| This dissertation presents new sheet-based algorithms for generating and modifying geometrically conforming all-hexahedral meshes. Hexahedral mesh generation is currently the most time consuming portion of the design through analysis cycle. The goal of this research is to decrease the user time required to build geometrically conforming all-hexahedral meshes, which will allow more design iterations in less time, increasing design reliability, and decreasing both time to market and development costs.;This dissertation approaches the problem of all-hexahedral meshing with research in both mesh generation and mesh modification. First, a new method, called Unconstrained Plastering, is proposed which uses an advancing front geometry partitioning approach from an unmeshed volume boundary. This approach reduces constraints on mesh generation by defining the volume boundary mesh as a by-product of the interior meshing process.;Second, a new method, called Mesh Matching, is proposed which modifies all-hexahedral meshes on assemblies with two or more components with non-conforming inter-component mesh interfaces. Mesh Matching modifies the element topology near the interfaces to be conforming.;Because Unconstrained Plastering starts from an unmeshed volume boundary, it cannot generate conforming meshes on assemblies. Mesh Matching can be used to post-process meshes from Unconstrained Plastering to be conforming at component interfaces. By allowing assembly components to be meshed independently, Mesh Matching also opens the door to new research in parallel generation of all-hexahedral meshes and non-template-based all-hexahedral refinement and provides an alternative to artificial constraints such as multi-point constraints and tied contacts.;While tetrahedral meshing is generally considered a solved problem, hexahedral meshing remains an open problem. Hexahedral elements must maintain a connectivity of eight nodes, twelve edges, and six quadrilateral faces. With tetrahedra, minor changes to element connectivity remain local. However, seemingly minor changes to all-hexahedral element connectivity propagate globally. In addition, attributes of skew and warp, non-factors with tetrahedra, are critical in hexahedral meshes.;We present an optimization-based automation of Mesh Matching with constraints of element quality, geometric conformity, and conforming elements across the interface. An objective function based on edge valences is developed which can be used for any all-hexahedral topology modification procedure. |
