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

• Published in: Computational mechanics 2021-02, Vol.67 (2), p.679-697
• Main Author: Gfrerer, Michael H.
• Format: Article
• Language: English
• Subjects: Approximation; Classical and Continuum Physics; Computational Science and Engineering; Continuum mechanics; Engineering; Error analysis; First principles; Numerical analysis; Original Paper; Parameterization; Shape functions; Spline functions; Tensors; Theoretical and Applied Mechanics; Thin walled shells
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-020-01956-5

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.