论文标题
壳的高阶微量有限元法
A Higher-order Trace Finite Element Method for Shells
论文作者
论文摘要
提出了针对Reissner-Mindlin壳的高阶虚拟域方法（FDM），该方法使用三维背景网格进行离散化。壳的中表面浸入高阶背景网格中，几何形状由级别集合函数暗示。机械模型基于切向差分（TDC），该微积分（TDC）将基于曲线坐标的经典模型扩展到隐式几何形状。壳模型由PDE在歧管上描述，所得的FDM通常称为Trace Fem。 FDM的三个标准关键方面也必须在跟踪FEM中解决，以允许使用更高阶段的准确方法：（i）在切割背景元素中的数值集成，（ii）稳定尴尬的切割情况和消除线性依赖性，以及（iii）使用Nitsche的方法来执行边界条件。数值结果证实，如果解决方案足够光滑，则通过提出的方法启用了高阶精度结果。
A higher-order fictitious domain method (FDM) for Reissner-Mindlin shells is proposed which uses a three-dimensional background mesh for the discretization. The midsurface of the shell is immersed into the higher-order background mesh and the geometry is implied by level-set functions. The mechanical model is based on the Tangential Differential Calculus (TDC) which extends the classical models based on curvilinear coordinates to implicit geometries. The shell model is described by PDEs on manifolds and the resulting FDM may typically be called Trace FEM. The three standard key aspects of FDMs have to be addressed in the Trace FEM as well to allow for a higher-order accurate method: (i) numerical integration in the cut background elements, (ii) stabilization of awkward cut situations and elimination of linear dependencies, and (iii) enforcement of boundary conditions using Nitsche's method. The numerical results confirm that higher-order accurate results are enabled by the proposed method provided that the solutions are sufficiently smooth.
