A C1-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces

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Abstract

A Trace-Finite-Cell-Method for the numerical analysis of thin shells is presented combining concepts of the TraceFEM and the Finite-Cell-Method. As an underlying shell model we use the Koiter model, which we re-derive in strong form based on first principles of continuum mechanics by recasting well-known relations formulated in local coordinates to a formulation independent of a parametrization. The field approximation is constructed by restricting shape functions defined on a structured background grid on the shell surface. As shape functions we use on a background grid the tensor product of cubic splines. This yields C1-continuous approximation spaces, which are required by the governing equations of fourth order. The parametrization-free formulation allows a natural implementation of the proposed method and manufactured solutions on arbitrary geometries for code verification. Thus, the implementation is verified by a convergence analysis where the error is computed with an exact manufactured solution. Furthermore, benchmark tests are investigated.
Original languageEnglish
Pages (from-to)679-697
Number of pages19
JournalComputational Mechanics
Volume67
Issue number2
Early online date24 Dec 2020
Publication statusPublished - Feb 2021

Keywords

  • Finite element method
  • Finite-Cell-Method
  • Implicit geometry
  • Koiter shell
  • TraceFEM

ASJC Scopus subject areas

  • Computational Mathematics
  • Mechanical Engineering
  • Ocean Engineering
  • Applied Mathematics
  • Computational Mechanics
  • Computational Theory and Mathematics

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