Automatic Meshing of Curved Three—Dimensional Domains: Curving Finite Elements and Curvature-Based Mesh Control
Specific issues associated with the automatic generation of finite element meshes for curved geometric domains are considered. A review of the definition of when a triangulation is a valid mesh, a geometric triangulation, for curved geometric domains is given. Consideration is then given to the additional operations necessary to maintain the validity of a mesh when curved finite elements are employed. A procedure to control the mesh gradations based on the curvature of the geometric model faces is also given.
KeywordsExpense Hull Clarification
Unable to display preview. Download preview PDF.
- H.L. de Cougny and M.S. Shephard, Refinement, derefinement and local retri-angulations in three-dimensions, 1994, in preparation for submission.Google Scholar
- E.B. de I’Isle and P.L. George, Optimization of tetrahedral meshes. Technical report, INRIA, Domaine de Voluceau. Rocquencourt, BP 105, 78153 Le Chesnay Cedex, Francc.Google Scholar
- S. Dey, Curvature sensitive refinements in 3D automatic mesh generation. Master’s thesis. Scientific Computation Research Center, Rensselaer Polytechnic Institute, Troy, NY 12180–3590, May 1993.Google Scholar
- G. Farin, Curves and Surface for Computer Aided Geometric Design. Academic Press Inc., 1990.Google Scholar
- P.L. George, Generation de maillages par une methode de type Voronoi, Par tie 2: le cas tridimensionnel. Technical Report RR INRIA n 1664, INRIA, Domaine de Voluceau, Rocquencourt, BP 105, 78153 Le Chesnay Cedex, France, 1993.Google Scholar
- D.H. Hoitsma, Surface curvature analysis. In Geometric Modeling for Product Engineering. North-Holland, Amsterdam, 1990.Google Scholar
- M. Mortenson, Geometric Modeling. J. Wiley and Sons, New York, 1985.Google Scholar
- PDA Engineering, PATRAN Division, 2975 Redhill Avenue, Costa Mesa, CA 92626. Patran Plus User Manual, Release 2. 5, October 1990.Google Scholar
- W.J. Schroeder, Geometric Triangulations: with Application to Fully Automatic 3D Mesh Generation. PhD thesis, Rensselaer Polytechnic Institute, Scientific Computation Research Center, RPI, Troy, NY 12180–3590, May 1991.Google Scholar
- W.J. Schroeder and M.S. Shephard, On rigorous conditions for automatically generated finite element meshes. In J. Turner, J. Pegna, and M. Wozny, editors, Product Modeling for Computer-Aided Design and Manufacturing, pages 267–281. North Holland, 1991.Google Scholar
- M.S. Shephard, Automatic generation of finite element models. In M. Papadrakais, editor. Solving Large Scale Problems in Mechanics: The Development and Applications of Computational Solution Methods, to appear 1992.Google Scholar
- O.C. Zienkiewics and R.L. Taylor, The Finite Element Method - Volume 1. McGraw-Hill Hook Co., New York, 4th edition, 1987.Google Scholar