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Volume 14, Issue 2
Finite Element Method Coupling Penalty Method for Flexural Shell Model

Xiaoqin Shen, Yongjie Xue, Qian Yang & Shengfeng Zhu

Adv. Appl. Math. Mech., 14 (2022), pp. 365-385.

Published online: 2022-01

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  • Abstract

In this paper, we propose a conforming finite element method coupling penalty method for the linearly elastic flexural shell to overcome computational difficulties. We start with discretizing the displacement variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements (linear element), and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher element (HCT element). Then, the existence, uniqueness, stability, convergence and a priori error estimate of the corresponding analyses are proven and analyzed. Finally, we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.

  • AMS Subject Headings

65N12, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{AAMM-14-365, author = {Shen , XiaoqinXue , YongjieYang , Qian and Zhu , Shengfeng}, title = {Finite Element Method Coupling Penalty Method for Flexural Shell Model}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2022}, volume = {14}, number = {2}, pages = {365--385}, abstract = {

In this paper, we propose a conforming finite element method coupling penalty method for the linearly elastic flexural shell to overcome computational difficulties. We start with discretizing the displacement variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements (linear element), and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher element (HCT element). Then, the existence, uniqueness, stability, convergence and a priori error estimate of the corresponding analyses are proven and analyzed. Finally, we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2020-0304}, url = {http://global-sci.org/intro/article_detail/aamm/20202.html} }
TY - JOUR T1 - Finite Element Method Coupling Penalty Method for Flexural Shell Model AU - Shen , Xiaoqin AU - Xue , Yongjie AU - Yang , Qian AU - Zhu , Shengfeng JO - Advances in Applied Mathematics and Mechanics VL - 2 SP - 365 EP - 385 PY - 2022 DA - 2022/01 SN - 14 DO - http://doi.org/10.4208/aamm.OA-2020-0304 UR - https://global-sci.org/intro/article_detail/aamm/20202.html KW - Flexural shell, conforming finite element method, penalty method, conical shell, cylindrical shell. AB -

In this paper, we propose a conforming finite element method coupling penalty method for the linearly elastic flexural shell to overcome computational difficulties. We start with discretizing the displacement variable, i.e., the two tangent components of the displacement are discretized by using conforming finite elements (linear element), and the normal component of the displacement is discretized by using conforming Hsieh-Clough-Tocher element (HCT element). Then, the existence, uniqueness, stability, convergence and a priori error estimate of the corresponding analyses are proven and analyzed. Finally, we present numerical experiments with a portion of the conical shell and a portion of the cylindrical shell to verify theoretical convergence results and demonstrate the effectiveness of the numerical scheme.

Xiaoqin Shen, Yongjie Xue, Qian Yang & Shengfeng Zhu. (2022). Finite Element Method Coupling Penalty Method for Flexural Shell Model. Advances in Applied Mathematics and Mechanics. 14 (2). 365-385. doi:10.4208/aamm.OA-2020-0304
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