H. M. Verhelst, A. Mantzaflaris, M. Möller, J. H. Den Besten
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引用次数: 0
摘要
网格自适应是一种在数值求解中提供细节的技术,无需在整个域中细化网格。等距几何分析中的网格自适应可由截断分层 B 样条线(THB 样条线)驱动,该样条线基于更精细的 B 样条线基局部增加自由度。细化元素的标记通常使用基于残差的误差估算器来完成。本文开发了用于等几何基尔霍夫-洛夫壳分析的自适应网格划分工作流程。该框架包括 THB-样条、细化和粗化相结合的网格容许性以及计算元素误差贡献的双加权残差(DWR)方法。DWR 可用于多个结构分析问题,允许用户指定感兴趣的目标量,用于标记元素和细化网格。该目标函数可涉及位移、应力、特征频率等。通过一系列不同的基准问题,包括模态分析、屈曲分析以及非线性快穿和分叉问题,对所提出的框架进行了评估,结果表明 DWR 估计器具有很高的准确性,并能为高级壳计算有效分配自由度。
Goal-adaptive Meshing of Isogeometric Kirchhoff–Love Shells
Mesh adaptivity is a technique to provide detail in numerical solutions without the need to refine the mesh over the whole domain. Mesh adaptivity in isogeometric analysis can be driven by Truncated Hierarchical B-splines (THB-splines) which add degrees of freedom locally based on finer B-spline bases. Labeling of elements for refinement is typically done using residual-based error estimators. In this paper, an adaptive meshing workflow for isogeometric Kirchhoff–Love shell analysis is developed. This framework includes THB-splines, mesh admissibility for combined refinement and coarsening and the Dual-Weighted Residual (DWR) method for computing element-wise error contributions. The DWR can be used in several structural analysis problems, allowing the user to specify a goal quantity of interest which is used to mark elements and refine the mesh. This goal functional can involve, for example, displacements, stresses, eigenfrequencies etc. The proposed framework is evaluated through a set of different benchmark problems, including modal analysis, buckling analysis and non-linear snap-through and bifurcation problems, showing high accuracy of the DWR estimator and efficient allocation of degrees of freedom for advanced shell computations.
期刊介绍:
Engineering with Computers is an international journal dedicated to simulation-based engineering. It features original papers and comprehensive reviews on technologies supporting simulation-based engineering, along with demonstrations of operational simulation-based engineering systems. The journal covers various technical areas such as adaptive simulation techniques, engineering databases, CAD geometry integration, mesh generation, parallel simulation methods, simulation frameworks, user interface technologies, and visualization techniques. It also encompasses a wide range of application areas where engineering technologies are applied, spanning from automotive industry applications to medical device design.