In this paper, analysis of linear and nonlinear buckling of relatively thick orthotropic graphene sheets is carried out under mechanical load based on elasticity theories. With the help of  nonlocal elasticity theory, the principle of virtual work, first order shear theory and Von-Karman nonlinear strain, the dominant relationship in terms of obtained displacements has been obtained, and the me...

In this study, the small scale effect on the linear free-field vibration of a nano-circular plate has been investigated using nonlocal elasticity theory. The formulation is based on the classical theory and the linear strain in cylindrical coordinates. To take into account the small scale and the linear geometric effects, the governing differential equation based on the nonlocal elasticity theo...

In this paper, local and nonlocal image processing are unified, within the same framework, by defining discrete derivatives on weighted graphs. These discrete derivatives allow to transcribe continuous partial differential equations and energy functionals to partial difference equations and discrete functionals over weighted graphs. With this methodology, we consider two gradient-based problems...

Buckling analysis of a functionally graded (FG) nanobeam resting on two-parameter elastic foundation is presented based on third-order shear deformation beam theory (TOSDBT). The in-plane displacement of TOSDBT has parabolic variation through the beam thickness. Also, TOSDBT accounts for shear deformation effect and verifies stress-free boundary conditions on upper and lower faces of FG nanobea...

Abstract The bending of sandwich nanoplates made functionally graded (FG) porous core and electromagnetic layers is explored for the first time through a nonlocal strain gradient theory four-unknown shear deformation theory. proposed model can account both impacts. Therefore, stiffness enhancement reduction processes are observed. porosities in nanoplate modeled with even uneven distribution pa...

We study the large time behavior of nonlinear and nonlocal equation \begin{document}$ v_t+(- \Delta_p)^sv = f \, , $\end{document} where $ p\in (1, 2)\cup (2, \infty) $, s\in (0, 1) and$ (- \Delta_p)^s v\, (x, t) 2 {\rm{P.V.}} \int_{ \mathbb{R}^n}\frac{|v(x, t)-v(x+y, t)|^{p-2}(v(x, t))}{|y|^{n+sp}}\, dy. $This arises as a gradient flow in fractional Sobolev spaces. obtain sharp decay estimates...

We study well-posedness of a class of nonlocal interaction equations with spatially dependent mobility. We also allow for the presence of boundaries and external potentials. Such systems lead to the study of nonlocal interaction equations on subsets M of Rd endowed with a Riemannian metric g. We obtain conditions, relating the interaction potential and the geometry, which imply existence, uniqu...