A smoothed finite element method for octree-based polyhedral meshes with large number of hanging nodes and irregular elements

Abstract

Techniques are now available to generate high-quality polyhedral elements offering a good alternative way for accurate stress analysis for solids. However, distorted polyhedral elements cannot be effectively used in standard finite element methods (FEM) without extra complicated treatments, due to the hanging nodes on the element edges and complex shape of polyhedral elements. On the contrary, the hanging nodes and complex shape of the elements can be naturally dealt with in the smoothed finite element method (S-FEM). This paper, utilizes the octree method to automatically and efficiently generate unstructured polyhedral meshes, using the standard tessellation language (STL). We develop three S-FEM models for octree meshes, using all existing node-based, edge-based and face-based smoothing domains. A subdomain smoothing technique is developed to re-cut the smoothing domain (SD), which simplifies the process of smoothing domain formation. The shapes of the subdomains have some common geometries that are much easier to handle, making use of the good features offered by the S-FEM formulation. The introduction of subdomains does not affect the results of the calculations, and the properties of the three S-FEMs are still preserved. Several demonstration examples are presented to verify the efficiency of the present S-FEM models.