Carry over matrix for nonlocal beams on an elastic foundation with application in nanotechnology

In this work, the stress resultants and displacements in a bar on an elastic half plane are calculated by using the method of initial values within the framework of nonlocal elasticity. The principal matrix required for the applicability of the method of initial values is presented. An example is solved. As is well-known that nanotechnology is the engineering of functional systems at the molecular scale. The results are used to display that nonlocal effects could be significant in nanotechnology.