Adaptation of CAD Surface Meshes to a Map of Sizes through the IGATOMM Concept

2nd Symposium on Trends in Unstructured Mesh Generation, University of Colorado, Boulder, August 1999

MESHING
RESEARCH
CORNER

Laboratory of Soils Solids and Structures, UJF-INPG-CNRS, Integrated Design Department, 1029, Rue de la piscine, BP 53, Grenoble Cedex 9
Frederic.Noel@hmg.inpg.fr

Abstract
Within a finite element step, whatever the kind of part under focus (either 3D volume or 3D free-form surfaces) one of the main sub-steps concerns the generation of a mesh adapted to the purpose of the analysis. The number of papers, which are published up to now, shows that the various solutions do not solve entirely this issue.

If big advances have been obtained for 3D volume meshes [1], the case of 3D surfaces stays hard to address. Basic solutions exist when single patches are concerned [2]. When multiple patch surfaces are undertaken the well-known technique that merges the meshes from single patches does not suit the treatment of industrial CAD cases where hundred of trimmed patches describe the whole surface [3].

Face to the complexity of mesh generation, when free-form surfaces issued from CAD environment are under focus, the author has developed the IGATOMM concept (Independent Geometric And Topologic Operators for Mesh Management). IGATOMM is based on a geometric operator able to place nodes at their best location (according to the shape of elements) through a patch independent process [4]. This operator does not modify the connections between nodes. A set of topologic operators is in charge to manage connections of the mesh regardless to the positions of nodes [5]. These operators allow either to cut or to swap selected edges or to remove selected nodes.

We call connectivity of a node the number of edges connected to this node. The swapping operator is used to decrease the connectivity of over-connected nodes. When edges are cut down related faces are split according to predefined topologic schemes and a refined grid is produced. On another hand when a node is removed every related faces are also removed. A topologic approach re-meshes the hole that has been produced and a coarsening operator is defined. Topologic operators do not care the position of nodes ; therefore they need the geometric operator to be applied consecutively to their application, for relaxing the mesh grid in order to make the shapes of faces the most equilateral as possible.

Applied successively, these operators allow either to coarsen or to refine meshes over the whole domain or in a local area. This technique controls the sizes of elements and can be used to make the mesh match a map of sizes defined according to purpose of the analysis.

References

[1] P. L. George, F. Hermeline 'Delaunay's mesh of a convex polyhedron in dimension d. Application to arbitrary polyhedra' International Journal For Numerical Methods In Engineering. Vol. 33, pp. 975-995 (1992).

[2] X. Sheng, B. E. Hirsch 'Triangulation of trimmed surfaces in parametric space' Computer Aided Design. Vol. 24, N. 8, pp. 185-194 (ao-t 1992).

[3] J. C. Leon 'Modelisation et construction de surfaces pour la CFAO' HERMES, Paris (mai 1991).

[4] F. Noel, J. C. Leon, P. 'A new approach to free-form surface mesh control in a CAD environment' International Journal For Numerical Methods In Engineering, Vol. 38, pp. 3121-3142(1994).

[5] F. Noel, J. C. Leon, P. Trompette 'New adaptive tools dedicated to surfacic meshes integrated into a CAD environment' Proceedings ASME design automation conference, Mineapolis (September 1994).