Automatic triangular mesh generation of trimmed parametric surfaces for finite element analysis

Computer Aided Geometric Design, Elsevier, Vol 15, pp.199-222, 1998

MESHING
RESEARCH
CORNER

Kenji Shimada
IBM Research, Tokyo Research Laboratory, IBM Japan, Ltd. 1623-14 Shinwtsuruma, Yamato-shi, Kanagawa 242, Japan

David C. Gossard
Computer Aided Design Laboratory, Massachusetts Institute of Technology, Suite 3-458, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Abstract
This paper describes a new computational method for fully automated triangulation of the trimmed parametric surfaces used in finite element analysis. The method takes as input the domain geometry and a node-spacing function, and then generates a mesh, or a set of connected triangles, that satisfies basic requirements such as (1) precise control over node spacing or triangle size, (2) node placement that is compatible with domnin boundaries, (3) generation of well-shaped triangles, and (4) continuous remeshing and local remeshing capabilities. The approach consists of two stages: placing initial nodes using recursive spatial subdivision, and relaxing the mesh by assuming the presence of proximity-based, repulsive/attractive internode forces and then performing dynamic simulation for a force-balancing configuration of nodes. In both stages, algorithms are developed in accordance with the observation that a pattern of tightly packed spheres mimics Voronoi polygons, from which well- shaped Delaunay triangles can be created by connecting the centers of the spheres.