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.

翻译：增材制造技术的数值模拟有望加速识别合适工艺参数的昂贵实验流程。我们近期提出了浮动等几何分析（FLIGA），这是一种新型计算固体力学方法，在特定空间方向上可避免网格畸变。FLIGA源于等几何分析，其关键创新在于：沿网格一个参数轴，B样条基函数可随变形实现"浮动"。前期研究表明，FLIGA不仅克服了该方向上的网格畸变问题，还能与物质点积分完美兼容，并具有与传统拉格朗日网格方法相当的稳定性。这些特性使该方法适用于具有历史相关本构行为的大变形问题模拟（如基于聚合物挤出的增材制造）。本研究对FLIGA初始版本进行了三项改进：(i) 新型积分方案，进一步提升抗网格畸变鲁棒性；(ii) 基函数浮动的自动调控流程（取代初始版本的手动操作）；(iii) 自适应细化策略。我们通过相关数值算例（含粘弹性挤出问题的典型案例）展示了增强型FLIGA的性能。