@Article{AAMM-16-2,
author = {Wu, Rongfang and Xiaoqin, Shen and Shi, Dongyang and Yu, Jiaping},
title = {Nonconforming Finite Element Methods for Two-Dimensional Linearly Elastic Shallow Shell Model},
journal = {Advances in Applied Mathematics and Mechanics},
year = {2024},
volume = {16},
number = {2},
pages = {493--518},
abstract = {<p style="text-align: justify;">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.</p>},
issn = {2075-1354},
doi = {https://doi.org/10.4208/aamm.OA-2022-0237},
url = {https://global-sci.com/article/72819/nonconforming-finite-element-methods-for-two-dimensional-linearly-elastic-shallow-shell-model}
}