发表机构
Institute for Applied Mathematics, LSIII, TU Dortmund University（多特蒙德工业大学应用数学研究所）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对型材挤出模具设计依赖人工且低效的问题，提出基于伴随形状优化的确定性框架，采用非边界贴合几何表示与重建技术，在三维复杂流道上显著提升性能指标，奠定自动化和可持续制造基础。
AI 中文摘要
由于聚合物熔体的复杂流变行为以及流道的几何复杂性，型材挤出模具的设计仍然是一项具有挑战性的任务。传统的依赖于人类经验的手动优化方法效率低下，并且常常采用未经验证的启发式方法。为了解决这些挑战，我们提出了一种基于伴随形状优化的确定性且可解释的自动模具设计框架。该方法能够计算灵敏度，直接指示流道几何的有益修改。此类优化过程中的一个主要困难在于生成与几何变化一致演化的边界贴合网格。为了克服这一问题，我们采用非边界贴合几何表示方法，消除了沿物理边界显式表面表示的需要。开发了一种专门的 reconstruction 技术，以在流体和固体区域之间的虚拟界面处恢复准确的灵敏度信息。所提出的算法在具有不同复杂度的三维几何体上进行了演示，包括真实的挤出模具流道。考虑了与工业应用相关的多个目标函数，例如出口处的流量平衡。结果凸显了性能指标的显著改善，同时保持了数值鲁棒性。这项工作展示了基于伴随的技术在仍主要由手动试错过程主导的领域中实现自动化模具设计的潜力，为使用计算流变学实现数据高效、可持续的制造流程奠定了基础。
英文摘要
The design of profile extrusion dies remains a challenging task due to the complex rheological behavior of polymer melts and the geometric intricacies of flow channels. Traditional manual optimization approaches, which rely heavily on human experience, are inefficient and often employ unvalidated heuristics. To address these challenges, we present a deterministic and explainable framework for automatic die design based on adjoint-based shape optimization. This approach enables the computation of sensitivities that directly indicate beneficial modifications to the flow channel geometry. A major difficulty in such optimization processes lies in generating boundary-conforming meshes that evolve consistently with changing geometries. To overcome this issue, we employ non-boundary conforming geometry representation methods that eliminate the need for an explicit surface representation along physical boundaries. A dedicated reconstruction technique is developed to recover accurate sensitivity information at the virtual interface between fluid and solid regions. The proposed algorithm is demonstrated on 3D geometries with varying complexity, including realistic extrusion die flow channels. Several objective functionals relevant to industrial applications, such as flow balance at the outflow, are considered. The results highlight significant improvements in performance metrics while maintaining numerical robustness. This work showcases the potential of adjoint-based techniques for automated die design in a domain still largely governed by manual trial-and-error procedures, establishing a foundation for data-efficient, sustainable manufacturing workflows using computational rheology.
