| Finite element mesh generation is an important research topic since finite element analysis requires a finite element mesh as input. This thesis presents a recursive volume decomposition method for automatic hexahedral mesh generation. Sub-volumes are separated from the volume of an object using sharp concavities on the object such that the final sub-volumes are meshable ;There are four steps to the current mesh generation approach. Hexahedral elements for solid models are produced by: (1) Loop-based shape element determination, (2) Loop-based decomposition of shape element, (3) MOB determination, and (4) MOB meshing.;Loop-based shape element determination decomposes the surface of a model by loops (a loop is a cycle consisting of either all convex or all concave edges) into several sub-surfaces called regions such that each region belongs to a unique volume called shape element.;Loop-based decomposition of shape element volume results in the object being decomposed into separated volumes.;MOB determination checks if a decomposed volume is a MOB. There are two types of MOBs: (1) convex MOB: a convex MOB that is convex and for which, depending upon the shape (a set of pre-defined MOB shapes are defined), its mesh is precisely known; (2) a pseudo-swept MOB for which the mesh is computed as a sweep of a 2D surface mesh.;MOB meshing creates a hexahedral mesh for each MOB and combines these different meshes results in a mesh for the entire part.;The philosophy in the current research is a localized mesh generation approach for determining the optimum mesh of an object. The fundamental strengths of such a localized meshing approach are (1) the algorithm is computationally efficient, (2) the ability to use simpler meshing algorithms, (3) the ability to parallelize the algorithm and software, and (4) this is the manner in which humans perform manual meshing.;The overall complexity of the meshing algorithm is O(N log(N)) for volume decomposition and O(N) for mesh generation, where N is the number of MOBs on the part. Based on the parts which have been tested in this thesis, the average computing time per MOB is 5 seconds. |
