Hybrid collocation-Galerkin approach for the analysis of surface represented 3D-solids employing SB-FEM

Chen, L.; Dornisch, Wolfgang; Klinkel, Sven

doi:10.1016/j.cma.2015.07.004

Cited by 27 publications

(16 citation statements)

References 20 publications

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“…The error indicator of each element is computed using the L 2 error norm

{(‖‖, u - ū)}_{L_{2} ((), Ω_{e})}

, where u stands for the exact solution and

ū

denotes the approximate solution . The relative error ε e of each element, needed for marking elements for refinement, is computed as

ε_{e} = \frac{{(‖‖, u - ū)}_{L_{2} ((), Ω_{e})}}{\sqrt{((), \int_{Ω_{e}} u^{T} \cdot u d normalΩ)}} .

…”

Section: Numerical Examplesmentioning

confidence: 99%

Cohesive fracture analysis using Powell‐Sabin B‐splines

Chen

Borst

2018

Num Anal Meth Geomechanics

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Summary Powell‐Sabin B‐splines, which are based on triangles, are employed to model cohesive crack propagation without a predefined interface. The method removes limitations that adhere to isogeometric analysis regarding discrete crack analysis. Isogeometric analysis requires that the initial mesh be aligned a priori with the final crack path to a certain extent. These restrictions are partly related to the fact that in isogeometric analysis, the crack is introduced in the parameter domain by meshline insertions. Herein, the crack is introduced directly in the physical domain. Because of the use of triangles, remeshing and tracking the real crack path in the physical domain is relatively standard. The method can be implemented in existing finite element programmes in a straightforward manner through the use of Bézier extraction. The accuracy of the approach to model free crack propagation is demonstrated by several numerical examples, including discrete crack modelling in an L‐shaped beam and the Nooru‐Mohamed tension‐shear test.

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“…The error indicator of each element is computed using the L 2 error norm

{(‖‖, u - ū)}_{L_{2} ((), Ω_{e})}

, where u stands for the exact solution and

ū

denotes the approximate solution . The relative error ε e of each element, needed for marking elements for refinement, is computed as

ε_{e} = \frac{{(‖‖, u - ū)}_{L_{2} ((), Ω_{e})}}{\sqrt{((), \int_{Ω_{e}} u^{T} \cdot u d normalΩ)}} .

…”

Section: Numerical Examplesmentioning

confidence: 99%

Cohesive fracture analysis using Powell‐Sabin B‐splines

Chen

Borst

2018

Num Anal Meth Geomechanics

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“…The SBFEM also excels in modelling unbounded domain problems [40,41]. 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].…”

mentioning

confidence: 99%

Automatic image‐based stress analysis by the scaled boundary finite element method

Saputra

Talebi

Tran

et al. 2016

Int. J. Numer. Meth. Engng

126

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SUMMARYDigital imaging technologies such as X-ray scans and ultrasound provide a convenient and non-invasive way to capture high-resolution images. The colour intensity of digital images provides information on the geometrical features and material distribution which can be utilised for stress analysis. The proposed approach employs an automatic and robust algorithm to generate quadtree (2D) or octree (3D) meshes from digital images. The use of polygonal elements (2D) or polyhedral elements (3D) constructed by the scaled boundary finite element method avoids the issue of hanging nodes (mesh incompatibility) commonly encountered by finite elements on quadtree or octree meshes. The computational effort is reduced by considering the small number of cell patterns occurring in a quadtree or an octree mesh. Examples with analytical solutions in 2D and 3D are provided to show the validity of the approach. Other examples including the analysis of 2D and 3D microstructures of concrete specimens as well as of a domain containing multiple spherical holes are presented to demonstrate the versatility and the simplicity of the proposed technique.

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“…Due to this property, higher‐order or lower‐order continuity can be achieved. This can be used to solve higher‐order differential equations, but also to insert a discontinuity Γ c ( ξ 1 , ξ 2 ) in the model …”

Section: Discrete Crack Representation In Igamentioning

confidence: 99%

Discrete fracture analysis using locally refined T‐splines

Chen

Verhoosel

Borst

2018

Numerical Meth Engineering

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Summary Locally refined T‐splines are used to model discrete crack propagation without a predefined interface. The crack is introduced by meshline insertions in the locally refined T‐mesh, which yields discontinuous basis functions. To implement the method in existing finite element programs, Bézier extraction is used. A detailed description is given as to how the crack path is inserted and how the domain is reparameterized after insertion. The versatility and accuracy of the approach to model discrete crack propagation without the crack path being predefined is demonstrated by two examples, namely, an L‐shaped beam and a single‐edge notched beam. When the crack approaches the physical boundaries, limitations to reparameterization arise, as will be discussed at the hand of a double‐edge notched specimen.

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Hybrid collocation-Galerkin approach for the analysis of surface represented 3D-solids employing SB-FEM

Cited by 27 publications

References 20 publications

Cohesive fracture analysis using Powell‐Sabin B‐splines

Cohesive fracture analysis using Powell‐Sabin B‐splines

Automatic image‐based stress analysis by the scaled boundary finite element method

Discrete fracture analysis using locally refined T‐splines

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