边界层级约束细化用于抑制显式等几何分析中裁剪引起的高频离群值

中文摘要 AI 辅助

在显式动力学中，临界时间步长由半离散系统的最大特征频率决定。在等几何分析（IGA）中，开放节点向量引入了一种特征性的谱边界效应，可能导致高频离群值并限制允许的时间步长。在本文考虑的行和集中质量（row-sum-lumped）设置下，扩展计算补丁并裁剪掉外部边界函数可缓解此时间步长惩罚，但未必能阻止边界相邻基函数主导最大特征频率。我们证明，即使对于节点精确裁剪（即不存在小切割单元），与裁剪边界相邻的缩减支撑基函数仍可能成为关键的谱贡献者。因此，小切割单元并非裁剪引起时间步长惩罚的必要条件。节点精确裁剪和任意裁剪代表了同一潜在机制内不同程度的支撑缩减。为控制此效应，我们提出了边界层级约束细化（BLCR）策略，这是一种针对LR-和THB样条的局部细化约束。BLCR约束其支撑与裁剪边界相交的基函数的细化层级，相对于细化内部基函数的层级。在我们研究的所有配置中，此约束确保最大特征频率由未裁剪的内部基函数主导，而非由细化的裁剪函数主导。因此，控制临界时间步长的裁剪引起的高频离群值被抑制，从而产生比具有相同内部分辨率的全局细化裁剪B样条更大的允许时间步长。

英文摘要

In explicit dynamics, the critical time step is governed by the maximum eigenfrequency of the semi-discrete system. In Isogeometric Analysis (IGA), open knot vectors introduce a characteristic spectral boundary effect that can lead to high-frequency outliers and restrict the admissible time step. In the row-sum-lumped setting considered here, extending the computational patch and trimming away the exterior boundary functions mitigates this time-step penalty, but does not necessarily prevent boundary-adjacent basis functions from governing the maximum eigenfrequency. We show that reduced-support basis functions adjacent to the trimming boundary can remain critical spectral contributors even for knot-exact trimming, i.e., in the absence of small cut cells. Hence, small cut cells are not required for trimming-induced time-step penalties. Knot-exact and arbitrary trimming represent different degrees of support reduction within the same underlying mechanism. To control this effect, we propose the Boundary-Level-Constrained Refinement (BLCR) strategy, a local refinement constraint for LR- and THB-splines. BLCR constrains the refinement level of basis functions whose support intersects the trimming boundary relative to that of the refined interior. In all configurations investigated in this work, this constraint ensures that the maximum eigenfrequency is governed by untrimmed interior basis functions rather than by refined trimmed functions. Consequently, the trimming-induced high-frequency outliers governing the critical time step are suppressed, yielding a larger admissible time step than globally refined trimmed B-splines with the same interior resolution.[...]

发表机构

• OTH Regensburg（雷根斯堡应用技术大学）
• Technische Universität München（慕尼黑工业大学）
• Ansys Italy（安思意大利公司）
• DYNAmore GmbH（DYNAmore有限公司）

机构由 AI 辅助整理，请以论文原文为准。