Derivation of the generalized Young-Laplace equation of curved interfaces in nanoscaled solids

By Tungyang Chen, M. Chiu, C. Weng. 2006

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Vibration and buckling analysis of a piezoelectric nanoplate considering surface effects and in-plane constraints (2012, methodology): “Existing experiments and atomistic simulations have confirmed that the elastic and piezoelectric coefficients of piezoelectric nanostructures vary with their dimensions (Zhao et al. 2004; Chen et al. 2006a; Zhang & Huang 2006; Stan et al. 2007; Agrawal et al. 2008; Zhang et al. 2010a).”
Effects of surface and flexoelectricity on a piezoelectric nanobeam (2014, background): “Based on the general expression of the Young–Laplace equation of curved interfaces in nano-scaled solids [19], the effects of the surface on the natural frequency of microbeams and on the critical loading of uniaxial compression microbeams have been analytically investigated [9, 13].”