An Estimate of the Influence of the Effect of Spatial Nonlocality on the Stress-Strain State of a Column

The use of nanotechnologies has led to a significant development of nanomechanics for investigation of the mechanical behavior of various types of nanostructures and nanosystems, such as nanorods, nanowires, nanotubes, nanoribbons, nanoshells etc. Typical applications of nanomechanics include nanoelectromechanical systems (NEMS) and microelectromechanical systems (MEMS).
In this paper, which is dedicated to the memory of G.N. Kuvyrkin, the influence of the effect of spatial nonlocality on strain and stress distributions is investigated by considering the problem of deformation of a vertical cylindrical column in a gravitational field. Analytical dependences are obtained taking into account different kinematic and force boundary conditions on the upper base of the column. For the linear stress distribution over the height of the column, a considerable nonlinearity of its strained state is established and the emergence of the edge effect is revealed. This edge effect arises due to the fact that the material of the column exhibits the property of spatial nonlocality. It is noted that the largest stresses (in absolute value) decrease in the column compared to the case where the material of the column does not exhibit the property of spatial nonlocality.