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.

中文翻译：

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隐式定义曲面上线性薄壳分析的 $$C^1$$-continuous Trace-Finite-Cell-Method

结合 TraceFEM 和有限单元法的概念，提出了一种用于薄壳数值分析的 Trace-Finite-Cell-Method。作为底层壳模型，我们使用 Koiter 模型，我们基于连续介质力学的第一原理，通过将在局部坐标中制定的众所周知的关系重新转换为独立于参数化的公式，以强形式重新推导出该模型。场近似是通过限制在壳表面的结构化背景网格上定义的形状函数来构建的。作为形状函数，我们在背景网格上使用三次样条的张量积。这产生了 $C^1$-连续近似空间，这是四阶控制方程所需的。无参数化公式允许在任意几何图形上自然实现所提出的方法和制造的解决方案，以进行代码验证。因此，通过收敛分析来验证实施，其中使用精确制造的解决方案计算误差。此外，还研究了基准测试。