On torsion of FG elastic nanobeams on nonlocal foundations

A plethora of challenging nanomechanical applications deals with ultrasmall composite structures interacting with nonlocal media. To capture size dependent behaviors, effective tools of Nonlocal Continuum Mechanics can be conveniently adopted, provided that the relevant structural problem is well-posed. A crucial improvement in modeling of nanobeams on nanofoundations is provided in the present work with respect to the formulation based on the Eringen–Wieghardt nonlocal approach. Scale effects on FG nanobeams under torsion are effectively captured by exploiting the consistent stress-driven integral theory of elasticity. A novel formulation of size dependent elastic foundations is here introduced. Notably, the constitutive behavior describing interaction between twisted nanobeams and surrounding media is modeled by spatial convolution driven by the torsional rotation field. It is shown that the governing structural problem is mathematically represented by an integro-differential formulation. An equivalent simpler differential problem is then proven to reduce computational burdens. Exemplar case-studies are finally examined to show efficacy of the developed nonlocal methodology.