使用局部还原基方法对修剪多补丁等几何基尔霍夫-洛夫壳进行快速参数分析

IF 8.7 2区 工程技术 Q1 Mathematics Engineering with Computers Pub Date : 2024-04-29 DOI:10.1007/s00366-024-01980-6
Margarita Chasapi, Pablo Antolin, Annalisa Buffa
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引用次数: 0

摘要

本文提出了一个模型阶次缩减框架,用于实时高效地解决修剪、多补丁等几何基尔霍夫-洛夫壳。在设计和形状优化等多种情况下,需要对给定的物理或几何参数集进行多次模拟。这一步骤的计算成本很高,尤其是在现实世界的实际应用中。我们对几何参数感兴趣,并利用花键的灵活性来表示复杂的几何形状。在这种情况下,算子与几何相关,通常以非曲线的方式依赖于参数。此外,从修剪域得到的解可能会因参数值的不同而有很大差异。因此,我们采用基于聚类技术和离散经验插值法的局部还原基础方法来构建仿射近似和高效的还原阶模型。此外,我们还讨论了还原策略在参数形状优化中的应用。最后,我们通过对包括复杂几何体在内的修剪过的多补丁网格进行基准测试,证明了所提出的框架在参数化 Kirchhoff-Love 壳体方面的性能。与标准的还原基方法相比,所提出的方法非常精确,并显著降低了在线计算成本。
本文章由计算机程序翻译,如有差异,请以英文原文为准。

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Fast parametric analysis of trimmed multi-patch isogeometric Kirchhoff-Love shells using a local reduced basis method

This contribution presents a model order reduction framework for real-time efficient solution of trimmed, multi-patch isogeometric Kirchhoff-Love shells. In several scenarios, such as design and shape optimization, multiple simulations need to be performed for a given set of physical or geometrical parameters. This step can be computationally expensive in particular for real world, practical applications. We are interested in geometrical parameters and take advantage of the flexibility of splines in representing complex geometries. In this case, the operators are geometry-dependent and generally depend on the parameters in a non-affine way. Moreover, the solutions obtained from trimmed domains may vary highly with respect to different values of the parameters. Therefore, we employ a local reduced basis method based on clustering techniques and the Discrete Empirical Interpolation Method to construct affine approximations and efficient reduced order models. In addition, we discuss the application of the reduction strategy to parametric shape optimization. Finally, we demonstrate the performance of the proposed framework to parameterized Kirchhoff-Love shells through benchmark tests on trimmed, multi-patch meshes including a complex geometry. The proposed approach is accurate and achieves a significant reduction of the online computational cost in comparison to the standard reduced basis method.

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来源期刊
Engineering with Computers
Engineering with Computers 工程技术-工程:机械
CiteScore
16.50
自引率
2.30%
发文量
203
审稿时长
9 months
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.
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