A rational beam-elastic substrate model with incorporation of beam-bulk nonlocality and surface-free energy

Abstract

In this study, a rational beam-elastic substrate model with inclusion of nonlocal and surface-energy effects is developed for bending and buckling analyses of nanobeams lying on elastic substrate media. The beam-section kinematics follows Euler–Bernoulli beam hypothesis. The thermodynamics-based strain gradient theory is employed to represent the beam-bulk nonlocality while the Gurtin–Murdoch surface theory is utilized to account for the surface-free energy. Interaction between the beam and its underlying substrate medium is described by the Winkler foundation model. The governing equilibrium equation and admissible natural boundary conditions are consistently obtained using the virtual displacement principle. To characterize bending and buckling responses of the new beam-elastic substrate model, three numerical examples are employed: the first demonstrates the capability of the proposed model in eliminating the paradoxical behavior present in the Eringen nonlocal differential model; the second characterizes the bending response of the free–free nanobeam-elastic substrate system; and the third examines the influences of several model parameters as well as the size-dependent effect on the buckling response of the simply supported nanobeam-elastic substrate system.