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Hierarchically refined isogeometric analysis of trimmed shells
Computational Mechanics ( IF 4.1 ) Pub Date : 2020-05-29 , DOI: 10.1007/s00466-020-01858-6
Luca Coradello , Davide D’Angella , Massimo Carraturo , Josef Kiendl , Stefan Kollmannsberger , Ernst Rank , Alessandro Reali

This work focuses on the study of several computational challenges arising when trimmed surfaces are directly employed for the isogeometric analysis of Kirchhoff-Love shells. To cope with these issues and to resolve mechanical and/or geometrical features of interest, we exploit the local refinement capabilities of hierarchical B-Splines. In particular, we show numerically that local refinement is suited to effectively impose Dirichlet-type boundary conditions in a weak sense, where this easily allows to overcome the issue of over-constraining of trimmed elements. Moreover, we highlight how refinement can alleviate the spurious coupling stemming from disjoint supports of basis functions in the presence of “small” trimmed geometrical features such as thin holes. These phenomena are particularly pronounced in surface models defined by complex trimming patterns and with details at different scales, where we show through several numerical examples the benefits and computational efficiency of the proposed methodology.

中文翻译:

修整壳的分级细化等几何分析

这项工作的重点是研究直接使用修剪曲面进行 Kirchhoff-Love 壳的等几何分析时出现的几个计算挑战。为了解决这些问题并解决感兴趣的机械和/或几何特征,我们利用分层 B 样条的局部细化能力。特别是,我们在数值上表明局部细化适用于在弱意义上有效地施加狄利克雷型边界条件,这很容易克服修剪元素的过度约束问题。此外,我们强调了在存在“小”修剪几何特征(如细孔)的情况下,细化如何减轻由基函数的不相交支持引起的虚假耦合。
更新日期:2020-05-29
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