Fady Massarwi (CS, Technion)
Isogeometric analysis (IGA) has brought new problems to the field of Computer Aided Geometry for Design (CAGD); in return the latter brings to the computation of solution of PDEs new methods and algorithms. The present work develops both aspects. In the first one, IGA has renewed the interest for trivariate spline objects and their manipulation: construction of multi patch primitives that are C0 or G1, construction of trivariate splines resulting from classic CSG operations such as extrusion, sweep, ruled volume, and volume of revolution. One must then analyse the singularities that these constructors may carry, as well as the possibility to get non-singular parameterisations.
Conversely, IGA implies the intrinsic usage of CAD elements. Hence (new) tools from geometric modelling can naturally be introduced to define new algorithms and higher precision computations or higher order approximations of domain boundaries defined by trimmed surfaces. This can beperformed by untrimming, i.e. precisely representing the trimmed surface by a set of higher order tensor product splines. Thus, function evaluations on such boundaries can be very accurate: by an up to machine precision determination of the exact position, as well normals and tangents (an important property for handling some boundary conditions such as flux preserving for incompressible fluid) and obviously integral properties.
The full ability of geometric modelling and IGA is used to address several key issues in the context of large deformation contact analysis. With the aid of unique precise analysis tools available from geometric modelling, we can investigate surface-to-surface algorithms, with reaction forces defined on medial surfaces or integral properties such as penetration area/volume rather than contact boundaries of a slave body, as is commonplace in currently available methods. As for the medial axis, we similarly present capabilities to employ precise algorithms to directly compute Bisectors and
Voronoi cells of splines.
The algorithms developed are included in the Irit geometric modelling library, and numerous examples are given using GuIrit, its graphical interface.