On bending of strain gradient elastic micro-plates

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Modeling and analysis of micro-sized plates resting on elastic medium using the modified couple stress theory (2013, background): “Throughout the past twenty years, various micro- and nano-sized problems have been modeled and studied by many researchers as static and dynamic analysis of structures [17–25].”
A non-classical Mindlin plate model based on a modified couple stress theory (2011, methodology): “were developed in [11] and [12] based on a modified couple stress theory [13,14], and another non-classical model for Kirchhoff thin plates was provided in [15] by employing a strain gradient elasticity theory that contains two additional length scale parameters—one related to the bulk strain energy”
Analysis of micro-sized beams for various boundary conditions based on the strain gradient elasticity theory (2012, methodology): “After this, modified couple stress, non-local elasticity, and strain gradient elasticity theories have been widely applied to static and dynamic analysis of beams [18–28], plates [29,30] and other type structures [31–33].”
Isogeometric analysis for sixth-order boundary value problems of gradient-elastic Kirchhoff plates (2017, methodology): “In [33,64,30], for instance, the partial derivative with respect to the z-coordinate in the higher-order gradient of (2.”