2015
DOI: 10.1016/j.engfracmech.2015.06.083
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Adaptation of quadtree meshes in the scaled boundary finite element method for crack propagation modelling

Abstract: A crack propagation modelling technique combining the scaled boundary finite element method and quadtree meshes is developed. This technique automatically satisfies the compatibility requirement between adjacent quadtree cells irrespective of the presence of hanging nodes. The quadtree structure facilitates efficient data storage and rapid computations. Only a single cell is required to accurately model the stress field near crack tips. Crack growth is modelled by splitting the cells in the mesh into two. The … Show more

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Cited by 121 publications
(57 citation statements)
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“…It has also been extended to analyse fracture problems [42][43][44][45] including crack propagation [46][47][48][49], electromagnetics [50], sloshing analysis [51] and to perform isogeometric analysis [52,53]. Recently, polygonal elements developed using the SBFEM have also been applied successfully in the analysis of fracture problems of functionally graded materials [54], elasto-plastic problems [55] and crack propagation using quadtree meshes [56]. It has been demonstrated in these works that the high flexibility of the shape of the polygonal elements significantly simplifies the meshing process.…”
mentioning
confidence: 99%
“…It has also been extended to analyse fracture problems [42][43][44][45] including crack propagation [46][47][48][49], electromagnetics [50], sloshing analysis [51] and to perform isogeometric analysis [52,53]. Recently, polygonal elements developed using the SBFEM have also been applied successfully in the analysis of fracture problems of functionally graded materials [54], elasto-plastic problems [55] and crack propagation using quadtree meshes [56]. It has been demonstrated in these works that the high flexibility of the shape of the polygonal elements significantly simplifies the meshing process.…”
mentioning
confidence: 99%
“…Recently, with the introduction of scaled boundary shape functions, the application of the SBFEM has expanded to include more complex fields in engineering such as heterogeneous media, elastoplasticity, and geometric and material nonlinearity . The flexibility of the SBFEM allows seamless implementation with quadtree‐ and octree‐meshes,() leading to full automation of the engineering analysis with minimal human interaction. In this paper, the application of the SBFEM will be further extended for coupled‐field problems in engineering.…”
Section: Scaled Boundary Femmentioning
confidence: 99%
“…Previous applications of quadtree meshes in the context of the SBFEM focused on examples containing very few (if not one) materials and mainly discussed static analysis or, for instance, crack propagation . For these cases, the same element order has been used for all subdomains, thus leading to strongly varying numbers of nodes per length.…”
Section: Application To Quadtree Meshesmentioning
confidence: 99%
“…For wave propagation problems, we will set the size h min of the smallest subdomain to h min 6 min 4 (32) where min denotes the smallest wavelength that may occur in the model. Previous applications of quadtree meshes in the context of the SBFEM focused on examples containing very few (if not one) materials [20,44] and mainly discussed static analysis or, for instance, crack propagation [45]. For these cases, the same element order has been used for all subdomains, thus leading to strongly varying numbers of nodes per length.…”
Section: Application To Quadtree Meshesmentioning
confidence: 99%