Curtin University Homepage
  • Library
  • Help
    • Admin

    espace - Curtin’s institutional repository

    JavaScript is disabled for your browser. Some features of this site may not work without it.
    View Item 
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item
    • espace Home
    • espace
    • Curtin Research Publications
    • View Item

    Dispersion-minimized mass for isogeometric analysis

    70380.pdf (396.4Kb)
    Access Status
    Open access
    Authors
    Deng, Quanling
    Calo, Victor
    Date
    2018
    Type
    Journal Article
    
    Metadata
    Show full item record
    Citation
    Deng, Q. and Calo, V. 2018. Dispersion-minimized mass for isogeometric analysis. Computer Methods in Applied Mechanics and Engineering. 341: pp. 71-92.
    Source Title
    Computer Methods in Applied Mechanics and Engineering
    DOI
    10.1016/j.cma.2018.06.016
    School
    School of Earth and Planetary Sciences (EPS)
    Remarks

    © 2018. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/

    URI
    http://hdl.handle.net/20.500.11937/70168
    Collection
    • Curtin Research Publications
    Abstract

    We introduce the dispersion-minimized mass for isogeometric analysis to approximate the structural vibration, which we model as a second-order differential eigenvalue problem. The dispersion-minimized mass reduces the eigenvalue error significantly, from the optimum order of 2p to the superconvergence order of 2p+2 for the pth order isogeometric elements with maximum continuity, which in return leads to a more accurate method. We first establish the dispersion error, where the leading error term is explicitly written in terms of the stiffness and mass entries, for arbitrary polynomial order isogeometric elements. We derive the dispersion-minimized mass in one dimension by solving a p-dimensional local matrix problem for the pth order approximation and then extend it to multiple dimensions on tensor-product grids. We show that the dispersion-minimized mass can also be obtained by approximating the mass matrix using optimally-blended quadratures. We generalize the lower order quadrature-blending results to arbitrary polynomial order isogeometric approximations as well as to arbitrary quadrature rules. Various numerical examples validate the eigenvalue and eigenfunction error estimates.

    Related items

    Showing items related by title, author, creator and subject.

    • Isogeometric spectral approximation for elliptic differential operators
      Deng, Quanling; Puzyrev, Vladimir; Calo, Victor (2018)
      © 2018 Elsevier B.V. We study the spectral approximation of a second-order elliptic differential eigenvalue problem that arises from structural vibration problems using isogeometric analysis. In this paper, we generalize ...
    • Generalization of the Pythagorean Eigenvalue Error Theorem and Its Application to Isogeometric Analysis
      Barton, M.; Calo, Victor; Deng, Quanling; Puzyrev, Vladimir (2018)
      © 2018, Springer Nature Switzerland AG. This chapter studies the effect of the quadrature on the isogeometric analysis of the wave propagation and structural vibration problems. The dispersion error of the isogeometric ...
    • Dispersion-minimizing quadrature rules for C1 quadratic isogeometric analysis
      Deng, Q.; Barton, M.; Puzyrev, Vladimir; Calo, Victor (2017)
      We develop quadrature rules for the isogeometric analysis of wave propagation and structural vibrations that minimize the discrete dispersion error of the approximation. The rules are optimal in the sense that they only ...
    Advanced search

    Browse

    Communities & CollectionsIssue DateAuthorTitleSubjectDocument TypeThis CollectionIssue DateAuthorTitleSubjectDocument Type

    My Account

    Admin

    Statistics

    Most Popular ItemsStatistics by CountryMost Popular Authors

    Follow Curtin

    • 
    • 
    • 
    • 
    • 

    CRICOS Provider Code: 00301JABN: 99 143 842 569TEQSA: PRV12158

    Copyright | Disclaimer | Privacy statement | Accessibility

    Curtin would like to pay respect to the Aboriginal and Torres Strait Islander members of our community by acknowledging the traditional owners of the land on which the Perth campus is located, the Whadjuk people of the Nyungar Nation; and on our Kalgoorlie campus, the Wongutha people of the North-Eastern Goldfields.