P.H. Wen¹, M.H. Aliabadi²

Structural Durability & Health Monitoring, Vol.8, No.3, pp. 223-248, 2012, DOI:10.32604/sdhm.2012.008.223

Abstract A mesh-free method for modelling crack growth in functionally graded materials is presented. Based on the variational principle of the potential energy, mesh-free method has been implemented with enriched radial bases interpolation functions to evaluate mixed-mode stress intensity factors, which are introduced to capture the singularity of stress at the crack tip. Paris law and the maximum principle stress criterion are adopted for defining the growth rate and direction of the fatigue crack growth respectively. The accuracy of the proposed method is assessed by comparison to other available solutions. More >

P.H. Wen¹, M.H. Aliabadi²

Structural Durability & Health Monitoring, Vol.3, No.2, pp. 107-120, 2007, DOI:10.3970/sdhm.2007.003.107

Abstract In the last decade, meshless methods for solving differential equations have become a promising alternative to the finite element and boundary element methods. Based on the variation of potential energy, the element-free Galerkin method is developed on the basis of finite element method by the use of radial basis function interpolation. An enriched radial basis function is formulated to capture the stress singularity at the crack tip. The usual advantages of finite element method are retained in this method but now significant improvement of accuracy. Neither the connectivity of mesh in the domain by the finite element method or integrations… More >

Wen-Hwa Chen¹, Cheng-Hung Chen²

CMES-Computer Modeling in Engineering & Sciences, Vol.8, No.3, pp. 177-190, 2005, DOI:10.3970/cmes.2005.008.177

Abstract An enriched meshless method, using meshless interpolations and a global Galerkin approach, is developed for the analysis of three-dimensional fracture problems. The displacement field which accounts for the stress singularity nearby the crack front and the boundary layer effect at the intersection between the crack front and the free surface of the structure is adopted to enrich the trial functions. The three-dimensional stress intensity factors can thus be treated as independent unknown parameters and calculated with the nodal displacements directly. To estimate the accuracy of the method developed, several representative three-dimensional cracks are analyzed. These include single-edge crack, embedded elliptical… More >

Xue-cong Liu¹, Qing Zhang^1,2, Xiao-zhou Xia¹

CMES-Computer Modeling in Engineering & Sciences, Vol.113, No.4, pp. 411-427, 2017, DOI:10.3970/cmes.2017.113.411

Abstract The manuscript titled “The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM,” has been retracted from the Computer Modeling in Engineering & Sciences (CMES), vol. 113, no. 4. Retraction of this article is made upon the request of the authors, Xue-cong Liu, Qing Zhang, and Xiao-zhou Xia. The authors submitted their manuscript on October 7, 2017, and the authors later made a separate request to withdraw their submission when it was still being reviewed. Due to the glitches of the old submission system and failed communications between the managing editor and the corresponding author, the withdraw… More >

R.D. Phillips¹, M.S. Hossain¹, L.T. Watson^1,2, R.H. Wynne³, Naren Ramakrishnan¹

CMES-Computer Modeling in Engineering & Sciences, Vol.97, No.2, pp. 175-197, 2014, DOI:10.3970/cmes.2014.097.175

Abstract Clusters, typically mined by modeling locality of attribute spaces, are often evaluated for their ability to demonstrate ‘enrichment’ of categorical features. A cluster enrichment procedure evaluates the membership of a cluster for significant representation in predefined categories of interest. While classical enrichment procedures assume a hard clustering definition, this paper introduces a new statistical test that computes enrichments for soft clusters. Application of the new test to several scientific datasets is given. More >

Y. Miao¹, T.G. HE¹, H. Luo^1,2, H.P. Zhu¹

CMES-Computer Modeling in Engineering & Sciences, Vol.85, No.6, pp. 481-498, 2012, DOI:10.3970/cmes.2012.085.481

Abstract Combined the hybrid boundary node method (Hybrid BNM) and the dual reciprocity principle, a truly boundary-type meshless method, namely, dual hybrid boundary node method (Dual Hybrid BNM) is presented for solving transient dynamic fracture problems. The enriched basis functions in moving least squares (MLS) approximation is presented for simulating the singularity of the stress field on the tip of the fracture. The solution in Dual Hybrid BNM is divided into particular solution and complementary solution. The complementary solution is solved by means of Hybrid BNM, and the particular solution is approximated by using radial basis functions (RBF). The inner nodes… More >

M. Ferronato¹, A. Mazzia¹, G. Pini¹

CMES-Computer Modeling in Engineering & Sciences, Vol.62, No.2, pp. 205-224, 2010, DOI:10.3970/cmes.2010.062.205

Abstract In the engineering practice meshing and re-meshing complex domains by Finite Elements (FE) is one of the most time-consuming efforts. Meshless methods avoid this task but are computationally more expensive than standard FE. A somewhat natural improvement can be attempted by combining the two techniques with the aim at emphasizing the respective merits. The present work describes a FE enrichment by the Meshless Local Petrov-Galerkin (MLPG) method. The basic idea is to add a limited number of moving MLPG points over a fixed coarse FE grid, in order to improve the solution accuracy in specific regions of the domain with… More >

W. Attaporn¹, H. Koguchi²

CMES-Computer Modeling in Engineering & Sciences, Vol.39, No.3, pp. 237-262, 2009, DOI:10.3970/cmes.2009.039.237

Abstract In the present study, a stress singularity field along free edges meeting at a corner in a three-dimensional joint structure is investigated. The order of stress singularity is determined using an eigen analysis based on a finite element method. Intensities of stress singularity not only at the corner but also along the free edge of interface are determined directly without any post-processing by a new FEM formulation referred to as a three-dimensional enriched FEM. Result in the present analysis is also compared with that in another numerical method. It was slightly larger than the intensity of stress singularity, which was… More >

Y.Y Zhang, L. Chen

CMES-Computer Modeling in Engineering & Sciences, Vol.31, No.3, pp. 189-200, 2008, DOI:10.3970/cmes.2008.031.189

Abstract A simplified meshless method for dynamic crack growth is presented. The method uses an extrinsic enrichment based on a local partition of unity concept. The crack is represented by a set of crack segments. The crack segments are required to pass through the entire domain of influence of node. They are introduced when the maximum principal stress exceeds the uniaxial tensile strength. The crack segments are allowed to rotate in order to avoid too stiff system responses. The major advantage of our method is that it does not require algorithms to track the crack path. More >

P.H. Wen¹, M.H. Aliabadi², Y.W. Liu³

CMES-Computer Modeling in Engineering & Sciences, Vol.30, No.3, pp. 133-148, 2008, DOI:10.3970/cmes.2008.030.133

Abstract Based on the variation of potential energy, the element-free Galerkin method (MFGM) has been investigated for structures with crack on the basis of radial base function interpolation. An enriched radial base function is introduced to capture the singularities of stress at the crack tips. The advantages of the finite element method are remained in this method and there is a significant improvement of accuracy, particularly for the crack problems of fracture mechanics. The applications of the element-free Galerkin method with enriched radial base function to two-dimensional fracture mechanics in functionally graded materials have been presented and comparisons have been made… More >