A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis
作者： N Vu-Bac , HB Nguyen-Xuan , L Chen , Stephane Bordas , Pierre Kerfriden
DOI: 10.3970/CMES.2011.073.331
关键词:
摘要: This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into extended (XFEM) form a novel numerical (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses strain smoothing technique over domains associated with nodes compute system stiffness matrix, which leads line integrations using directly shape function values along boundaries domains. As result, we avoid integration stress singularity at crack tip. It is not necessary divide elements cut by cracks when replace interior boundary integration, simplifying discontinuous approximation. The key advantage NS-XFEM that it provides more accurate solutions compared XFEM-T3 element. We will show two examples significantly improves results in energy norm and intensity factors. For studied, obtain super-convergent
elsevier.com
techscience.com
researchgate.net 参考文章(33)
Timon Rabczuk, Pedro Areias, A Meshfree Thin Shell for Arbitrary Evolving Cracks Based on An Extrinsic Basis Cmes-computer Modeling in Engineering & Sciences. ,vol. 16, pp. 115- 130 ,(2006) , 10.3970/CMES.2006.016.115
G.R. Liu, T. Nguyen-Thoi, K.Y. Lam, An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids Journal of Sound and Vibration. ,vol. 320, pp. 1100- 1130 ,(2009) , 10.1016/J.JSV.2008.08.027
T. Rabczuk, J. Eibl, Modelling dynamic failure of concrete with meshfree methods International Journal of Impact Engineering. ,vol. 32, pp. 1878- 1897 ,(2006) , 10.1016/J.IJIMPENG.2005.02.008
F.Z. Li, C.F. Shih, A. Needleman, A COMPARISON OF METHODS FOR CALCULATING ENERGY RELEASE RATES Engineering Fracture Mechanics. ,vol. 21, pp. 405- 421 ,(1985) , 10.1016/0013-7944(85)90029-3
Hung Nguyen-Xuan, Timon Rabczuk, Stéphane Bordas, Jean-François Debongnie, None, A smoothed finite element method for plate analysis Computer Methods in Applied Mechanics and Engineering. ,vol. 197, pp. 1184- 1203 ,(2008) , 10.1016/J.CMA.2007.10.008
Timon Rabczuk, Goangseup Zi, A meshfree method based on the local partition of unity for cohesive cracks Computational Mechanics. ,vol. 39, pp. 743- 760 ,(2007) , 10.1007/S00466-006-0067-4
Nhon Nguyen-Thanh, Timon Rabczuk, Hung Nguyen-Xuan, Stéphane PA Bordas, None, An alternative alpha finite element method (AαFEM) for free and forced structural vibration using triangular meshes Journal of Computational and Applied Mathematics. ,vol. 233, pp. 2112- 2135 ,(2010) , 10.1016/J.CAM.2009.08.117
T. Nguyen-Thoi, G. R. Liu, K. Y. Lam, G. Y. Zhang, A face‐based smoothed finite element method (FS‐FEM) for 3D linear and geometrically non‐linear solid mechanics problems using 4‐node tetrahedral elements International Journal for Numerical Methods in Engineering. ,vol. 78, pp. 324- 353 ,(2009) , 10.1002/NME.2491
T. Nguyen-Thoi, H.C. Vu-Do, T. Rabczuk, H. Nguyen-Xuan, A node-based smoothed finite element method (NS-FEM) for upper bound solution to visco-elastoplastic analyses of solids using triangular and tetrahedral meshes Computer Methods in Applied Mechanics and Engineering. ,vol. 199, pp. 3005- 3027 ,(2010) , 10.1016/J.CMA.2010.06.017
B. Moran, C.F. Shih, Crack tip and associated domain integrals from momentum and energy balance Engineering Fracture Mechanics. ,vol. 27, pp. 615- 642 ,(1987) , 10.1016/0013-7944(87)90155-X