Modified nonlocal elasticity theory for functionally graded materials

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Size-dependent thermo-electrical buckling analysis of functionally graded piezoelectric nanobeams (2015, methodology): “…be pointed out that the material properties of FG nanobeam are only functions of thickness coordinate z, thus for the present problem, the modified nonlocal theory is converted to Eringen’s nonlocal theory, similar to the assumption considered in (Niknam and Aghdam 2015, Salehipour et al 2015).”
Longitudinal vibrations of nano-rods by stress-driven integral elasticity (2019, methodology): “These gradient theories of elasticity were then extended to the following size-dependent models as, unified gradient elasticity theory [16]–[18], higher-order gradient Eringen model [19], nonlocal strain elasticity theory [20], [21] and nonlocal-couple stress elasticity theory [22], [23].”