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Computational Mechanics
Erschienen in: Computational Mechanics 4/2021

07.07.2021 | Original Paper

A gradient reproducing kernel based stabilized collocation method for the static and dynamic problems of thin elastic beams and plates

verfasst von: Lihua Wang, Yijia Liu, Yueting Zhou, Fan Yang

Erschienen in: Computational Mechanics | Ausgabe 4/2021

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Abstract

The reproducing kernel (RK) approximation based direct collocation method (DCM) requires the complex and time-consuming derivatives calculation of the approximation function, and the DCM has the poor accuracy and stability, which hinder the extensive application of this method. Therefore, in this work, we propose a gradient reproducing kernel (GRK) based stabilized collocation method (SCM) which can manage the computational complexity of the RK derivatives calculation and significantly improve the efficiency by directly constructing the GRK approximations, and handle the accuracy and stability problems of the DCM by employing the SCM. Moreover, the computation cost of the SCM is about the same level of the DCM, which is much more efficient than the Galerkin meshfree methods. The proposed method is particularly suitable for solving the thin beam and plate problems which requests the fourth-order differentiation in the strong form. The implementations of this method for the static and dynamical problems are detailedly exhibited. Numerical examples confirm that the presented algorithm provides high efficiency and good performance for the beam and plate simulations.
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Metadaten
Titel
A gradient reproducing kernel based stabilized collocation method for the static and dynamic problems of thin elastic beams and plates
verfasst von
Lihua Wang
Yijia Liu
Yueting Zhou
Fan Yang
Publikationsdatum
07.07.2021
Verlag
Springer Berlin Heidelberg
Erschienen in
Computational Mechanics / Ausgabe 4/2021
Print ISSN: 0178-7675
Elektronische ISSN: 1432-0924
DOI
https://doi.org/10.1007/s00466-021-02031-3

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