Adaptive mesh refinements for analyses of 2D linear elasticity problems using the Kriging-based finite element method

Abstract

Finite element analyses of irregular structures require adaptive mesh refinement to achieve more accurate results in an efficient manner. This is also true for a non-conventional finite element method with Kriging interpolation, called the Kriging-based finite element method (K-FEM). This paper presents a study of automatic adaptive meshing procedures for analyses of two-dimensional linear elasticity problems using the K-FEM. The Matlab Partial Differential Equation Toolbox was utilized for generating meshes with Delaunay triangulation. Three error indicators, namely, the strain energy error, the gradient of effective stresses, and the element-free Galerkin strain energy error, were employed for estimating the element errors. To find the most effective error indicator, the resulting total number of elements and configurations of the final meshes were compared. The results show that the resulting final meshes were affected by the initial mesh configurations, the refinement criteria, and the termination criteria. The gradient of effective stresses indicator was found to be the most effective error indicator for the K-FEM, as it can accurately estimate the element errors.