## 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 C^{1}-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 language | English |
---|---|

Pages (from-to) | 679-697 |

Number of pages | 19 |

Journal | Computational Mechanics |

Volume | 67 |

Issue number | 2 |

DOIs | |

Publication status | Published - 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