Exact variational nonlocal stress modeling with asymptotic higher-order strain gradients for nanobeams

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Bending and buckling analyses of functionally graded material (FGM) size-dependent nanoscale beams including the thickness stretching effect (2015, methodology): “These investigations include static analysis (Wang and Liew 2007, Pijaudier-Cabot and Bažant 1987, Lim and Wang 2007, Reddy and Pang 2008), buckling calculations (Zhang et al. 2004, 2006, Wang et al. 2006, Murmu and Pradhan 2009a, Amara et al. 2010, Narendar and Gopalakrishnan 2011a, Tounsi et al.…”
Bending analysis of microtubules using nonlocal Euler–Bernoulli beam theory (2011, background): “It is also accepted that some mechanical properties such as vibration, bending and buckling of beam like micro structures based on nonlocal elasticity theory are entirely different from their counterparts based on the classical (macro) beam theory [22–36].”