Comparison of the basic and the discontinuity formulation of the 3D-dual boundary element method

Partheymüller, P.; Haas, Mark; Kühn, G.

doi:10.1016/s0955-7997(00)00060-6

Cited by 28 publications

(23 citation statements)

References 17 publications

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“…The side view in Figure 30 is similar to the two-dimensional propagation of the pair of cracks in Section 5.5 of Reference [29]. Our result is in agreement with the result of References [54,55] obtained by the boundary element method with different dimensions.…”

Section: A Pair Of Penny-shaped Cracks Under Tensionsupporting

confidence: 88%

A meshless method with enriched weight functions for three‐dimensional crack propagation

Duflot

2005

Numerical Meth Engineering

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SUMMARYThe propagation of cracks in three dimensions is analysed by a meshless method. The cracks are modelled by a set of triangles that are added when the propagation occurs. Since the method is meshless, no remeshing of the domain is necessary during the propagation. To avoid using a large number of degrees of freedom, the stress singularity along the front of the cracks is taken into account by an enrichment of the shape functions of the meshless method by means of appropriate weight functions. This enrichment technique is an extension of the technique that proved to be successful in two dimensions in a previous paper. Several algorithms for efficiently implementing the meshless method in three dimensions are detailed. The accuracy of the enrichment is first assessed on simple examples and some results of non-planar propagation of multiple cracks are then presented.

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Section: A Pair Of Penny-shaped Cracks Under Tensionsupporting

confidence: 88%

A meshless method with enriched weight functions for three‐dimensional crack propagation

Duflot

2005

Numerical Meth Engineering

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“…in such a case, even a single traction BIE can be used for fracture problems [26]. DDM was later proved to be a special case of DBEM by Partheymüller et al [27], who also extended the application of DDM from symmetric loaded cracks to asymmetric loaded cracks. However the displacement eld on the crack surface is indirect since only displacement discontinuity is obtained.…”

Section: Discontinuitiesmentioning

confidence: 99%

Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

et al. 2016

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We propose a method for simulating linear elastic crack growth through an isogeometric boundary element method directly from a CAD model and without any mesh generation. To capture the stress singularity around the crack tip, two methods are compared: (1) a graded knot insertion near crack tip; (2) partition of unity enrichment. A well-established CAD algorithm is adopted to generate smooth crack surfaces as the crack grows. The M integral and J k integral methods are used for the extraction of stress intensity factors (SIFs). The obtained SIFs and crack paths are compared with other numerical methods.

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“…For the integration procedure of the hypersingular traction BIE C 0,α continuity for the tractions, C 1,α continuity for the displacements and a smooth boundary are assumed. Meeting these continuity requirements, the crack surfaces are discretized with discontinuous elements [1,18]. Continuous elements are used on the surface n .…”

Section: The 3d Dual Discontinuity Methodsmentioning

confidence: 99%

“…The corresponding tractions are defined by the product of the stress tensor σ ji (x) and the outward-looking normal vector n i (x), which is known as the Cauchy formula The linear elastic BVP of cracked specimens as described in Sect. 2.1 is solved by a special formulation of the BEM -the 3D dual discontinuity method (DDM) [18]. Modeling the crack, the DDM exploits the technique of dual integral formulations, cf.…”

Section: Statement Of the Bvpmentioning

confidence: 99%

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The advanced simulation of fatigue crack growth in complex 3D structures

Kolk¹,

Kühn²

2006

Arch Appl Mech

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An advanced incremental crack growth algorithm for the three-dimensional (3D) simulation of fatigue crack growth in complex 3D structures with linear elastic material behavior is presented. To perform the crack growth simulation as effectively as possible an accurate stress analysis is done by the boundaryelement method (BEM) in terms of the 3D dual BEM. The question concerning a reliable 3D crack growth criterion is answered based on experimental observations. All criteria under consideration are numerically realized by a predictor-corrector procedure. The agreement between numerically determined and experimentally observed crack fronts will be shown on both fracture specimens and an industrial application.

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Comparison of the basic and the discontinuity formulation of the 3D-dual boundary element method

Cited by 28 publications

References 17 publications

A meshless method with enriched weight functions for three‐dimensional crack propagation

A meshless method with enriched weight functions for three‐dimensional crack propagation

Linear elastic fracture simulation directly from CAD: 2D NURBS-based implementation and role of tip enrichment

The advanced simulation of fatigue crack growth in complex 3D structures

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