ASPECTS OF 3-DIMENSIONAL CONSTRAINED DELAUNAY MESHING

Presented in this paper are the theoretical aspects of node addition t o a non-convex, multiboundary mesh of tetrahedral elements as used in finite element modelling. The method used is derived from Watson1 and Shenton and Cendes2 and is extended to deal with node addition on inte r-material boundaries. Several situations are identified that result i n an illegal insertion polyhedron (IP), these could be caused by the ' constrained' nature of the mesh, adjacent objects with different mater ial properties, or degenerate node configurations. A new Delaunay algo rithm is described that checks for illegal cases of the IP and then co rrects them, this checking relies on the consistent ordering of the el ement nodes. It is shown that a particular type of illegal IP can easi ly be identified and corrected using this technique. The Delaunay algo rithm is then applied to automatic mesh generation, and modification t o the basic Delaunay algorithm is described so that previously meshed edges and faces of the current object being meshed are not deleted dur ing the addition of subsequent nodes. This 'protection' method only be comes viable by recognizing the node ordering sense of the IP faces.