Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model

Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model

Year:    2024

Author:    Rongfang Wu, Xiaoqin Shen, Dongyang Shi, Jiaping Yu

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 2 : pp. 493–518

Abstract

A shell whose height is far less than the minimum size covering the bottom is called the shallow shell. As a branch of linear elastic shell, it is a special shell with large span and has been widely applied in engineering fields. The main aim of this paper is to construct a general nonconforming finite element framework for a two-dimensional shallow shell model proposed by Ciarlet and Miara. Based on the different regularities of the displacement components, we give the special properties satisfied by the general framework and provide several nonconforming finite element discretization schemes. Then, the existence and uniqueness of the numerical solutions are proved, with the rate of convergence derived. Finally, numerical experiments are carried out for the paraboloid, spherical dome and cylindrical bridge, which validates the theoretical analyses. Moreover, the computing cost of discretizing the shallow shell model is evidently less than that of discretizing the general shell model with comparable accuracy when the shell is the large span shell.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2022-0237

Advances in Applied Mathematics and Mechanics, Vol. 16 (2024), Iss. 2 : pp. 493–518

Published online:    2024-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    26

Keywords:    Shallow shell nonconforming FEMs numerical analysis.

Author Details

Rongfang Wu

Xiaoqin Shen

Dongyang Shi

Jiaping Yu