Enhanced Floating Isogeometric Analysis

TL;DR

This work advances Floating Isogeometric Analysis (FLIGA) by introducing three key enhancements to enable distortion-free, large-deformation simulations of viscoelastic extrusion: (i) a novel quadrature scheme that preserves the material-point character of integration points, (ii) an automated PDE-based regulation of floating B-spline basis functions to remove shear distortion in the characteristic direction, and (iii) an adaptive local refinement strategy to mitigate dilatational distortion. The enhanced FLIGA (FLIGA 2.0) is integrated with a Lagrangian viscoelastic continuum model (Oldroyd-B) and stabilized mixed IGA discretization, enabling accurate, stable simulations of planar extrusion and extrusion-based AM, as well as patch tests and Taylor-Couette benchmarks. Results show substantial improvements in accuracy and stability over the prior FLIGA version, with dramatic reductions in patch-test errors and extended stability in the Taylor-Couette problem, while maintaining manageable computational overhead through controlled floating updates. The framework aligns closely with CAD-based IGA benefits while addressing mesh distortion in one characteristic direction, offering a practical tool for simulating complex, history-dependent polymer extrusion processes in AM. Future work includes extending to multi-patch geometries, relaxing the q=1 restriction in the normal direction, and deeper numerical analysis of stability and convergence.

Abstract

The numerical simulation of additive manufacturing techniques promises the acceleration of costly experimental procedures to identify suitable process parameters. We recently proposed Floating Isogeometric Analysis (FLIGA), a new computational solid mechanics approach, which is mesh distortion-free in one characteristic spatial direction. FLIGA emanates from Isogeometric Analysis and its key novel aspect is the concept of deformation-dependent "floating" of individual B-spline basis functions along one parametric axis of the mesh. Our previous work showed that FLIGA not only overcomes the problem of mesh distortion associated to this direction, but is also ideally compatible with material point integration and enjoys a stability similar to that of conventional Lagrangian mesh-based methods. These features make the method applicable to the simulation of large deformation problems with history-dependent constitutive behavior, such as additive manufacturing based on polymer extrusion. In this work, we enhance the first version of FLIGA by (i) a novel quadrature scheme which further improves the robustness against mesh distortion, (ii) a procedure to automatically regulate floating of the basis functions (as opposed to the manual procedure of the first version), and (iii) an adaptive refinement strategy. We demonstrate the performance of enhanced FLIGA on relevant numerical examples including a selection of viscoelastic extrusion problems.

Figures (21)

• Figure 1: Element concepts in IGA and FLIGA.
• Figure 2: Exemplary "floating" movement of four basis functions along the characteristic elements in the physical space.
• Figure 3: Examples of classical (left) and floating (right) tensor product structure.
• Figure 4: Summary of the construction procedure for classical B-Spline surfaces.
• Figure 6: Mesh distortion in IGA.