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An Extended Virtual Element Method for the Shallow Shell Model
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DOI：10.1002/num.70047.png)
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Abstract
En 中文
In this work, we develop an extended virtual element discrete scheme for the shallow shell model proposed by Ciarlet and Miara. The shallow shell model is a fourth-order variable coefficient shell, and when applying traditional H-1 and H-2 virtual element approximations, it becomes necessary to increase the degrees of freedom to ensure the computability of each term in the shallowshell equation. To address this, we introduce an extended discrete space with the minimum degrees of freedom by employing an L-2 projection operator that satisfies the orthogonality condition. For the same error magnitude, the number of degrees of freedom required in the extended virtual element method is significantly lower than that in the finite element method. Moreover, we obtainthe existence and uniqueness of the virtual element discrete solution, and analyze the error estimation under the energy norm.Finally, numerical experiments on paraboloid, regular saddle surface, and irregular saddle surface on polygonal meshes verify thatthe discrete scheme is convergent and stable.
Keywords:
paraboloid shell
polygon mesh
saddle shell
shallow shell
virtual element
Journal
N
IF:
1.7
Papers:
60
Citations:
3.9K