Abstract

Classical methods by which computer-aided design (CAD) geometries are represented for both design and analysis involve meshing. However, the current process of converting a CAD model into an analysis-suitable surface mesh for the automotive industry takes a significant amount of time and labor, results in a faceted representation of the original smooth geometry, and generates representations that are prohibitively expensive for use in high-order explicit dynamics computations. This research focuses on accurately and efficiently rebuilding given CAD surfaces or meshes, such as shell-like components of automotive vehicles, into smooth, single trimmed spline surface approximations (rather than typical piecewise-linear approximations), making them suitable for use in isogeometric analysis (IGA). Spline-based discretizations exhibit higher accuracy per degree of freedom than their piecewise-faceted counterparts, possess high-order continuity (e.g., for use in Kirchhoff-Love shell analysis), and have potential for much larger stable time steps in explicit dynamics analyses than traditional finite-element methods, which make them a compelling alternative to traditional piecewise-linear alternatives. Our proposed method accurately represents and automatically recontructs these structures by converting a CAD geometry into a feature-aware triangulation, which is then flattened using theory from conformal or differential geometry to define the parametric domain and trimming curves of the intended spline. The flattened geometry is then extended to fill its bounded parametric domain, with its extended vertices given a spatial position by minimizing their biharmonic energy. Subsequently, the bijection between this flattened geometry and its original spatial representation is then used to inform a mapping of a basis spline (B-spline) back into the spatial domain. Once the spatial surface is achieved, it is trimmed using the boundary of the original geometry, thereby reconstructing the intended geometry as a single trimmed B-spline surface. Resulting spline geometries are ultimately used for structural engineering analysis to demonstrate their suitability for analysis.

Degree

College and Department

Ira A. Fulton College of Engineering; Civil and Construction Engineering

Rights

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