Nonlinear bending of shear deformable nanobeams subject to a temperature field is investigated in this paper based on von Kármán type nonlinearity and nonlocal elasticity theory. By using the variational principle approach, new higher-order governing differential equations and the corresponding higher-order boundary conditions both in the transverse and axial directions are derived and discusse...

The aim of this paper is to study the elastic stress and strain fields of dislocations and disclinations in the framework of Mindlin’s gradient elasticity. We consider simple but rigorous versions of Mindlin’s first gradient elasticity with one material length (gradient coefficient). Using the stress function method, we find modified stress functions for all six types of Volterra defects (dislo...

This paper is concerned with the surface and small scale effects on transverse vibration of a viscoelastic single-layered graphene sheet (SLGS) subjected to an in-plane magnetic field. The SLGS is surrounded by an elastic medium which is simulated as Visco-Pasternak foundation. In order to investigate the small scale effects, the nonlocal elasticity theory is employed due to its simplicity and ...

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...

Nonlocal problems is a major research area in many branches of modern physics, biotechnology, chemistry and engineering, which arises when it is impossible to determine the boundary values of unknown function and its derivatives. Increasingly often, there arise problems with nonlocal integral boundary conditions, especially in particle diffusion [1] and heat conduction [2, 3]. Partial different...

In this chapter, the dual-support smoothed particle hydrodynamics are presented as a special case of nonlocal operator method in Chap. 3. Several numerical examples linear/nonlinear elasticity presented.

Nanotechnology is one of the pillars of human life in the future. This technology is growing fast and many scientists work in this field. The behavior of materials in nano size varies with that in macro dimension. Therefore scientists have presented various theories for examining the behavior of materials in nano-scale. Accordingly, mechanical behavior of nano-plates, nanotubes nano-beams and n...

In this paper we study two different ways of coupling a local operator with nonlocal one so that the resulting equation is related to an energy functional. first strategy given via source terms in equation, and second flux condition part appears. For both models prove existence uniqueness solution obtained direct minimization extend these ideas local/nonlocal elasticity which couple classical p...