Examining and calculation of non-classical in the solutions to the true elastic cable under concentrated loads in nanofilm

Due to high surface-to-volume ratio of nanoscale structures, surface stress effects have a significant influence on their behavior. In this paper, a two-dimensional problem for an elastic layer that is bonded to a rigid substrate and subjected to an inclined concentrated line load acting on the surface of the layer is investigated based on Gurtin-Murdoch continuum model to consider surface stress effects. Fourier integral transforms are used to solve the non-classical boundary-value problem related to inclined point load and an analytical solution is obtained for the corresponding boundary-value problem. Selected numerical results are presented for different values of loading angle and are compared with the classical ones to illustrate the influence of the surface stress effects on the stiffness of nano-coating and ultra-thin films. It is found that the surface stress effects have a quite large influence on the response of the nanofilm especially for more vertical loading (higher values of the angle of loading) and make the layer stiffer than the classical case.

Keywords:

Boundary-value problem , Elasticity , Nanomechanics , Point loading , Surface stress