Variational formulation of a simplified strain gradient elasticity theory and its application to a pressurized thick-walled cylinder problem

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Analytical Solution for a Pressurized Thick-Walled Spherical Shell Based on a Simplified Strain Gradient Elasticity Theory (2009, methodology): “8) that has 21 non-zero components for the spherical shell problem here, while it has only 10 non-zero components for the cylinder problem [12].”
Geometrically nonlinear higher-gradient elasticity with energetic boundaries (2013, unknown): “…Altan et al. (1996); Huang et al. (1997); Chambon et al. (1998); Anthoine (2000); Altan et al. (2003); Lam et al. (2003); Li et al. (2004); Gao and Park (2007); Kong et al. (2009); Gao and Ma (2010); Han (2010); Kahrobaiyan et al. (2011); Shvartsburg and Erokhin (2011); Akgoz and Civalek…”
A non-classical Mindlin plate model based on a modified couple stress theory (2011, methodology): “Applying the fundamental lemma of the calculus of variations (e.g., [ 5 ,31]) to Eq. (25) then gives, with the arbitrariness of δu, δv, δw, δφx and δφy,”