An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids
An edge-based smoothed finite element method (ES-FEM) for static, free and forced vibration analyses of solids
复制标题
DOI：
10.1016/j.jsv.2008.08.027
复制
发表时间：
2009-03
影响因子：
4.7
通讯作者：
Guirong Liu;T. Nguyen-Thoi;K. Lam
中科院分区：
文献类型：
--
作者：
Guirong Liu;T. Nguyen-Thoi;K. Lam
本文提出了一种基于边的光滑有限元法（ES-FEM），以显着提高有限元法（FEM）的精度，而不需要太多的改变标准的有限元设置。ES-FEM可以使用不同形状的单元，但更喜欢三角形单元，可以很容易地自动生成复杂的区域。在ES-FEM中，使用在与三角形的边缘相关联的平滑域上平滑的应变来计算系统刚度矩阵。大量的数值计算结果表明，ES-FEM具有以下优良特性：（1）ES-FEM模型具有接近精确的刚度：它比“过刚度”有限元模型软得多，比“过软”NS-FEM模型硬得多;（2）结果经常被发现是超收敛和超精确的：其精度远高于线性三角形单元，甚至高于同样节点数的四边形单元;（3）没有发现虚假的非零能量模式，因此该方法也是时间稳定的并且对于振动分析工作良好，以及（4）该方法的实现是直接的并且没有使用惩罚参数，计算效率优于采用相同节点集的有限元法。此外，提出了一种新的基于域的选择性方案，导致一个组合ES/NS-FEM模型，是免疫体积锁定，因此工作得很好，几乎不可压缩的材料。这些属性的ES-FEM证实使用的例子，静态，自由和强迫振动分析的固体。
This paper presents an edge-based smoothed finite element method (ES-FEM) to significantly improve the accuracy of the finite element method (FEM) without much changing to the standard FEM settings. The ES-FEM can use different shape of elements but prefers triangular elements that can be much easily generated automatically for complicated domains. In the ES-FEM, the system stiffness matrix is computed using strains smoothed over the smoothing domains associated with the edges of the triangles. Intensive numerical results demonstrated that the ES-FEM possesses the following excellent properties: (1) the ES-FEM model possesses a close-to-exact stiffness: it is much softer than the “overly-stiff” FEM and much stiffer than the “overly-soft” NS-FEM model; (2) the results are often found superconvergence and ultra-accurate: much more accurate than the linear triangular elements of FEM and even more accurate than those of the FEM using quadrilateral elements with the same sets of nodes; (3) there are no spurious non-zeros energy modes found and hence the method is also temporally stable and works well for vibration analysis and (4) the implementation of the method is straightforward and no penalty parameter is used, and the computational efficiency is better than the FEM using the same sets of nodes. In addition, a novel domain-based selective scheme is proposed leading to a combined ES/NS-FEM model that is immune from volumetric locking and hence works very well for nearly incompressible materials. These properties of the ES-FEM are confirmed using examples of static, free and forced vibration analyses of solids.