The longitudinal, transverse and torsional wave dispersion curves in single walled carbon nanotubes (SWCNT) are used to estimate the non-local kernel for use in continuum elasticity models of nanotubes. The dispersion data for an armchair (10,10) SWCNT was obtained using lattice dynamics of SWNTs while accounting for the helical symmetry of the tubes. In our approach, the Fourier transformed ke...

The longitudinal, transverse and torsional wave dispersion curves in single walled carbon nanotubes (SWCNT) are used to estimate the non-local kernel for use in continuum elasticity models of nanotubes. The dispersion data for an armchair (10,10) SWCNT was obtained using lattice dynamics of SWNTs while accounting for the helical symmetry of the tubes. In our approach, the Fourier transformed ke...

Abstract: In this paper we solve a simple dead load problem for an isotropic constrained material according to the linearized finite theory of elasticity. We show that the solution of such a problem can be obtained by linearizing with respect to the displacement gradient the solution of the corresponding problem in finite elasticity for an isotropic material subject to the same constraint, exac...

Using differential quadrature method (DQM), this study investigated pull-in instability of beam-type nano-switches under the effects of small-scale and intermolecular forces including the van der Waals (vdW) and the Casimir forces. In these nano-switches, electrostatic forces served as the driving force, and von-Karman type nonlinear strain was used to examine nonlinear geometric effects. To de...

The nature of elastic deformation is examined in the light of the potential theory. The concepts and mathematical treatment of elasticity and the choice of equilibrium conditions are adopted from the mechanics of discrete bodies, e. g., celestial mechanics; they are not applicable to a change of state. By nature, elastic deformation is energetically a Poisson problem since the buildup of an ela...

In this article thermoelastic damping in nano-beam resonators is investigated based on nonlocal theory of elasticity and the Euler-Bernoulli beam assumptions. The governing equation of deflection of the beam is obtained from shear and moment resultants and stress–strain relationship of the nonlocal elasticity model and also the governing equations of thermoelastic damping are established by usi...

The theory of local homology modules was initiated by Matlis in 1974. It is a dual version of the theory of local cohomology modules. Mohammadi and Divaani-Aazar (2012) studied the connection between local homology and Gorenstein flat modules by using Gorenstein flat resolutions. In this paper, we introduce generalized local homology modules for complexes and we give several ways for computing ...

The modeling of the elastic properties of disordered or nanoscale solids requires the foundations of the theory of elasticity to be revisited, as one explores scales at which this theory may no longer hold. The only cases for which microscopically based derivations of elasticity are documented are (nearly) uniformly strained lattices. A microscopic approach to elasticity is proposed. As a first...