An apporach to automatic three‐dimensional finite element mesh generation

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Abstract
Recently developed solid modelling systems for the design of complex physical solids using interactive computer graphics offer the exciting possibility of an integrated design/analysis system. Called geometric modellers, these systems build complex solids from primitive solids (cubes, cylinders, spheres, solid patches, etc.) and macro solids (combination of primitives)3, 4, 8, 16, 18, 25, 38. To provide an effective structural analysis capability for these systems, methods must be devised to ease the burden of discretizing the solid geometry into a user controlled (usually locally graded) finite element mesh. The purpose of this paper is to describe an interactive solid mesh generation system capable of generating valid meshes of well‐proportional tetrahedral finite elements for the decomposition of multiply connected solid structures. The system uses a semi‐automatic node insertion procedure to locate element node points within and on the surface of a structure. An independent automatic three‐dimensional triangulator then accepts these nodes as input and connects them to form a valid finite element mesh oftetrahedral elements. Although this report makes use of a modeller based on a constructive solid geometry representation (a so‐called CSG modeller), the mesh generation strategy elaborated herein is completely general and makes no particular use of the CSG representation.

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