Thin plate theory including surface effects

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Size-dependent elastic behavior of FGM ultra-thin films based on generalized refined theory (2009, unknown): “Also presented are d u3 for the cases I-s and II-s obtained by Lu et al. (2006), and d u1 and d u3 for I-d, II-d and FGM films obtained by Lu et al.”
Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints (2012, methodology): “…+ v 2w vy2 ) = N ∗xx v2w vx2 + 2N ∗xy v2w vxvy + N ∗yy v2w vy2 , (2.10) where N ∗ab and M ∗ ab are the generalized resultant forces and moments with consideration of surface effects, which are defined by Lu et al. (2006), N ∗ab = Nab + (ssab)u + (ssab)l and M ∗ab = Mab − h 2 [(ssab)u − (ssab)l].”
Continuum Models Incorporating Surface Energy for Static and Dynamic Response of Nanoscale Beams (2010, background): “[16] generalized the thin plate model to include the normal stresses in the bulk and presented a modified theory for thin and thick plates.”
On the shell theory on the nanoscale with surface stresses (2011, methodology): “…the theory of elasticity with surface stresses is applied to the modifications of the twodimensional theories of nanosized plates and shells, see (Altenbach et al., 2009; Dahmen et al., 2000; Eremeyev et al., 2009; Huang, 2008; Lu et al., 2006; Wang & Zhao, 2009; Zhu, Wang, & Karihaloo, 2009).”