Free and Forced Vibration Analysis of Two-Dimensional Linear Elastic Solids Using the Finite Element Methods Enriched by Interpolation Cover Functions

Yancheng Li, Sina Dang, Wei Li and Yingbin Chai
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Yancheng Li: Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, China
Sina Dang: Air and Missile Defense College, Air Force Engineering University, Xi’an 710051, China
Wei Li: School of Naval Architecture and Ocean Engineering, Huazhong University of Science and Technology, Wuhan 430074, China
Yingbin Chai: Key Laboratory of High Performance Ship Technology, Wuhan University of Technology, Ministry of Education, Wuhan 430063, China

Mathematics, 2022, vol. 10, issue 3, 1-21

Abstract: In this paper, a novel enriched three-node triangular element with the augmented interpolation cover functions is proposed based on the original linear triangular element for two-dimensional solids. In this enriched triangular element, the augmented interpolation cover functions are employed to enrich the original standard linear shape functions over element patches. As a result, the original linear approximation space can be effectively enriched without adding extra nodes. To eliminate the linear dependence issue of the present method, an effective scheme is used to make the system matrices of the numerical model completely positive-definite. Through several typical numerical examples, the abilities of the present enriched three node triangular element in forced and free vibration analysis of two-dimensional solids are studied. The results show that, compared with the original linear triangular element, the present element can not only provide more accurate numerical results, but also have higher computational efficiency and convergence rate.

Keywords: interpolation cover functions; finite element method; solid mechanics; free and forced vibration analysis; low order linear element (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (9)

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