Numerical method for two-dimensional linearly elastic clamped plate model

ABSTRACT

In this paper, we propose an efficient numerical method for the two-dimensional (2D) linearly elastic clamped plate model. Specifically, we choose the linear Lagrange element to discretize the first two components in the vector displacement space, as well as the Morley element to discretize the third component. Moreover, the existence of discrete solution, uniqueness and a-priori error estimate is analysed. Finally, numerical experiments are presented to verify theoretical results.

KEYWORDS:

• clamped plate model
• linear Lagrange element
• Morley element
• numerical analyses

MATHEMATICS SUBJECT CLASSIFICATIONS:

• 65N12
• 65N15
• 65N30

Acknowledgments

Part of the work has been done during X. Shen's visit to the State Key Laboratory of Scientific and Engineering Computing, Chinese Academy of Sciences. The first author is much obliged to Prof. P. G. Ciarlet for his valuable direction and advice.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This paper has been supported by the National Natural Science Foundation of China (NSFC.11971379) and the Distinguished Youth Foundation of Shaanxi Province (2022JC-01).