2021/10/22 by Helge C. Hille, Siddhant Kumar, Laura De Lorenzis
Computer Science · Engineering · Mathematics · #3D Shape Modeling and Analysis #Advanced Numerical Analysis Techniques #Applied mathematics #Basis (linear algebra) #Basis function #Computational Geometry and Mesh Generation #Computer science #Engineering #Finite element method #Geometry #Isogeometric analysis #Mathematical analysis #Mathematics #Numerical integration #Parametric statistics #Physics #Quadrature (astronomy) #Radial basis function #Structural engineering #cs.CE
paper · pdf · doi:10.1016/j.cma.2022.114684
arxiv created 2021/10/22 · openalex publication_date 2022/02/11 · arxiv updated 2022/02/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
We propose Floating Isogeometric Analysis (FLIGA), which extends IGA to 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, thus 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.