NURBS solid modelling using an operator-based approach

The isogeometric analysis is a rather new variant of the finite element method (FEM). The key concept of this method is to directly employ a geometric model described by parametric functions as a mesh for the FEM. The models for the isogeometric analysis have been usually based on non-uniform rational B-Splines (NURBS). The applications so far include both twoand three-dimensional models. This leads to new problems: the creation and modification of NURBS surfaces is a common task in the field of computer graphics, but not the modelling of NURBS solids. This article describes a novel approach to modelling and storage of NURBS-based solid bodies. It is based on considering the modelling process as a sequence of operators. The motivation for this work is the integration of structural analysis with building information modelling. Recent research that employed the classical FEM with volumetric elements has shown the general feasibility. However, it has not achieved a full coupling of the digital building models with the FEM models. That is, the numerical models have to be rebuilt with every model revision which occurs quite often during the planning process. This has been caused by the huge amounts of data that are necessary for describing a mesh. Hence, setting up dependencies between the geometry of a building and the elements of the numerical model would be prohibitively expensive. With the isogeometric analysis based on NURBS solids a more compact formulation is available that allows a volumetric formulation of the problem. This article describes the representation of solid bodies via NURBS. Modifications of this structure can be formulated as single operations that either modify the basis functions of the solid or that transform its control points. A prototype has been set up that includes these operations. It has shown the general feasibility of this approach.