Nonlocal dynamic Kirchhoff plate formulation based on nonlocal operator method

  • In this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher orderIn this study, we propose a nonlocal operator method (NOM) for the dynamic analysis of (thin) Kirchhoff plates. The nonlocal Hessian operator is derived based on a second-order Taylor series expansion. The NOM does not require any shape functions and associated derivatives as ’classical’ approaches such as FEM, drastically facilitating the implementation. Furthermore, NOM is higher order continuous, which is exploited for thin plate analysis that requires C1 continuity. The nonlocal dynamic governing formulation and operator energy functional for Kirchhoff plates are derived from a variational principle. The Verlet-velocity algorithm is used for the time discretization. After confirming the accuracy of the nonlocal Hessian operator, several numerical examples are simulated by the nonlocal dynamic Kirchhoff plate formulation.show moreshow less

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Metadaten
Document Type:Article
Author: Yongzheng Zhang
DOI (Cite-Link):https://doi.org/10.1007/s00366-021-01587-1Cite-Link
URN (Cite-Link):https://nbn-resolving.org/urn:nbn:de:gbv:wim2-20220209-45849Cite-Link
URL:https://link.springer.com/article/10.1007/s00366-021-01587-1
Parent Title (English):Engineering with Computers
Publisher:Springer
Place of publication:London
Language:English
Date of Publication (online):2022/02/07
Date of first Publication:2022/01/25
Release Date:2022/02/09
Publishing Institution:Bauhaus-Universität Weimar
Institutes and partner institutions:Fakultät Bauingenieurwesen / Institut für Strukturmechanik
Volume:2022
Pagenumber:35
First Page:1
Last Page:35
Tag:dual-support; nonlocal Hessian operator; nonlocal operator method; operator energy functional; variational principle
GND Keyword:Angewandte Mathematik
Dewey Decimal Classification:500 Naturwissenschaften und Mathematik
BKL-Classification:31 Mathematik / 31.80 Angewandte Mathematik
56 Bauwesen / 56.03 Methoden im Bauingenieurwesen
Licence (German):License Logo Creative Commons 4.0 - Namensnennung (CC BY 4.0)