A parameter-free variational coupling approach for trimmed isogeometric thin shells

Yujie Guo, Martin Ruess, Dominik Schillinger

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35 Scopus citations

Abstract

The non-symmetric variant of Nitsche’s method was recently applied successfully for variationally enforcing boundary and interface conditions in non-boundary-fitted discretizations. In contrast to its symmetric variant, it does not require stabilization terms and therefore does not depend on the appropriate estimation of stabilization parameters. In this paper, we further consolidate the non-symmetric Nitsche approach by establishing its application in isogeometric thin shell analysis, where variational coupling techniques are of particular interest for enforcing interface conditions along trimming curves. To this end, we extend its variational formulation within Kirchhoff–Love shell theory, combine it with the finite cell method, and apply the resulting framework to a range of representative shell problems based on trimmed NURBS surfaces. We demonstrate that the non-symmetric variant applied in this context is stable and can lead to the same accuracy in terms of displacements and stresses as its symmetric counterpart. Based on our numerical evidence, the non-symmetric Nitsche method is a viable parameter-free alternative to the symmetric variant in elastostatic shell analysis.

Original languageEnglish (US)
Pages (from-to)693-715
Number of pages23
JournalComputational Mechanics
Volume59
Issue number4
DOIs
StatePublished - Apr 1 2017

Bibliographical note

Funding Information:
The authors gratefully acknowledge the Minnesota Supercomputing Institute (MSI) of the University of Minnesota for providing computing resources that have contributed to the research results reported within this paper (https://www.msi.umn.edu/ ). The first author (Y. Guo) would like to acknowledge the support of the Natural Science Foundation of Jiangsu Province (Grant no. BK20160783), the start-up funding awarded by the Nanjing University of Aeronautics and Astronautics (Grant no. 90YAH16028) and the support of National Science Foundation of China (Grant no. 11602106). The last author (D. Schillinger) was supported by the National Science Foundation through Grant CISE-1565997, which is also gratefully acknowledged.

Publisher Copyright:
© 2016, Springer-Verlag Berlin Heidelberg.

Keywords

  • Isogeometric thin shell analysis
  • Non-symmetric Nitsche method
  • Trimmed NURBS surfaces
  • Weak boundary and coupling conditions

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