Floating Isogeometric Analysis

TL;DR

Floating Isogeometric Analysis (FLIGA) extends traditional IGA by allowing basis functions to 'float' with deformation, enabling accurate Lagrangian analysis of extreme deformations without remeshing, demonstrated through flow and additive manufacturing simulations.

Contribution

The paper introduces FLIGA, a novel tensor-product B-Spline construction that overcomes mesh distortion in Lagrangian extreme deformation analysis without remeshing.

Findings

FLIGA successfully passes numerical patch tests.

The method accurately simulates Newtonian and viscoelastic flows.

Application to additive manufacturing demonstrates practical effectiveness.

Abstract

We propose Floating Isogeometric Analysis (FLIGA), which extends the concepts of IGA to Lagrangian extreme deformation analysis. The method is based on a novel tensor-product construction of B-Splines for the update of the basis functions in one direction of the parametric space. With basis functions 'floating' deformation-dependently in this direction, mesh distortion is overcome for problems in which extreme deformations occur predominantly along the associated (possibly curved) physical axis. In doing so, we preserve the numerical advantages of splines over many meshless basis functions, while avoiding remeshing. We employ material point integration for numerical quadrature attributing a Lagrangian character to our technique. The paper introduces the method and reviews the fundamental properties of the FLIGA basis functions, including a numerical patch test. The performance of FLIGA is then numerically investigated on the benchmark of Newtonian and viscoelastic Taylor-Couette flow. Finally, we simulate a viscoelastic extrusion-based additive manufacturing process, which served as the original motivation for the new approach.