Subdivision surfaces are a way of describing a free-form geometry. Unlike NURBS, subdivision surfaces are not limited to a rigid parameter space. The fundamental concept of subdivision surfaces is to repeatedly refine a control point net that roughly describes the desired free-form geometry. By "cutting away" peaks in the control point net, each subdivision step gives a smoother description of the geometry. In the limit this converges to a smooth surface. For the regular case, the limit surface of the Loop subdivision algorithm is a triangular element. It can be described by parametric Box-Spline basis functions. By combining the subdivision algorithm for arbitrary control point nets with the parametric description of a regular element, it is possible to describe the limit surface of arbitrary control point nets parametrically. Isogeometric analysis is a calculation procedure that uses a parametric geometry description directly for the analysis process. This thesis develops an algorithm for the isogeometric analysis of Loop subdivision surfaces. The element formulation is based on the Kirchhoff-Love shell theory and was implemented into the Carat++ Code of the Chair of Structural Analysis at the TU München. The implementation of regular elements was tested with benchmark geometries and the convergence for refinements in the control point net was compared to isogeometric analysis with NURBS. In order to compute irregular meshes another standalone C++ code was written. It is based on a framework that uses a list of control points and a list with the triangular faces of the control point net as input values. Using this code, the results for irregular and regular meshes have been compared to each other.     «

Subdivision surfaces are a way of describing a free-form geometry. Unlike NURBS, subdivision surfaces are not limited to a rigid parameter space. The fundamental concept of subdivision surfaces is to repeatedly refine a control point net that roughly describes the desired free-form geometry. By "cutting away" peaks in the control point net, each subdivision step gives a smoother description of the geometry. In the limit this converges to a smooth surface. For the regular case, the limit sur...     »