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Influences of surface effects on large deflections of nanomembranes with arbitrary shapes by the coupled BE-RBFs method

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Abstract

This paper aims to analyze large deflections of nanomembranes including surface effects with arbitrary shapes. The nonlinear differential equations of nanomembranes are formulated by using the nonlinear kinematic relations and the surface elasticity theory of Gurtin–Murdoch. The principle of virtual work is applied to establish the three governing partial differential equations of nanomembranes. The coupled boundary element-radial basis functions (BE-RBFs) method is developed to solve the complicated nonlinear problem of nanomembranes. The proposed methodology is based on the analog equation method in conjunction with radial basis functions in order that the boundary line integrals and boundary elements are only involved. The validation and accuracy of the present method are evaluated by comparing the obtained results with those available from other numerical solutions. The proposed formulation can provide the numerical results that correspond to the experimental findings of the monolayer circular graphene membrane by specifying the proper surface properties. The influences of the surface elastic constants and residual surface stress on large deflection responses of nanomembranes are evidently investigated. Moreover, some numerical results of the present formulations could serve as a benchmark for the numerical evaluation of future research. Finally, the interesting results of large deflection analysis of the various nanomembrane shapes using the coupled BE-RBFs method are highlighted.

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Acknowledgements

The authors gratefully acknowledge the financial support by the Thailand Research Fund (TRF) and the Office of the Higher Education Commission under the Grant No. MRG6280098.

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering, Faculty of Engineering, Rajamangala University of Technology Lanna, Chiang Rai, 57120, Thailand

    Monchai Panyatong

  2. Department of Civil Engineering, Faculty of Engineering, King Mongkut’s University of Technology Thonburi, Bangkok, 10140, Thailand

    Boonme Chinnaboon & Somchai Chucheepsakul

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  1. Monchai Panyatong
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Correspondence to Monchai Panyatong.

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Panyatong, M., Chinnaboon, B. & Chucheepsakul, S. Influences of surface effects on large deflections of nanomembranes with arbitrary shapes by the coupled BE-RBFs method. Arch Appl Mech 90, 1157–1177 (2020). https://doi.org/10.1007/s00419-020-01662-x

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