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- W4287749511 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." @default.
- W4287749511 created "2022-07-26" @default.
- W4287749511 creator A5051734818 @default.
- W4287749511 date "2020-06-30" @default.
- W4287749511 modified "2023-09-25" @default.
- W4287749511 title "A $C^1$-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces" @default.
- W4287749511 doi "https://doi.org/10.48550/arxiv.2007.00075" @default.
- W4287749511 hasPublicationYear "2020" @default.
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