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...

This paper proposes a numerical method to the two-dimensional hyperbolic equations with nonlocal integral conditions. The nonlocal integral equation is of major challenge in the frame work of the numerical solutions of PDEs. The method benefits from collocation radial basis function method, the generalized thin plate splines radial basis functions are used.Therefore, it does not require any str...

[1] A local formulation of the sediment flux on a hillslope describes the flux as a unique function of local hillslope conditions at any contour position x, whereas a nonlocal formulation must take into account nonlocal (upslope or downslope) conditions that influence the flux at x. Local formulations are reasonable when particle motions involve small length scales associated with localized bio...

In this article we present the first results on domain decomposition methods for nonlocal operators. We present a nonlocal variational formulation for these operators and establish the well-posedness of associated boundary value problems, proving a nonlocal Poincaré inequality. To determine the conditioning of the discretized operator, we prove a spectral equivalence which leads to a mesh size ...

We exploit a recently developed nonlocal vector calculus to provide a variational analysis for a general class of nonlocal diffusion problems given by a linear integral equation on bounded domains in R. The ubiquity of the nonlocal operator is illustrated by a number of applications ranging from continuum mechanics to graph theory. These applications elucidate different interpretations of the o...

The present paper deals with the eigenvalue problems for oneand two-dimensional second order differential operators with given nonlocal coupled boundary conditions. The corresponding finite-difference (discrete) problems have been investigated in the paper [1]. First of all, we will consider the eigenvalue problem for one-dimensional differential operator with given nonlocal coupled boundary co...