Finite Element Mesh Sizing for Surfaces Using Skeleton

The finite element (FE) mesh sizing has great influence on computational time, memory usage, and accuracy of FE analysis. Based on a systematic in-depth study of the geometric complexity of a set of connected surfaces, a computational procedure for the generation of FE mesh sizing function is proposed. The computational procedure has three main steps: (1) Generation of source points that determine the size and gradient at certain points on the surface; (2) generation of an octree lattice for storing the sizing function; and (3) interpolation of mesh size on the lattice. The source points are generated automatically using a set of tools that are sufficient to completely measure the geometric complexity of surfaces. A disconnected skeleton of the input surface is generated, and it is then used as one of the tools to measure the proximity between curves and vertices that form the boundary of a surface. Octree lattice is used as it reduces the time for calculating the mesh size at a point during meshing. The size at the octree lattice-nodes is calculated by interpolating the size of the source points. The computational procedure is independent of the meshing algorithm; it can handle non-geometric factors, and it is capable of generating variety of meshes by providing the user with enough control of mesh size and gradation. The proposed approach has been tested on many industrial models, and graded surface meshes have been generated successively.