Date of Award
Doctor of Philosophy (PhD)
John A. Evans
This dissertation presents two novel contributions to the fields of isogeometric analysis and p-version finite elements. First, we present a framework for geometrically exact volumetric mesh generation. By leveraging ideas from both traditional mesh generation as well as isogeometric analysis, we develop a framework for volumetric mesh generation using rational Bernstein--Bézier discretizations. Within this framework, we provide a set of easily verifiable sufficient conditions for guaranteeing that a mesh will be geometrically exact. Second, we develop a complete theory of mesh quality for these rational Bernstein--Bézier elements. From this, we derive a set of easily computable mesh quality metrics for verifying that a rational Bernstein--Bézier discretization will be analysis suitable.
Engvall, Luke H., "Geometrically Exact and Analysis Suitable Mesh Generation Using Rational Bernstein–Bezier Elements" (2018). Mechanical Engineering Graduate Theses & Dissertations. 170.