Bending analysis of embedded carbon nanotubes resting on an elastic foundation using strain gradient theory

In this study, static bending response of single-walled carbon nanotubes (SWCNTs) embedded in an elastic medium is investigated on the basis of higher-order shear deformation microbeam models in conjunction with modified strain gradient theory. The governing differential equations and related boundary conditions are obtained by implementing a variational principle. The interactions between SWCNTs and surrounding elastic medium are simulated by Winkler elastic foundation model. The Navier-type solution is utilized to obtain an analytical solution for the bending problem of the simply supported embedded SWCNTs under uniform and sinusoidal loads. The influences of material length scale parameter-to-diameter ratio, slenderness ratio, loading type, shear correction factor and Winkler modulus on deflections of the embedded SWCNTs are discussed in detail. The present results illustrate that the bending behavior of SWCNTs is dependent on the small-size, stiffness of the elastic foundation and also effects of shear deformation, especially for smaller slenderness ratios.