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.

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...

the present paper investigates the potential application of graphene sheets with attached nanoparticles as resonant sensors by introducing a nonlocal shear deformation plate model. to take into account an elastic connection between the nanoplate and the attached nanoparticle, the nanoparticle is considered as a mass-spring system. then, a combination of pseudo-spectral and integral quadrature m...

Complete dynamical PDE systems of one-dimensional nonlinear elasticity satisfying the principle of material frame indifference are derived in Eulerian and Lagrangian formulations. These systems are considered within the framework of equivalent nonlocally related PDE systems. Consequently, a direct relation between the Euler and Lagrange systems is obtained. Moreover, other equivalent PDE system...

Thickness stretching effect based on shear and normal deformation theory is used in this paper for magneto-electro-elastic vibration analysis of a three-layered curved nanobeam including a nano core and two piezo-magnetic layers. Size-dependency is included in derivation of governing equations of motion based Eringen's nonlocal elasticity theory. The initial curvature is accounted in calculatio...

In the present study, small scale effect on critical buckling loads of triangular nano- composite plates under uniform in-plane compression is studied. Since at nano-scale the structure of the plate is discrete, the size dependent nonlocal elasticity theory is employed to develop an equivalent continuum plate model for this nanostructure incorporating the changes in its mechanical behavior. The...

This study deals with the vibration and stability analysis of double-graphene nanoribbon-system (DGNRS) based on different nonlocal elasticity theories such as Eringen's nonlocal, strain gradient, and modified couple stress within the framework of Rayleigh beam theory. In this system, two graphene nanoribbons (GNRs) are bonded by Pasternak medium which characterized by Winkler modulus and shear...

In the present study, nonlinear free vibration behavior of nanobeam subjected to magnetic field is investigated based on Eringen’s nonlocal elasticity and Euler–Bernoulli beam theory. The Hamilton’s principal is adopted to derive the governing equations together with Euler–Bernoulli beam theory and the von-Kármán’s nonlinear strain–displacement relationships. An approximate analytical solution ...