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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.…
Document Type: | Article |
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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 (ISM) |
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): | Creative Commons 4.0 - Namensnennung (CC BY 4.0) |