A computational framework for automating generation of finite element mesh sizing function via skeletons

This thesis proposes a computational framework for automating generation of finite element (FE) sizing function for meshing surfaces, solids, and assemblies. Meshing CAD models is generally the most time consuming phase of FE based simulations routinely undertaken in the analysis stage of product development. With appropriate sizing control a high-quality mesh with a reduced number of elements can be obtained sooner; this decreases computational time and memory use during FE simulations without sacrificing accuracy. In developing a framework, geometric factors and other non-geometric factors that influence the mesh sizing should be considered, as most mesh generators do not recognize these factors. Also, these factors should be automatically identified and measured since specifying the sizing function manually is tedious and time consuming that may not be practical in some complex models. A detailed systematic study is performed to identify the geometric factors of surfaces, solids, and assemblies. The non-geometric factors such as user-defined size, pre-meshed entities, mesh scheme, etc., which influence the size, are also considered. The computational framework consists of generating a set of source entities for providing sizing information based on geometric and non-geometric factors, generating a background octree grid for storing the sizing function, and interpolating the sizing on the background octree grid using the source entities. A set of tools are proposed to effectively measure the geometric factors. Disconnected skeletons are extracted and used as tools to measure 3D and 2D proximity, which are two of the geometric factors. The skeletons and other tools are then used to generate source entities which determine the size and local sizing function at certain regions in the domain. A background grid is generated by refining the cells using geometric data and source entities. The interpolation module calculates a smooth sizing function over the background grid using the source entities. The framework has been implemented in CUBIT, Sandia National Lab's mesh generator, and tested on many industrial models. The framework effectively meets the industrial needs by generating a variety of meshes with lower computational costs. This thesis concludes by highlighting some of the potential applications of the technologies developed herein.