Computer-aided (design +engineering)

Computer-aided design and computer-aided engineering have developed independently of each other. Not surprisingly, different mathematical surface descriptions are employed in the two fields. This difference leads to a gap that is currently bridged by time consuming model conversion, making the geometry optimisation of new products expensive.

Scientists working on the project SIGMACADE (Subdivision based isogeometric modelling applied to computer aided design and engineering) have bridged this gap by using the same mathematical representation of the geometry for both modelling and analysis, referred to as isogeometric analysis. They used a subdivision surface representation as the primary tool for isogeometric analysis.

This iterative refinement generates a series of finer and finer nets that converge to a continuous mesh with the required resolution. More importantly, the main advantage of subdivision surfaces is their ability to model arbitrary geometries gap free using one single surface.

SIGMACADE scientists explored two different types of mesh refinements that are of importance in finite element analysis. The number of subdivision steps is adjusted to reach the number of degrees of freedom necessary for a simulation. However, the polynomial degree of the basis functions also needs to be finely tuned to improve conversion to the solution.

Non-uniform, rational B-splines (NURBS) are the most widely used basis function in computer-aided design. For exploration of subdivision surface representation, the scientists used SubDNURBS, a subdivision algorithm compatible with NURBS. This representation enables, for the first time, the use of arbitrary degrees, non-uniform knots spacing and rational expressions when using subdivision surfaces for analysis. The team developed two plug-ins for the free and open-source suite Blender: one which enables modelling using SubDNURBS, a second which enables the isogeometricanalysis of thin shells. This development led to a prototype modelling software which, for the first time, merged design and isogeometric analysis within one software environment. The team demonstrated that such a combined approach leads not only to faster product development cycles, but also enables new physics based modelling approaches.

The SIGMACADE project led to the extension of isogeometric analysis to NURBS compatible subdivision surfaces. The SIGMACADE approach has the potential to revolutionise airplane, automobile and ship design by allowing models to be developed, tested and adjusted in one stage. The new technology allows for flexible design while ensuring time and cost savings for the development of new products. A teaser video shows the additional physics based modeling mode.