An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems

Nguyen, Bang Van; Tran, Han D.; Anitescu, Cosmin; Zhuang, Xiaoying; Rabczuk, Timon

doi:10.1016/j.cma.2016.04.002

Cited by 96 publications

(29 citation statements)

References 34 publications

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“…they do not necessarily lie on the surface they define. Equation (20) represents a single NURBS surface patch. A general NURBS surface can consist of a combination of several patches.…”

Section: Nurbs Bases and Surfacesmentioning

confidence: 99%

“…This paper therefore introduces a NURBS-based isogeometric implementation of an indirect variational boundary integral formulation. Aside from some preliminary studies applying the iBEM in IGA in two dimensions [19,20], most isogeometric BEM implementations so far have used a direct approach. To the authors' knowledge, this work is the first application 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 of an indirect boundary integral formulation within an isogeometric framework in three dimensions.…”

Section: Introductionmentioning

confidence: 99%

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An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

Coox

Atak

Vandepitte

et al. 2017

Computer Methods in Applied Mechanics and Engineering

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This work introduces an indirect Boundary Element Method (BEM) within a NURBSbased isogeometric framework for solving three-dimensional acoustic problems in the frequency domain. Developments of isogeometric boundary elements so far have focused on the direct BEM. Yet, a multitude of common problems in acoustics involves openboundary surfaces, which require a more involved, indirect, boundary element formulation. The current work presents an indirect variational BEM which makes use of NURBS shape functions. Additionally, a novel technique for coupling (strongly) non-conforming patches is introduced to allow the analysis of more complex geometries. The proposed isogeometric indirect boundary element method is verified against analytical solutions and benchmarked against the conventional polynomial-based indirect BEM. Also two open-boundary problems are studied, including analyses over wider frequency ranges, and one industrial-type, complex geometry containing multiple non-conforming patches. The proposed method is found to be not only significantly more efficient than its polynomialbased counterpart, but also very robust against strong non-conformities in the NURBS descriptions.

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“…they do not necessarily lie on the surface they define. Equation (20) represents a single NURBS surface patch. A general NURBS surface can consist of a combination of several patches.…”

Section: Nurbs Bases and Surfacesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

Coox

Atak

Vandepitte

et al. 2017

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

show abstract

“…The BEM formulation has been used also to construct parameterizations for computational domains of interest in the general Galerkin‐IgA context . Recently, the novel combination of the IgA paradigm with symmetric Galerkin BEM (IgA‐SGBEM) has revealed to be very effective among BEM schemes. Moreover, the full potential of B‐splines over the more common Lagrangian basis has been recently exploited in the work of Aimi et al…”

Section: Introductionmentioning

confidence: 99%

An adaptive IgA‐BEM with hierarchical B‐splines based on quasi‐interpolation quadrature schemes

Falini

Giannelli

Kanduč

et al. 2018

Numerical Meth Engineering

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Summary The isogeometric formulation of the boundary element method (IgA‐BEM) is investigated within the adaptivity framework. Suitable weighted quadrature rules to evaluate integrals appearing in the Galerkin BEM formulation of 2D Laplace model problems are introduced. The proposed quadrature schemes are based on a spline quasi‐interpolation (QI) operator and properly framed in the hierarchical setting. The local nature of the QI perfectly fits with hierarchical spline constructions and leads to an efficient and accurate numerical scheme. An automatic adaptive refinement strategy is driven by a residual‐based error estimator. Numerical examples show that the optimal convergence rate of the Galerkin solution is recovered by the proposed adaptive method.

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“…This method has been successfully applied for solving geotechnical and structural upper limit problems, showing its robustness and high efficiency. Compared with existed element‐based numerical methods such as previous studies, DLO is node based, taking a very wide search space into account since the introduced potential discontinuities are permitted to cross over one another but not only considered at the edges of elements. This property of DLO also simplifies its preprocessing and eliminates possible discretization bias in other methods.…”

Section: Introductionmentioning

confidence: 99%

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

Zhang

Zhuang

Lackner

2018

Num Anal Meth Geomechanics

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Summary For tunnel constructed by New Austrian Tunnelling Method, the crown is the upper part of tunnel section, constructed during excavation process and supported by shotcrete. The stability of the crown has great influence on the safety of tunnel itself and the buildings above, which correlates, among others, with geometrical setup of tunnel and material properties of shotcrete and soil/rock. In this paper, aiming at analyzing the stability of shotcrete supported crown, a recently presented numerical method discontinuity layout optimization is adopted, which introduces a great amount of potential discontinuities cross over one another and provides a wide search space for efficient upper limit analysis. In the analysis, a well‐established hydration model of cementitious material is implemented for accounting the hydration of shotcrete. Then assumptions based on convergence‐confinement method are used for accounting the 3‐dimensional effect in 2‐dimensional analysis, finally providing time‐space–dependent assessments of stability of shotcrete supported crown.

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An isogeometric symmetric Galerkin boundary element method for two-dimensional crack problems

Cited by 96 publications

References 34 publications

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

An isogeometric indirect boundary element method for solving acoustic problems in open-boundary domains

An adaptive IgA‐BEM with hierarchical B‐splines based on quasi‐interpolation quadrature schemes

Stability analysis of shotcrete supported crown of NATM tunnels with discontinuity layout optimization

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