Free vibration analysis of cracked thin plates by quasi-convex coupled isogeometric-meshfree method

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• 作者：Hanjie Zhang ; Junzhao Wu ; Dongdong Wang
• 关键词：meshfree method ; isogeometric analysis ; quasi ; convex isogeometric ; meshfree method ; free vibration ; cracked thin plate
• 刊名：Frontiers of Architecture and Civil Engineering in China
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：9
• 期：4
• 页码：405-419
• 全文大小：4,137 KB
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• 作者单位：Hanjie Zhang (1) (2)
  Junzhao Wu (1) (2)
  Dongdong Wang (1) (2)
  
  1. Department of Civil Engineering, Xiamen University, Xiamen, 361005, China
  2. Fujian Provincial Key Laboratory of Mathematical Modeling and High-Performance Scientific Computation, Xiamen University, Xiamen, 361005, China
  
• 刊物类别：Engineering
• 刊物主题：Civil Engineering
  Cities, Countries and Regions
  Chinese Library of Science
  
• 出版者：Higher Education Press, co-published with Springer-Verlag GmbH
• ISSN：1673-7512

文摘

The free vibration analysis of cracked thin plates via a quasi-convex coupled isogeometric-meshfree method is presented. This formulation employs the consistently coupled isogeometric-meshfree strategy where a mixed basis vector of the convex B-splines is used to impose the consistency conditions throughout the whole problem domain. Meanwhile, the rigid body modes related to the mixed basis vector and reproducing conditions are also discussed. The mixed basis vector simultaneously offers the consistent isogeometric-meshfree coupling in the coupled region and the quasi-convex property for the meshfree shape functions in the meshfree region, which is particularly attractive for the vibration analysis. The quasi-convex meshfree shape functions mimic the isogeometric basis function as well as offer the meshfree nodal arrangement flexibility. Subsequently, this approach is exploited to study the free vibration analysis of cracked plates, in which the plate geometry is exactly represented by the isogeometric basis functions, while the cracks are discretized by meshfree nodes and highly smoothing approximation is invoked in the rest of the problem domain. The efficacy of the present method is illustrated through several numerical examples. Keywords meshfree method isogeometric analysis quasi-convex isogeometric-meshfree method free vibration cracked thin plate