A stress-driven model incorporating surface energy effects for the bending analysis of functionally graded nanobeams with loading discontinuities

In this study, the stress-driven model incorporating surface energy effects (SSDM), developed by one of the authors for study the mechanical response of a functionally graded (FG) nanobeams under constant distributed transverse loading, is extended and applied for the bending analysis of FG nanobeams in presence of discontinuous distributed loadings. Compared to its original formulation, the novel proposed approach assumes that the nanobeam is divided in two parts due the load discontinuity at an internal point of the nanobeam axis. Therefore, the governing equations and the related standard boundary conditions are derived by applying the principle of virtual work in each part of the FG nanobeam. As widely discussed in literature, additional compatibility boundary conditions and constitutive continuity conditions must be satisfied at the interior point where the loading discontinuity occurs. Several results of a parametric analysis are presented to show the effectiveness of the proposed novel approach.