Solid NURBS Conforming Scaffolding for Isogeometric Analysis

TL;DR

This paper presents a novel scaffolding framework using conforming NURBS elements for solid structures, enabling advanced isogeometric analysis with high continuity and applicability to complex geometries and biological data.

Contribution

It introduces a new topological and geometrical subdivision method for conforming NURBS scaffolding, supporting arbitrary branching and higher continuity in solid modeling.

Findings

Successfully applied to synthetic and real-world geometries.

Achieved higher than positional continuity in scaffolding.

Demonstrated scalable performance in isogeometric analysis.

Abstract

This work introduces a scaffolding framework to compactly parametrise solid structures with conforming NURBS elements for isogeometric analysis. A novel formulation introduces a topological, geometrical and parametric subdivision of the space in a minimal plurality of conforming vectorial elements. These determine a multi-compartmental scaffolding for arbitrary branching patterns. A solid smoothing paradigm is devised for the conforming scaffolding achieving higher than positional geometrical and parametric continuity. Results are shown for synthetic shapes of varying complexity, for modular CAD geometries, for branching structures from tessellated meshes and for organic biological structures from imaging data. Representative simulations demonstrate the validity of the introduced scaffolding framework with scalable performance and groundbreaking applications for isogeometric analysis.