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Applied Mathematics and Mechanics (English Edition) ›› 2009, Vol. 30 ›› Issue (12): 1519-.doi: https://doi.org/10.1007/s10483-009-1204-1

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A novel four-node quadrilateral element with continuous nodal stress

唐旭海1 郑超1 吴圣川2,3 张建海1   

  1. 1. State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China;
    2. Centre for Advanced Materials Joining and Computations (AMJC), School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, P. R. China;
    3. Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 117576, Singapore
  • 收稿日期:2009-03-13 修回日期:2009-09-07 出版日期:2009-12-23 发布日期:2009-12-01

A novel four-node quadrilateral element with continuous nodal stress

TANG Xu-Hai1, ZHENG Chao1, WU Sheng-Chuan2,3, ZHANG Jian-Hai1   

  1. 1. State Key Lab of Hydraulics and Mountain River Engineering, Sichuan University, Chengdu 610065, P. R. China;
    2. Centre for Advanced Materials Joining and Computations (AMJC), School of Materials Science and Engineering, Hefei University of Technology, Hefei 230009, P. R. China;
    3. Centre for Advanced Computations in Engineering Science (ACES), Department of Mechanical Engineering, National University of Singapore, 117576, Singapore
  • Received:2009-03-13 Revised:2009-09-07 Online:2009-12-23 Published:2009-12-01

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摘要： Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress (Q4-CNS) are presented. Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element (FE-LSPIM QUAD4), which is a hybrid FE-meshless method. Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation. It is found that, compared with the standard four-node quadrilateral element (QUAD4), Q4-CNS can achieve significantly better accuracy and higher convergence rate. It is also found that Q4-CNS exhibits high tolerance to mesh distortion. Moreover, since derivatives of Q4-CNS shape functions are continuous at nodes, Q4-CNS is potentially useful for the problem of bending plate and shell models.

关键词: Q4-CNS, four-node quadrilateralelement, partition of unity, continuous nodal stress, accuracy, mesh distortion

Abstract: Formulation and numerical evaluation of a novel four-node quadrilateral element with continuous nodal stress (Q4-CNS) are presented. Q4-CNS can be regarded as an improved hybrid FE-meshless four-node quadrilateral element (FE-LSPIM QUAD4), which is a hybrid FE-meshless method. Derivatives of Q4-CNS are continuous at nodes, so the continuous nodal stress can be obtained without any smoothing operation. It is found that, compared with the standard four-node quadrilateral element (QUAD4), Q4-CNS can achieve significantly better accuracy and higher convergence rate. It is also found that Q4-CNS exhibits high tolerance to mesh distortion. Moreover, since derivatives of Q4-CNS shape functions are continuous at nodes, Q4-CNS is potentially useful for the problem of bending plate and shell models.

Key words: Q4-CNS, four-node quadrilateralelement, partition of unity, continuous nodal stress, accuracy, mesh distortion

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