A Breakthrough Enhancement of FEM using Kriging Interpolation

During the last two decades, a large variety of mesh-free methods have been introduced as alternatives to the conventional finite element method (FEM). However, the acceptance in professional practices seems to be slow due to their implementation complexities. Recently, a convenient implementation of the element-free Galerkin method using Kriging interpolation (KI), which can be viewed as an enhancement of the FEM, was proposed. This method is subsequently referred to as Kriging-based FEM (K-FEM). In this method, field variables are approximated by “element-by-element” piecewise KI. Layers of finite elements around each element are adopted as its domain of influence (DOI). The distinctive advantage of the proposed method is its inheritance of the computational procedure of the FEM. Any existing FE code can be easily extended to K-FEM thus, it has a higher chance to be accepted in the practice. This paper presents overview of the K-FEM. The formulation of KI and the concept of layered-element DOI are reviewed. The two-dimensional elastostatics problem is unitized as a vehicle to convey the concepts. Several examples are presented to demonstrate the reliability of the K-FEM.