On the mechanics of functionally graded nanobeams based on surface stress-driven nonlocal model
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Static and dynamic behavior of Bernoulli-Euler nanobeams made of a functionally graded (FG) material are investigated in this manuscript by a stress-driven model incorporating surface energy effects [1,2]. In particular, the FG nanobeam is composed of a bulk volume and a surface layer regarded as a membrane of zero thickness perfectly adhered to the bulk continuum. The bulk material is made of a mixture of metal and ceramic, whose distributions spatially vary from the bottom to the top surface of the FG nanobeams [3]. The nonlocal governing equations of the elastostatic bending problem are derived by using the virtual work principle while Hamilton’s principle is applied to derive the size-dependent motion equation. The main results of a parametric investigation, carried out considering several different kinematic boundary conditions, are also presented and discussed, varying the nonlocal parameter and the material gradient index. The results show how the proposed model is able to capture surface energy effects on the overall mechanical behavior of functionally graded Bernoulli-Euler nanobeams and provides a cost-effective method for the design and the optimization of nano-scaled structures.
