Isogeometric Analysis for use in Industry

The term ‘isogeometric analysis' was coined by Dr.Thomas J.R.Hughes et. al in the 2005 paper, “Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement”. This paper popularized and laid the methodological foundation for the idea of using the same geometric basis for both computer-aided design (CAD) and finite element analysis (FEA). For decades, mainstream FEA has relied on the faceted, non-smooth Lagrange basis, while mainstream CAD has used the smooth spline basis. The Lagrange basis had well-understood properties important for FEA, such as efficiency, robustness, and continuity ("watertightness"), while the splines used in CAD (usually trimmed non-uniform rational B-splines or NURBS) had important properties for design and machining, such as smoothness. Dr. Hughes showed that untrimmed NURBS are actually a mathematically suitable basis for FEA. In the succeeding years, over 4000 papers have been published exploring and proving the following benefits of using spline bases for FEA: Accuracy: the exact or improved representation of the CAD geometry in a coarse spline mesh Precision: the exact preservation of geometry in all subsequently refined meshes Scalability: highly scalable, geometrically-exact adaptive algorithms Efficiency: the ability to vary the smoothness of the spline basis functions, sometimes called k-refinement, which allows for tremendous efficiency gains in accuracy per degree of freedom Improved computation: new approaches to linear solver development leverage the natural multi-grid structure of IGA mesh refinement. With these benefits established in theory, industrial efforts to commercialize IGA have begun. Coreform has developed Coreform IGA, based on the unique properties of unstructured spline bases and the flex representation method, to bring the full value of IGA to industry. In this presentation, we will introduce IGA and demonstrate the above-listed benefits through several benchmark examples.