In this article, eigenfrequencies of nano-beams under axial loads are assessed by making recourse to the well-posed stress-driven nonlocal model (SDM) and strain-driven two-phase local/nonlocal formulation (NstrainG) elasticity Bernoulli-Euler kinematics. The developed methodology is applicable a wide variety nano-engineered materials, such as carbon nanotubes, modern small-scale beam-like devi...

We present a general finite deformation higher-order gradient elasticity theory. The governing equations of the solid along with boundary conditions various orders are derived from variational principle using integration by parts on surface. objectivity energy functional is achieved carefully selecting invariants under rigid-body transformation. third-order theory includes more than 10.000 mate...

bending analysis of multilayer graphene sheets (mlgss) subjected to non-uniform shear and normal tractions is presented. the constitutive relations are considered to be non-classical based on nonlocal theory of elasticity. based on the differential transformation method, numerical illustrations are carried out for circular and annular geometries. the effects of nano scale parameter, radius of c...

We present a brief survey of nonclassical linear theories continuum mechanics. Thus, we give concise characterization the Eringen–Edelen nonlocal theory elasticity, polar and micropolar media, Toupin couple-stress Eringen–Suhubi–Mindlin micromorphic theory, Mindlin gradient also local deformation elastic media that takes into account mass displacements.

A study of existence and uniqueness weak solutions to boundary value problems describing an elastic body with weakly nonlocal surface elasticity is presented. The chosen model incorporates the strain energy as a quadratic function tensor deformation gradients up Nth order. virtual work principle, extended for higher-order gradient media, serves basis defining solution. In order characterize smo...

Following recent technological advancements, a great attention has been paid to mechanical behaviour of structural elements nanosize. In this study, some solutions problems bars nanosize is examined using Eringen’s two-phase nonlocal elasticity. Assuming the fraction coefficient part material small, perturbation expansion with respect it performed. With procedure, original problem broken into s...