Lixiang Wang¹, Longfei Wen^2,3, Rong Tian^2,3,*, Chun Feng^1,4,*

The International Conference on Computational & Experimental Engineering and Sciences, Vol.30, No.3, pp. 1-2, 2024, DOI:10.32604/icces.2024.011137

Abstract The extended finite element method (XFEM) has been successful in crack analysis but faces challenges in modeling multiple cracks. One challenge is the linear dependence and ill-conditioning of the global stiffness matrix, while another is the geometric description for multiple cracks. To address the first challenge, the Improved XFEM (IXFEM) [1–9] is extended to handle multiple crack problems, effectively eliminating issues of linear dependence and ill-conditioning. Additionally, to overcome the second challenge, a novel level set templated cover cutting method (LSTCCM) [10] is proposed, which combines the advantages of the level set method and cover More >

N. Vu-Bac¹, H. Nguyen-Xuan², L. Chen³, S. Bordas⁴, P. Kerfriden⁴, R.N. Simpson⁴, G.R. Liu⁵, T. Rabczuk¹

CMES-Computer Modeling in Engineering & Sciences, Vol.73, No.4, pp. 331-356, 2011, DOI:10.3970/cmes.2011.073.331

Abstract This paper aims to incorporate the node-based smoothed finite element method (NS-FEM) into the extended finite element method (XFEM) to form a novel numerical method (NS-XFEM) for analyzing fracture problems of 2D elasticity. NS-FEM uses the strain smoothing technique over the smoothing domains associated with nodes to compute the system stiffness matrix, which leads to the line integrations using directly the shape function values along the boundaries of the smoothing domains. As a result, we avoid integration of the stress singularity at the crack tip. It is not necessary to divide elements cut by cracks More >