Nonlinear bending analysis of nonlocal nanoplates with general shapes and boundary conditions by the boundary-only method
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Author list: Panyatong M., Chinnaboon B., Chucheepsakul S.
Publisher: Elsevier
Publication year: 2018
Journal: Engineering Analysis with Boundary Elements (0955-7997)
Volume number: 87
Start page: 90
End page: 110
Number of pages: 21
ISSN: 0955-7997
eISSN: 1873-197X
Languages: English-Great Britain (EN-GB)
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Abstract
In this paper, the geometrically nonlinear bending analysis of nanoplates with general shapes and boundary conditions is highlighted. The governing equations are derived based on the classical plate theory using nonlocal differential constitutive relation of Eringen and von Kแrmแn's nonlinear strains. The boundary-only method is developed by using the principle of the analog equation (PAE). According to the PAE, the original governing differential equations are replaced by three uncoupled equations with fictitious sources under the same boundary conditions, namely two Poisson equations and one biharmonic equation. Subsequently, the fictitious sources are established using a technique based on the boundary element method and approximated by using the radial basis functions. The solution of the actual problem is attained from the known integral representations of the potential and plate problems. Therefore, the kernels of the boundary integral equations are conveniently established and readily calculated that the complex nanoplates can be easily analyzed. The accuracy of the proposed methodology is evaluated by comparing the obtained results with available solutions. Moreover, the influences of nonlocal parameter on the various characteristics of effective distributed loads are elucidated. Finally, the effects of nonlocal parameter, von Kแrmแn's nonlinearity and aspect ratio on nonlinear bending responses are studied. ฉ 2017 Elsevier Ltd
Keywords
Analog equation method, Nonlinear bending
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