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...

Abstract The derivation of nonlocal strong forms for many physical problems remains cumbersome in traditional methods. In this paper, we apply the variational principle/weighted residual method based on operator elasticity, thin plate, gradient electro-magneto-elasticity and phase-field fracture method. governing equations are expressed as an integral form support dual-support. first example sh...

Linear dynamic response of simply supported nanobeams subjected to a variable axial force is assessed by Galerkin numerical approach. Constitutive behavior is described by three functional forms of elastic energy densities enclosing nonlocal and strain gradient effects and their combination. Linear stationary dynamics of nanobeams is modulated by an axial force which controls the global stiffne...

this paper proposed analytical solutions for the buckling analysis of rectangular single-layered graphene sheets under in-plane loading on all edges simply is supported. the characteristic equations of the graphene sheets are derived and the analysis formula is based on the nonlocal mindlin plate. this theory is considering both the small length scale effects and transverse shear deformation ef...

In this chapter, we apply the variational principle/weighted residual method based on nonlocal operator for derivation of forms elasticity, thin plate, gradient electro–magneto-elasticity and phase field fracture method. The governing equations are expressed as integral support dual-support. first example shows that elasticity has same form dual-horizon non-ordinary state-based peridynamics. is...

Classical effective descriptions of heterogeneous materials fail to capture the influence of the spatial scale of the heterogeneity on the overall response of components. This influence may become important when the scale at which the effective continuum fields vary approaches that of the microstructure of the material and may then give rise to size effects and other deviations from the classic...

In this paper, the buckling of carbon nanotubes, modeled as nonlocal one dimensional continua within the framework of Euler–Bernoulli beams, is considered. Both a stress gradient and a strain gradient approach are considered and a variational approach is adopted to obtain the variationally consistent boundary conditions. The dependence of the buckling load on the nonlocal parameter has been det...