Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory

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Longitudinal vibration analysis for microbars based on strain gradient elasticity theory (2014, background): “…that length scale parameters play a major role on the mechanical behavior of microstructures (Fleck et al., 1994; Chong and Lam, 1999; Senturia, 2001; Haque and Saif, 2003; Lam et al., 2003; Zhang et al., 2005a; Lou et al., 2006; Liew et al., 2006; Demir et al., 2010; Civalek and Demir, 2011).”
A Semi-analytical Method for Vibrational and BucklingAnalysis of Functionally Graded Nanobeams Consideringthe Physical Neutral Axis Position (2015, methodology): “Civalek and Demir (2011) developed a nonlocal beam model for the bending analysis of microtubules based on the Euler–Bernoulli beam theory.”
A Nonlocal Higher-Order Shear Deformation Beam Theory for Vibration Analysis of Size-Dependent Functionally Graded Nanobeams (2015, neutral): “In another study, Civalek and Demir [10] presented a nonlocal beam theory to analyzing of bending of microtubules using EBT.”