Exact solution of Eringen's nonlocal integral model for bending of Euler–Bernoulli and Timoshenko beams

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A review on the mechanics of nanostructures (2018, methodology): “Moreover, Tuna and Kirca [131] examined the static deformation of nanobeams using the nonlocal integral model; exact results were obtained for both Euler–Bernoulli and Timoshenko nanobeams.”
Vibrations of Bernoulli-Euler beams using the two-phase nonlocal elasticity theory (2017, unknown): “Therefore, Fern´andez-S´aez et al. (2016); Tuna and Kirca (2016a,b); Eptaimeros et al. (2016) proposed improper solutions (numerical or analytical) for a problem which is in fact unsolvable in most of the practical cases, since the constitutive boundary conditions are not fulﬁlled.”
Bending and buckling of nonlocal strain gradient elastic beams (2017, methodology): “The closed-form bending solutions of Euler–Bernoulli beams and Timoshenko beams subjected to different loading and boundary conditions were carried out by Tuna and Kirca [16].”
Nonlocal elasticity in nanobeams: the stress-driven integral model (2017, unknown): “The situation was actively debated, with recent attempts of overcoming paradoxical results ( Barretta, Feo, Luciano, & Marotti de Sciarra, 2016; Fernández-Sáez, Zaera, Loya, & Reddy, 2016; Tuna & Kirca, 2016; Wang & Liew, 2007; Xu, Deng, Zhang, & Xu, 2016 ).”