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

Abstract

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 (W 2) 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.

juSFEM: A Julia-based open-source package of parallel Smoothed Finite Element Method (S-FEM) for elastic problems

“…The area of each triangular face S ∆ABC is calculated in Eq. (11). For the internal face unit, there are six faces.…”

“…In reference [11], a set of connectivity lists was developed for the S-FEM. These connectivity lists will be created simultaneously, which will reduce computation and time consumption.…”

“…As a variation of the S-FEM, the edge-based smooth element method (ES-FEM) is parallelized on the GPU [9].Because the process of the S-FEM is quite similar to the FEM, most current S-FEM programs are modified on the basis of the FEM [10]. Reference [11] introduced an effective algorithm for establishing the smoothing domains, realizing the automation of 3D entity calculation and adaptive analysis. However, the current S-FEM program, which uses a programming language such as C/C++ or Fortran, usually requires high demand of programming skill, and the code is difficult to read and modify.…”

Exploring Mesh Generation and Quality Enhancement with Open Source Codes

“…In order to apply the FEM, the problem domain should be continuously divided into sub-domains with simple geometry (triangles, squares, cubes, tetrahedral and others), named finite elements, which must be connected without overlapping regions or failures to compose a valid mesh (Lo, 2012;Nunes et al, 2011;Owen, 1998;Ho-Le, 1988). Thus, the automatic mesh generation may be classified into two main groups, structured mesh generation and unstructured mesh generation (Li et al, 2016;George et al, 2004;Mavriplis, 1995). Automatic methods for structured meshes employ a construction technique which follows an interconnection of parametrization curves, with these ones describing the boundary domain.…”

“…The proposed method was tested considering solids with complex geometries: "C-type" magnet, turbocompressor device, Klein bottle and an electrical motor with supplementary permanent magnets. These choices were motivated by the several studies focused on computational electromagnetics considering similar geometries (Li et al, 2016;Chen and Biro, 2012;Wall et al, 2012;Zhao et al, 2012;Bracken et al, 2012;Zhang and Kumar, 2011;Ho et al, 2011;Chang et al, 2010;Jang et al, 2007;Cho et al, 2006).…”