Automatic mesh generation for 3D smoothed finite element method (S-FEM) based on the weaken-weak formulation

The creation of smoothing domains based on a mesh of problem domain is one of the key tasks in the smoothed finite element method (S-FEM), especially for three dimensional (3D) problems. Traditionally, the smoothed strains in the 3D S-FEM implementations are calculated by using a volume-weighted average of the "raw" strains (strains in finite element method (FEM)) on the neighboring elements. In order to use the standard formulation based on the weaken-weak (W²) formulation, we need to know not only the smoothing domains, but also the area and the outer normal vector of each surface as well as volume of smoothing domains. This paper is the first time to present a comprehensive procedure and efficient algorithms for creating smoothing domains systematically with all the necessary information required for the surface-integral needed in the smoothed strain calculations. Several algorithms are given, including two for establishing connectivity lists among nodes, edges, faces and elements and three for the generation of smoothing domains for various S-FEM models. Besides, we introduce a simple but efficient approach to determine the outer normal vector of segmental surfaces for each smoothing domain. Three examples are presented to show the effectiveness of the given algorithms.