Abstract
A version of nonlocal elasticity theory is employed to develop a nonlocal shear deformable shell model. The governing equations are based on higher order shear deformation shell theory with a von Karman-type of kinematic nonlinearity and include small scale effects. These equations are then used to solve buckling problems of microtubules (MTs) embedded in an elastic matrix of cytoplasm subjected to bending. The surrounding elastic medium is modeled as a Pasternak foundation. The thermal effects are also included and the material properties are assumed to be temperature-dependent. The small scale parameter e0a is estimated by matching the buckling curvature of MTs observed from measurements with the numerical results obtained from the nonlocal shear deformable shell model. The numerical results show that buckling loads are decreased with the increasing small scale parameter e0a. The results reveal that the lateral constraint has a significant effect on the buckling moments of a microtubule when the foundation stiffness is sufficiently large.
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