Stability and dynamic analysis of in-plane heterogeneous orthotropic nanoplates: effect of elastic foundation and surface layer with variable thickness

This paper develops a framework for buckling and free vibration analysis of in-plane heterogeneous orthotropic nanoplates, considering nonlocal elasticity, surface effects and elastic foundation, by formulating a simple boundary method whose basis functions are set to approximately satisfy the governing equilibrium equation, as in Trefftz methods. The novelty of the work is in two points: first, the surface effects based on Gurtin-Murdoch model are formulated considering variable thickness of the nanoplate; second, for the first time, simultaneous effect of surface layer, elastic foundation and in-plane heterogeneity are investigated on the behavior of orthotropic nanoplates along with nonlocal effects, considering simple, clamped, free and guided edges. The boundary conditions are imposed by collocation, which enhances the versatility of the method, while the solution has complete continuity over the entire domain. Verification with the literature reflects very good accuracy of the implemented method. In the numerical study, it was observed that the ratio of the buckling load and the free vibration frequency, with and without nonlocal and surface effects, is larger for the cases with constant thickness than those with variable thickness. Moreover, nanoplates with free or guided edges showed less variation of the ratio with respect to the nonlocal effect, than those with simple and clamped edges.