论文标题
a $ c^1 $ - 连续痕量 - 纤维细胞 - 用于隐式定义表面上的线性薄外壳分析
A $C^1$-continuous Trace-Finite-Cell-Method for linear thin shell analysis on implicitly defined surfaces
论文作者
论文摘要
提出了用于薄壳的数值分析的痕量细胞方法，结合了痕量FEM的概念和有限的细胞方法。作为基础壳模型，我们使用Koiter模型，我们通过重铸在局部坐标中提出的众所周知的关系到独立于参数化的公式，以强大的形式重新衍生。场近似是通过限制在壳表面上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了立方花纹的张量产物。这产生了$ c^1 $ - 连续近似空间，这是第四阶的管理方程所要求的。无参数化公式允许自然实施提出的方法和对代码验证的任意几何形状的制造解决方案。因此，通过收敛分析验证了实现，其中使用精确的制造解决方案计算误差。此外，还研究了基准测试。
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.
