, France, 1983.
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.