  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.
