Generalization of FEM Using Node-Based Shape Functions
Abstract: 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.
Keywords: Finite element;
kriging interpolation; node-based shape function; satellite nodes
Journal Code: jptsipilgg150024
