Browse > Article
http://dx.doi.org/10.12989/sem.2016.59.5.901

Strategy for refinement of nodal densities and integration cells in EFG technique  

Patel, Bhavana S.S. (National Institute of Technology Karnataka)
Narayan, Babu K.S. (National Institute of Technology Karnataka)
Venkataramana, Katta (National Institute of Technology Karnataka)
Publication Information
Structural Engineering and Mechanics / v.59, no.5, 2016 , pp. 901-920 More about this Journal
Abstract
MeshFree methods have become popular owing to the ease with which high stress gradients can be identified and node density distribution can be reformulated to accomplish faster convergence. This paper presents a strategy for nodal density refinement with strain energy as basis in Element-Free Galerkin MeshFree technique. Two popular flat plate problems are considered for the demonstration of the proposed strategies. Issue of integration errors introduced during nodal density refinement have been addressed by suggesting integration cell refinement. High stress effects around two symmetrical semi-circular notches under in-plane axial load have been addressed in the first problem. The second considers crack propagation under mode I and mode II fracture loading by the way of introducing high stress intensity through line crack. The computational efficacy of the adaptive refinement strategies proposed has been highlighted.
Keywords
adaptive refinement; element-free Galerkin; crack propagation; stress intensity; stress concentration;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Amani, J., Saboor Bagherzadeh, A. and Rabczuk, T. (2014), "Error estimate and adaptive refinement in mixed discrete least squares meshless method", Math. Prob. Eng., Article ID 721240, 16
2 Belytschko, T., Lu, Y.Y. and Gu, L. (1995), "Crack propagation by element-free Galerkin methods", Eng. Fract. Mech., 51(2), 295-315.   DOI
3 Belytschko, T. and Black, T. (1999), "Elastic crack growth in finite elements with minimal remeshing", Int. J. Numer. Methd. Eng., 45(5), 601-620.   DOI
4 Bordas, S., Rabczuk, T. and Zi, G. (2008), "Three-dimensional crack initiation, propagation, branching and junction in non-linear materials by an extended meshfree method without asymptotic enrichment", Eng. Fract. Mech., 75(5), 943-960.   DOI
5 Bouchard, P.O., Bay, F. and Chastel, Y. (2003), "Numerical modelling of crack propagation: automatic remeshing and comparison of different criteria", Comp. Methd. Appl. Mech. Eng., 192(35), 3887-3908.   DOI
6 Chen, L., Zhang, G.Y., Zhang, J., Nguyen-Thoi, T. and Tang, Q. (2011), "An adaptive edge-based smoothed point interpolation method for mechanics problems", Int. J. Comput. Math., 88(11), 2379-2402.   DOI
7 Chow, W.T. and Atluri, S.N. (1995), "Finite element calculation of stress intensity factors for interfacial crack using virtual crack closure integral", Comput. Mech., 16(6), 417-425.   DOI
8 Dolbow, J., Moes, N. and Belytschko, T. (2000), "Discontinuous enrichment in finite elements with a partition of unity method", Finite Elem. Anal. Des., 36(3), 235-260.   DOI
9 Eigel, M., George, E. and Kirkilionis, M. (2010), "A mesh-free partition of unity method for diffusion equations on complex domains", IMA J. Numer. Anal., 30(3), 629-653.   DOI
10 Fleming, M., Chu, Y.A., Moran, B., Belytschko, T., Lu, Y.Y. and Gu, L. (1997), "Enriched element-free Galerkin methods for crack tip fields", Int. J. Numer. Meth. Eng., 40(8), 1483-1504   DOI
11 Giner, E., Sukumar, N., Tarancon, J.E. and Fuenmayor, F.J. (2009), "An Abaqus implementation of the extended finite element method", Eng. Fract. Mech., 76(3), 347-368.   DOI
12 Haussler-Combe, U. and Korn, C. (1998), "An adaptive approach with the element-free-Galerkin method", Comput. Meth. Appl. Mech. Eng., 162(1), 203-222.   DOI
13 Joldes, G.R., Wittek, A. and Miller, K. (2015), "Adaptive numerical integration in Element-Free Galerkin methods for elliptic boundary value problems", Eng. Anal. Bound. Elem., 51, 52-63.   DOI
14 Krysl, P. and Belytschko, T. (1999), "The Element Free Galerkin method for dynamic propagation of arbitrary 3D cracks", Int. J. Numer. Meth. Eng., 44(6), 767-800.   DOI
15 Liu, G.R. and Tu, Z.H. (2002), "An adaptive procedure based on background cells for meshless methods", Comput. Meth. Appl. Mech. Eng., 191(17), 1923-1943.   DOI
16 Liu, G.R. (2009), Meshfree methods: moving beyond the finite element method, Taylor & Francis.
17 Menouillard, T. and Belytschko, T. (2010), "Dynamic fracture with meshfree enriched XFEM", Aata Mechanica, 213(1-2), 53-69.   DOI
18 Mergheim, J., Kuhl, E. and Steinmann, P. (2005), "A finite element method for the computational modelling of cohesive cracks", Int. J. Numer. Meth. Eng., 63(2), 276-289.   DOI
19 Patricio, M. and Mattheij, R. (2007), Crack propagation analysis, CASA Report, 07-03
20 Pant, M., Singh, I.V. and Mishra, B.K. (2013), "A novel enrichment criterion for modeling kinked cracks using element free Galerkin method", Int. J. Mech. Sci., 68, 140-149.   DOI
21 Rabczuk, T., Bordas, S. and Zi, G. (2007), "A three-dimensional meshfree method for continuous ultiplecrack initiation, propagation and junction in statics and dynamics", Comput. Mech., 40(3), 473-495.   DOI
22 Rabczuk, T. and Zi, G. (2007), "A meshfree method based on the local partition of unity for cohesive cracks", Comput. Mech., 39(6), 743-760.   DOI
23 Sukumar, N. and Belytschko, T. (2000), "Arbitrary branched and intersecting cracks with the extended finite element method", Int. J. Numer. Meth. Eng., 48, 1741-1760.   DOI
24 Sukumar, N., Moes, N., Moran, B. and Belytschko, T. (2000), "Extended finite element method for three-dimensional crack modeling", Int. J. Numer. Meth. Eng., 48(11), 1549-1570.   DOI
25 Ullah, Z. and Augarde, C.E. (2013), "Finite deformation elasto-plastic modelling using an adaptive meshless method", Comput. Struct., 118, 39-52.   DOI
26 Wu, Y., Magallanes, J.M., Choi, H.J. and Crawford, J.E. (2012), "Evolutionarily coupled finite-element meshfree formulation for modeling concrete behaviors under blast and impact loadings", J. Eng. Mech., 139(4), 525-536.
27 Zi, G., Rabczuk, T. and Wall, W. (2007), "Extended meshfree methods without branch enrichment for cohesive cracks", Comput. Mech., 40(2), 367-382.   DOI