A new optimal formulation of the selective cell-based smoothed finite element method using 10-node tetrahedral elements (SelectiveCS-FEM-T10) is proposed for nearly incompressible large deformation problems. SelectiveCS-FEM-T10 is a generic name for S-FEM formulations that apply the selective reduced integration (SRI) and the cell-based S-FEM (CS-FEM) simultaneously to the 10-node tetrahedral (T10) elements, and thus it has various formulation variations. The conventional SelectiveCS-FEM-T10 naturally subdivides a T10 element into twelve 4-node tetrahedral (T4) subelements with a dummy node at the element center. Meanwhile, the new SelectiveCS-FEM-T10 radially subdivides it into sixteen T4 subelements around the dummy node. Owing to this radial element subdivision, all the edges of the subelements, including the frame edges, are subjected to strain smoothing only via the edge-based S-FEM (ES-FEM) within an element. Besides, SelectiveCS-FEM-T10 can be implemented into general finite element codes as a T10 element because it is a CS-FEM, which only applies intra-element strain smoothing. Our demonstrative analyses reveal that the new SelectiveCS-FEM-T10 is more robust than the best available T10 element against severe large deformation. They also show that the accuracy of the new SelectiveCS-FEM-T10 is almost equal to the conventional T10 elements as it does not cause shear/volumetric locking and pressure checkerboarding.

针对几乎不可压缩的大变形问题，提出了一种使用 10 节点四面体单元 (SelectiveCS-FEM-T10) 的基于选择性单元的平滑有限元方法的新优化公式。SelectiveCS-FEM-T10 是 S-FEM 公式的通用名称，它将选择性缩减积分 (SRI) 和基于单元的 S-FEM (CS-FEM) 同时应用于 10 节点四面体 (T10) 单元，因此它有各种配方变化。传统的 SelectiveCS-FEM-T10 自然地将 T10 单元细分为 12 个 4 节点四面体 (T4) 子单元，在单元中心有一个虚拟节点。同时，新的 SelectiveCS-FEM-T10 将其径向细分为虚拟节点周围的 16 个 T4 子单元。由于这种径向元素细分，子元素的所有边缘，包括框架边缘，仅通过单元内基于边缘的 S-FEM (ES-FEM) 进行应变平滑处理。此外，SelectiveCS-FEM-T10 可以作为 T10 单元实现为通用有限元代码，因为它是一个 CS-FEM，它只应用单元内应变平滑。我们的示范分析表明，新的 SelectiveCS-FEM-T10 比现有的最佳 T10 元件更能抵抗严重的大变形。他们还表明，新的 SelectiveCS-FEM-T10 的精度几乎与传统的 T10 元件相等，因为它不会导致剪切/体积锁定和压力棋盘格。我们的示范分析表明，新的 SelectiveCS-FEM-T10 比现有的最佳 T10 元件更能抵抗严重的大变形。他们还表明，新的 SelectiveCS-FEM-T10 的精度几乎与传统的 T10 元件相等，因为它不会导致剪切/体积锁定和压力棋盘格。我们的示范分析表明，新的 SelectiveCS-FEM-T10 比现有的最佳 T10 元件更能抵抗严重的大变形。他们还表明，新的 SelectiveCS-FEM-T10 的精度几乎与传统的 T10 元件相等，因为它不会导致剪切/体积锁定和压力棋盘格。