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.

In this study, the elastic bending of sector graphene sheet has been studied based on elasticity using Eringen Nonlocal Elasticity Theory. In order to do this, the balance equations governing the sector graphene sheet have been solved in terms of displacements with regard to nonlocal relationship of stress, shear theory of the first order, and obtained linear strains using developed Kantorovich...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

In this paper, using energy method, small scale effects on the buckling analysis of a double-walled carbon nanotube (DWCNT) under external radial pressure is studied. The constitutive equations derived for a DWCNT using the nonlocal theory of elasticity which Eringen are presented for the first time. By minimizing the second variation of the total energy for a DWCNT, hence, the value of the non...

Free vibration characteristics of polymer composite plates reinforced by graphene nanosheets employing the Eringen nonlocal elasticity theory were investigated. Theoretical formulations are derived based on Hamilton’s principle implementing linear orthotropic constitutive equations of lamina while the behavior of nanostructure points affected by all other nonlocal points is also taken into acco...

The Hamilton principle is applied to deduce the free vibration frequencies of a cantilever single-walled carbon nanotube (SWCNT) in the presence of an added mass, which can be distributed along an arbitrary part of the span. The nonlocal elasticity theory by Eringen has been employed, in order to take into account the nanoscale effects. An exact formulation leads to the equations of motion, whi...

In this work, the nonlocal elastic waves in a fluid conveying armchair thermo elastic single walled carbon nanotube under moving harmonic load is studied using Eringen nonlocal elasticity theory via Euler Bernoulli beam equation. The governing equations that contains partial differential equations for single walled carbon nanotube is derived by considering thermal and Lorenz magnetic force. The...

Imperfection sensitivity of large amplitude vibration of curved single-walled carbon nanotubes (SWCNTs) is considered in this study. The SWCNT is modeled as a Timoshenko nano-beam and its curved shape is included as an initial geometric imperfection term in the displacement field. Geometric nonlinearities of von Kármán type and nonlocal elasticity theory of Eringen are employed to derive govern...

The present study investigates the buckling of a thick sandwich plate under the biaxial non-uniform compression using the modified couple stress theory with various boundary conditions. For this purpose, the top and bottom faces are orthotropic graphene sheets and for the central core the isotropic soft materials are investigated. The simplified first order shear deformation theory (S-FSDT) is ...