Torsion of functionally graded nonlocal viscoelastic circular nanobeams

The elastostatic problem of functionally graded circular nanobeams under torsion, with nonlocal elastic behavior proposed by Eringen, is preliminarily formulated. Exact solutions are detected for nanobeams with arbitrary axial gradations of elastic properties and radially quadratic distributions of shear moduli. Extension of the treatment to nonlocal viscoelastic composite circular nanobeams is then performed. An effective solution procedure based on Laplace transform is developed, providing a new correspondence principle in nonlocal viscoelasticity for functionally graded materials. Displacements, shear strains and stresses are established for nonlocal viscoelastic nanobeams made of periodic fiber-reinforced materials, with polymeric matrix described by a Maxwell model connected in series with a Voigt model.