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Volume 29, Issue 1
Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model

Xiaoqin Shen, Qian Yang, Lin Bai & Kaitai Li

DOI: 10.4208/cicp.OA-2019-0215

Commun. Comput. Phys., 29 (2021), pp. 186-210.

Published online: 2020-11

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  • Abstract

In this study, the dynamics of elliptic membrane shell model has been proposed and discussed numerically for the first time. Firstly, we show that the solution of this model exists and is unique. Secondly, we consider spatial and time discretizations of the time-dependent elliptic membrane shell by finite element method and Newmark scheme, respectively. Then, the corresponding existence, uniqueness, stability, convergence and a priori error estimate are given. Finally, we present numerical results involving a portion of an ellipsoidal shell and a portion of a spherical shell to verify the efficiency and convergence of the numerical scheme.

  • Keywords

Elliptic membrane shell, finite element method, full discretization, ellipsoidal shell, spherical shell.

  • AMS Subject Headings

65N12, 65N15, 65N30

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

ktli@xjtu.edu.cn (Kaitai Li)

  • BibTex
  • RIS
  • TXT
@Article{CiCP-29-186, author = {Shen , XiaoqinYang , QianBai , Lin and Li , Kaitai}, title = {Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model}, journal = {Communications in Computational Physics}, year = {2020}, volume = {29}, number = {1}, pages = {186--210}, abstract = {

In this study, the dynamics of elliptic membrane shell model has been proposed and discussed numerically for the first time. Firstly, we show that the solution of this model exists and is unique. Secondly, we consider spatial and time discretizations of the time-dependent elliptic membrane shell by finite element method and Newmark scheme, respectively. Then, the corresponding existence, uniqueness, stability, convergence and a priori error estimate are given. Finally, we present numerical results involving a portion of an ellipsoidal shell and a portion of a spherical shell to verify the efficiency and convergence of the numerical scheme.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2019-0215}, url = {http://global-sci.org/intro/article_detail/cicp/18427.html} }
TY - JOUR T1 - Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model AU - Shen , Xiaoqin AU - Yang , Qian AU - Bai , Lin AU - Li , Kaitai JO - Communications in Computational Physics VL - 1 SP - 186 EP - 210 PY - 2020 DA - 2020/11 SN - 29 DO - http://doi.org/10.4208/cicp.OA-2019-0215 UR - https://global-sci.org/intro/article_detail/cicp/18427.html KW - Elliptic membrane shell, finite element method, full discretization, ellipsoidal shell, spherical shell. AB -

In this study, the dynamics of elliptic membrane shell model has been proposed and discussed numerically for the first time. Firstly, we show that the solution of this model exists and is unique. Secondly, we consider spatial and time discretizations of the time-dependent elliptic membrane shell by finite element method and Newmark scheme, respectively. Then, the corresponding existence, uniqueness, stability, convergence and a priori error estimate are given. Finally, we present numerical results involving a portion of an ellipsoidal shell and a portion of a spherical shell to verify the efficiency and convergence of the numerical scheme.

Xiaoqin Shen, Qian Yang, Lin Bai & Kaitai Li. (2020). Full Discretization Scheme for the Dynamics of Elliptic Membrane Shell Model. Communications in Computational Physics. 29 (1). 186-210. doi:10.4208/cicp.OA-2019-0215
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