a b s t r a c tIn this paper, elastic beam model using nonlocal elasticity theory is developed for the bending analysis of microtubules (MTs) based on the Euler-Bernoulli beam theory. The size effect is taken into consideration using the Eringen's non-local elasticity theory. The derivation of governing equation of bending from shear and moment resultants of the beam and stress-strain relationship of the one-dimensional nonlocal elasticity model is presented. The model is then applied on the studies of static analysis of microtubules using the method of differential quadrature (DQ). After the developed DQ method is numerically validated, detailed numerical analyses about the effects of boundary conditions and load types are conducted and the influence of nonlocal parameter on the static response of MTs is discussed. It is hoped that the results in the manuscript may present a benchmark in the study of bending in microtubules.

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The equations of motion and bending of Euler-Bernoulli beam are formulated using the nonlocal elasticity theory for cantilever microtubules (MTs). The method of differential quadrature (DQ) has been used for numerical modeling. The size effect is taken into consideration using the Eringen's non-local elasticity theory. Frequencies and deflections of MTs are obtained. Numerical results are presented to show the effect of small-scale effect on bending and vibration of MTs.

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