Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements

Zou, Z.; Hughes, T. J.R.; Scott, M. A.; Sauer, R. A.; Savitha, E. J.

doi:10.1016/j.cma.2021.113757

Title: Galerkin formulations of isogeometric shell analysis: Alleviating locking with Greville quadratures and higher-order elements

Journal Article · Mon Mar 29 00:00:00 EDT 2021 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2021.113757· OSTI ID:1760475

Zou, Z. ^[1]; Hughes, T. J.R. ^[2]; Scott, M. A. ^[3];

^[4];

^[5]

University of Texas, Austin, TX (United States); Coreform LLC, Orem, UT (United States)
University of Texas, Austin, TX (United States)
Brigham Young University, Provo, UT (United States); Coreform LLC, Orem, UT (United States)
RWTH Aachen University (Germany); Indian Institute of Technology (IIT), Kanpur (India); Gdansk University of Technology (Poland)
RWTH Aachen University (Germany)

Here we propose new quadrature schemes that asymptotically require only four in-plane points for Reissner–Mindlin shell elements and nine in-plane points for Kirchhoff–Love shell elements in B-spline and NURBS-based isogeometric shell analysis, independent of the polynomial degree p of the elements. The quadrature points are Greville abscissae associated with pth-order B-spline basis functions whose continuities depend on the specific Galerkin formulations, and the quadrature weights are calculated by solving a linear moment fitting problem in each parametric direction. The proposed shell element formulations are shown through numerical studies to be rank sufficient and to be free of spurious modes. The studies reveal comparable accuracy, in terms of both displacement and stress, compared with fully integrated spline-based shell elements, while at the same time reducing storage and computational cost associated with forming element stiffness and mass matrices and force vectors. The high accuracy with low computational cost makes the proposed quadratures along with higher-order spline bases, in particular polynomial orders, p = 5 and 6, good choices for alleviating membrane and shear locking in shells.

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Research Organization:: Kansas City Plant (KCP), Kansas City, MO (United States); Univ. of Texas, Austin, TX (United States)

Sponsoring Organization:: USDOE National Nuclear Security Administration (NNSA); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); US Department of Defense (DoD); US Department of the Navy, Office of Naval Research (ONR)

Grant/Contract Number:: NA0002839; SC0017051; N68335-18-C-0289; N00014-17-1-2039; N68335-18-C-0014

OSTI ID:: 1760475

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 380; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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