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  • Open Access


    Fracture & Fatigue Analyses: SGBEM-FEM or XFEM? Part 1: 2D Structures

    Leiting Dong1,2, Satya N. Atluri1,3

    CMES-Computer Modeling in Engineering & Sciences, Vol.90, No.2, pp. 91-146, 2013, DOI:10.3970/cmes.2013.090.091

    Abstract In this paper, and its companion Part 2 [Dong and Atluri (2013b)], the Symmetric Galerkin Boundary Element Method (SGBEM), and the SGBEM-FEM alternating/coupling methods, are compared with the recently popularized Extended Finite Element Method (XFEM), for analyzing fracture and fatigue crack propagation in complex structural geometries. The historical development, and the theoretical/algorithmic formulations, of each method are succinctly reviewed. The advantages and disadvantages of each method are critically discussed. A comprehensive evaluation of the performances of the SGBEM-based methods, and their comparison with XFEM, in modeling cracked solid structures undergoing fatigue crack-growth is carried out.… More >

  • Open Access


    A Node-Based Smoothed eXtended Finite Element Method (NS-XFEM) for Fracture Analysis

    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 >

  • Open Access


    The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

    Xue-cong Liu1, Qing Zhang1,*, Xiao-zhou Xia1

    CMC-Computers, Materials & Continua, Vol.53, No.3, pp. 187-206, 2017, DOI:10.3970/cmc.2017.053.203

    Abstract This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method (XFEM). A new enrichment scheme of crack tip is proposed within the framework of XFEM. Then the governing equations are derived and evolved into the discretized form. For dynamic problem, the lumped mass and the explicit time algorithm are applied. With different grid densities and different forms of Newmark scheme, the Dynamic Stress Intensity Factor (DSIF) is computed by using interaction integral approach to reflect the dynamic response. The effectiveness of the More >

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