Stable isogeometric analysis of trimmed geometries

Benjamin Marussig, Jürgen Zechner, Gernot Beer, Thomas Peter Fries

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.

Originalspracheenglisch
Seiten (von - bis)497-521
FachzeitschriftComputer Methods in Applied Mechanics and Engineering
Jahrgang316
DOIs
PublikationsstatusVeröffentlicht - 2017

Fingerprint

splines
Splines
Geometry
geometry
Stabilization
stabilization
collocation
interpolation
Elasticity
Interpolation
Substitution reactions
elastic properties
substitutes
formulations
matrices

Schlagwörter

    ASJC Scopus subject areas

    • !!Computational Mechanics
    • !!Mechanics of Materials
    • !!Mechanical Engineering
    • !!Physics and Astronomy(all)
    • !!Computer Science Applications

    Dies zitieren

    Stable isogeometric analysis of trimmed geometries. / Marussig, Benjamin; Zechner, Jürgen; Beer, Gernot; Fries, Thomas Peter.

    in: Computer Methods in Applied Mechanics and Engineering, Jahrgang 316, 2017, S. 497-521.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    @article{b373e3a5e8f142ca9728b93718bdf7bb,
    title = "Stable isogeometric analysis of trimmed geometries",
    abstract = "We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.",
    keywords = "Extended B-splines, Isogeometric analysis, Non-uniform, Stabilization, Trimmed NURBS, WEB-splines",
    author = "Benjamin Marussig and J{\"u}rgen Zechner and Gernot Beer and Fries, {Thomas Peter}",
    year = "2017",
    doi = "10.1016/j.cma.2016.07.040",
    language = "English",
    volume = "316",
    pages = "497--521",
    journal = "Computer Methods in Applied Mechanics and Engineering",
    issn = "0045-7825",
    publisher = "Elsevier B.V.",

    }

    TY - JOUR

    T1 - Stable isogeometric analysis of trimmed geometries

    AU - Marussig, Benjamin

    AU - Zechner, Jürgen

    AU - Beer, Gernot

    AU - Fries, Thomas Peter

    PY - 2017

    Y1 - 2017

    N2 - We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.

    AB - We explore extended B-splines as a stable basis for isogeometric analysis with trimmed parameter spaces. The stabilization is accomplished by an appropriate substitution of B-splines that may lead to ill-conditioned system matrices. The construction for non-uniform knot vectors is presented. The properties of extended B-splines are examined in the context of interpolation, potential, and linear elasticity problems and excellent results are attained. The analysis is performed by an isogeometric boundary element formulation using collocation. It is argued that extended B-splines provide a flexible and simple stabilization scheme which ideally suits the isogeometric paradigm.

    KW - Extended B-splines

    KW - Isogeometric analysis

    KW - Non-uniform

    KW - Stabilization

    KW - Trimmed NURBS

    KW - WEB-splines

    UR - http://www.scopus.com/inward/record.url?scp=84994086546&partnerID=8YFLogxK

    U2 - 10.1016/j.cma.2016.07.040

    DO - 10.1016/j.cma.2016.07.040

    M3 - Article

    VL - 316

    SP - 497

    EP - 521

    JO - Computer Methods in Applied Mechanics and Engineering

    JF - Computer Methods in Applied Mechanics and Engineering

    SN - 0045-7825

    ER -