Generalization of FEM Using Node-Based Shape Functions

In standard FEM, the stiffness of an element is exclusively influenced by nodes associated with the element via its element-based shape functions. In this paper, the authors present a method that can be viewed as a generalization of FEM for which the influence of a node is not limited by a hat function around the node. Shape functions over an element can be interpolated over a predefined set of nodes around the element. These node-based shape functions employ Kriging Interpolations commonly found in geostatistical technique. In this study, a set of influencing nodes are covered by surrounding layers of elements defined as its domain of influence (DOI). Thus, the element stiffness is influenced by not only the element nodes, but also satellite nodes outside the element. In a special case with zero satellite nodes, the method is specialized to the conventional FEM. This method is referred to as Node-Based Kriging FEM or K-FEM. The K-FEM has been tested on 2D elastostatic, Reissner-Mindlin’s plate and shell problems. In all cases, exceptionally accurate displacement and stress fields can be achieved with relatively coarse meshes. In addition, the same set of Kringing shape functions can be used to interpolate the mesh geometry. This property is very useful for representing the curved geometry of shells. The distinctive advantage of the K-FEM is its inheritance of the computational procedure of FEM. Any existing FE code can be easily extended to K-FEM; thus, it has a higher chance to be accepted in practice.