Solid NURBS Parametrisation for Iso-geometric Analysis

­Summary: A resolution-free parametrisation of complex 3D structures using Non-Uniform Rational B-Splines (NURBS) to enable next-generation of simulations with iso-geometric analysis.
A method to compactly parametrise 3D solid structures for next-generation finite-element analysis from different input data. The method uses a minimal plurality of 3D Non-Uniform Rational B-Splines (NURBS) solid elements and determines a conforming parametric scaffolding specifically formulated for modelling bifurcations, such as vascular networks.
Numerical simulations are becoming a paramount tool in manufacturing and industrial engineering, as well as in digital medicine and personalised healthcare, where the design and the analysis of complex irregular structures require high accuracy and performance.
However, conventional methods employ meshes with millions of elements to accurately model the solid structure. Hence, the respective computational simulations represent a time-consuming and cumbersome task for experienced engineers, often with high costs and limited throughput.
The technology allows to automatically determine a compact and resolution-free geometrical model of any solid structure having a bifurcation, using a parametric scaffolding based on NURBS.  This allows to model complex geometries with high degree of continuity and smoothness.
The parametric scaffolding is fully compatible with next-generation numerical models, which do not require heavy and finite-resolution meshes. Instead, simulations with the parametric scaffolding may provide continuous solution profiles, without geometrical approximation errors. Such simulations can also reach ground-breaking performance compared to conventional finite-elements methods, with high scalability for complex composite structures.
As a way of example, the proposed technology can be used to efficiently design and simulate complex shapes for industrial applications, as well as anatomical structures, e.g. the vasculature and hollow chambers, for digital medicine and personalised healthcare.
The technology is protected by a PCT application and is available for licensing. Substantial funding has been secured for commercial translation. The code has been implemented following standard development practices and for being compliant with QMS criteria. Suitable commercial partners are sought for integrating the method in a commercial software package and for commercialisation.
The Science
The proposed method processes different input data (tessellations, points cloud, volumetric scans, and the like) to parametrise 3D solid structures with complex and irregular shape. Convoluted objects with arbitrary branching patterns and smooth or sharp profiles are modelled with a minimal plurality of solid NURBS elements. This constitutes an organised and structured parametric scaffolding with stringent conforming constraints, specifically designed for computational simulations with isogeometric analysis.
Structures with arbitrary topology and geometrical features can be recovered exactly in a vectorial (resolution-free) form. Higher parametric continuity and geometrical smoothness is achieved with ad-hoc regularisation and smoothing paradigms for solid NURBS lattices, based on computer-graphics algorithms.
An automatic pipeline is devised for anatomical branched geometries, and a guided interface is provided for fitting general-purpose objects and designing CAD structures. Several numerical solutions can be used to solve partial differential equations with the proposed parametric scaffolding and isogeometric analysis, including fluid simulation, linear elastic (stress, deformation) problems, electromagnetic and thermal diffusions with high performance and scalability.

a) Gallery of structures parametrised with the solid NURBS scaffolding: CAD designs, organic models, and branching anatomical structures.
b) Computational simulations with the parametric scaffolding and isogeometric analysis (fluid and elastic solution profiles).
Patent Status
WO 2021 161 038 A1: pending PCT application
Further Information
Moriconi, S. et al., (2022) "Solid NURBS Conforming Scaffolding for Isogeometric Analysis", arXiv:2206.04421, doi:10.48550/arXiv.2206.04421
Patent Information:
For Information, Contact:
Lorenza Grechy
King's College London
Jorge Cardoso
Stefano Moriconi
Sebastien Ourselin
Parashkev Nachev