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Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models

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Abstract

This paper is concerned with the bending behaviour of small-scale simply supported plates as predicted by using the Eringen nonlocal plate model (ENM), the Hencky bar-net model (HBM) and the continualised nonlocal plate model (CNM). HBM comprises rigid beam segments connected by rotational and torsional springs. CNM is a nonlocal model derived by using a continualisation approach that does away with the unknown scale coefficient \(e_{0}\) in ENM. The exact bending solutions for simply supported rectangular nano-plates are derived by using ENM, HBM and CNM. By making the segment length \(\ell \) of HBM equal to the scale length of continualised and Eringen’s nonlocal plate model and noting the phenomenological similarities between ENM, HBM and CNM, the Eringen’s length scale value \(e_0 \) is found to be dependent on the aspect ratio of the simply supported plate and independent of the applied transverse loading. For a very small scale length \(\ell \), \(e_0\) of ENM converges to values ranging from \(1/\sqrt{8}\) to \(1/\sqrt{6}\) for square plate to longish rectangular plate when calibrated by either HBM or CNM.

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Authors and Affiliations

  1. School of Mechanical and Mining Engineering, University of Queensland, St Lucia, QLD, 4072, Australia

    Y. P. Zhang

  2. IRDL (CNRS UMR 6027), Centre de Recherche, Université Bretagne Sud, Rue de Saint Maudé, BP92116, 56321, Lorient Cedex, France

    N. Challamel

  3. School of Civil Engineering, University of Queensland, St Lucia, QLD, 4072, Australia

    C. M. Wang & H. Zhang

  4. School of Mechatronical Engineering, Beijing Institute of Technology, Beijing, 100081, People’s Republic of China

    H. Zhang

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  1. Y. P. Zhang
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Correspondence to N. Challamel.

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Zhang, Y.P., Challamel, N., Wang, C.M. et al. Comparison of nano-plate bending behaviour by Eringen nonlocal plate, Hencky bar-net and continualised nonlocal plate models. Acta Mech 230, 885–907 (2019). https://doi.org/10.1007/s00707-018-2326-9

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