Title: Extraction and Applications of Skeletons in Finite Element Mesh Generation Speaker: Dr. William Roshan Quadros Date/Time: Monday, June 23, 2008, 11:15 am Location: CSRI/90 Brief Abstract: My research interest is in developing computational methods for solving geometry-centered problems in engineering design, analysis, and manufacturing. For almost ten years, I have been working on developing algorithms mainly in the area of finite element (FE) mesh generation using skeletons of CAD models. The term “skeletons of CAD models” can be visualized as analogous to the “skeleton of human body”. Skeletons have proved to be a great tool in analyzing geometric complexity of CAD models as they are symmetric with reduced dimension and provide local thickness information. This talk focuses on extraction of skeletons such as medial axis transform (MAT), chordal axis transform (CAT), mid surface, and disconnected skeletons, and its applications. The application areas include quad meshing, hex meshing of thin-wall solids, and mesh sizing. I developed Lay-Tracks, a novel quad-meshing algorithm, in collaboration with Stanford University during my M.S. at Indian Institute of Science. Lay-Tracks uses the MAT, a continuous skeleton, to combine the merits of two tradition approaches: (1) advancing front method (AFM) and (2) method of decomposition. MAT avoids the expensive interference checks of AFM by using the two-way mapping to decompose the complex domain into simpler tracks. Later at Carnegie Mellon University (CMU), Hex-Layer was developed as a 3D extension of Lay-Tracks for generating hexahedral meshes of thin-wall solids. In Hex-Layer, the CAT, a less-expensive discrete skeleton, is used to extract the mid-surface of thin-wall solids. The mid-surface reduces the 3D hexahedral meshing problem into a 2D quadrilateral meshing problem, i.e., a layered anisotropic hexahedral mesh is obtained by extruding a quad-mesh on the mid-surface using two-way mapping. At ALGOR, further improvements were made to extract non-manifold mid-surface of general thin-wall industrial solid models such as plastic injection mold components, sheet metal parts, automobile body parts, paint coating, etc. During my Ph.D. project, which was sponsored by Sandia National Labs, algorithms for extracting disconnected skeletons of both surfaces and solids were developed. The radius function of these facet and octree based disconnected skeletons accurately measure 2D and 3D proximity, respectively. These skeletons and other tools were then used to completely measure the geometric complexity while generating a geometry-based mesh size function for surfaces, solids, and assemblies. The computational mesh sizing framework that uses these skeletons generates variety of meshes to obtain high quality isotropic mesh with fewer elements; therefore, accurate FE analysis results can be obtained with less computational cost. The talk concludes by highlighting few potential application areas where my work on extraction and application of skeletons can be further utilized. CSRI POC: Steve Owen (505) 284-6599 |