Unfolding geometries: A utility for manufacturing applications and engineering analysis

This work integrates surface modeling, wireframe conversion, thin sheet product design, and boundary mesh generation within the theme of unfolding. The unfolding philosophy creates the object in three dimensions and using advanced computational resources unfolds the geometry into its flat pattern for cutting and punching operations.; A great number of thin sheet products are manufactured by folding thin sheets to desired 3D shapes such as sheet metal fabrication. Our unfolding is to starts from the original 3D design model, electronically unfolds the model to a flat pattern while applying appropriate constraints. Surface cuts or seams are introduced automatically or via user instructions to facilitate the 2D pattern formation. The 2D layout accounts for material thickness. Overlaps or fastening flaps can be added to seams. A stress-relief hole option exists to relieve buckling at corners. Slots, cutouts, and other geometric entities are preserved in the layout. An animation option enhances the clarity of the unfolding process.; However, unfolding requires a surface (as opposed to a wireframe) representation. A geometric modeler that converts wireframes to B-rep data structure was developed. This convertor can supplement a solid modeler removing various wireframe problems such as coincidence of points, colinearity of lines, coplanarity of planes, and tolerance buildups. An innovative feature of this geometric modeller is the octal decomposition utilization which reduces the tolerance cumulation problem. Advanced data structures are employed to handle certain non-manifold features in real life sheet products.; The Boundary Element Method is well suited for solving linear engineering problems. Since BEM requires only a surface mesh for three dimensional analysis, it is a prime candidate for CAD integration. To bring this idea to reality mesh generation routines within the CAD shell were developed. The mesh generation is completely automatic requiring no user intervention. Utility routines were developed to allow interactive exchange between the user and system as a supplement.; Integration of engineering analysis within the shell of a CAD system defines the current state of art. This thesis advances the current state by developing and merging multiple new ideas into an operational shell that is familiar to the user.