Bernoulli–Euler beam model based on a modified couple stress theory

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Size-dependent axial buckling analysis of functionally graded circular cylindrical microshells based on the modified strain gradient elasticity theory (2014, background): “For example, Park and Gao [18], Ma et al.”
Analytical solutions for bending, vibration, and buckling of FGM plates using a couple stress-based third-order theory (2013, positive): “These features make the modified couple stress model preferred for variational formulation of beam and plate theories [6,7,10,11,20].”
A non-classical Mindlin plate model based on a modified couple stress theory (2011, methodology): “It has been used in developing non-classical models for Bernoulli–Euler beams [18], Timoshenko beams [19], Reddy–Levinson beams [20], and Kirchhoff plates [11,12].”
A general third-order theory of functionally graded plates with modified couple stress effect and the von Kármán nonlinearity: theory and finite element analysis (2015, background): “Park and Gao [25] studied a bending problem of Bernoulli–Euler beam theory, while Ma et al.”
Closed-form solutions for nonlinear bending and free vibration of functionally graded microplates based on the modified couple stress theory (2015, methodology): “For example, Park and Gao [11] developed a Euler–Bernoulli beam model for the bending analysis of nanobeams.”