In-plane vibration analysis of plates in curvilinear domains by a differential quadrature hierarchical finite element method

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• 作者：Cuiyun Liu ; Bo Liu ; Yufeng Xing ; J. N. Reddy ; A. M. A. Neves…
• 关键词：In ; plane vibration ; Differential quadrature method ; Hierarchical finite element method ; Isogeometric analysis ; Frequency
• 刊名：Meccanica
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：52
• 期：4-5
• 页码：1017-1033
• 全文大小：
• 刊物类别：Physics and Astronomy
• 刊物主题：Classical Mechanics; Civil Engineering; Automotive Engineering; Mechanical Engineering;
• 出版者：Springer Netherlands
• ISSN：1572-9648
• 卷排序：52

文摘

Free in-plane vibration analysis of plates is carried out by a differential quadrature hierarchical finite element method (DQHFEM). The NURBS (Non-Uniform Rational B-Splines) patches of geometries were first transformed into differential quadrature hierarchical (DQH) patches, and then the elastic field was discretized by the same DQH basis. The DQHFEM solved the compatibility problem caused by different parametrization of neighbouring patches of isogeometric analysis using NURBS. And mesh refinement in DQHFEM does not propagate from patch to patch. The DQHFEM matrices also have the embedding property as the hierarchical finite element method (HFEM). In-plane vibration analyses of plates of several planforms showed that the DQHFEM is similar as the fixed interface mode synthesis method that can analyse a structure using a few nodes on the boundary of substructure elements and only several clamped modes inside each substructure element, but the DQHFEM does not need modal analysis and is of high accuracy. The accuracy and convergence of the DQHFEM were validated through comparison with exact and approximate results in literatures and computed by the authors.