We describe an approach to nonlocal, nonlinear advection in one dimension that extends the usual pointwise concepts to account for nonlocal contributions to the flux. The spatially nonlocal operators we consider do not involve derivatives. Instead, the spatial operator involves an integral that, in a distributional sense, reduces to a conventional nonlinear advective operator. In particular, we...

In this research, analysis of nonlocal magneto-electro-thermo-elastic of a functionally graded nanobeamdue to magneto-electro-elastic loads has been done. In order to formulate the problem the Timoshenko theory of beams is utilized. The principle of virtual work, Hamilton’s principle as well as nonlocal magneto-electro-thermo-elastic relations has been recruited to derive the governing eq...

This study presents a generalized multiscale nonlocal elasticity theory that leverages distributed order fractional calculus to accurately capture coexisting and effects within macroscopic continuum. The behavior is captured via constitutive relations derived from thermodynamic formulation. governing equations of the inhomogeneous continuum are obtained Hamilton principle. As generalization con...

The present work mainly studies the free vibration of circular magneto-electro-elastic (MEE) nano-plates based on the Kirchhoff’s plate theory within the framework of nonlocal elasticity theory to account for the small scale effect. The MEE nano-plate studied here is considered to be fully clamped and subjected to the external magnetic and electric potentials. Using nonlocal constitutive relati...

In this paper, we apply Shannon wavelet and Galerkin method to deal with the numerical solution of the natural boundary integral equation of plane elasticity probem in the upper half-plane. The fast algorithm is given and only 3K entries need to be computed for one 4K × 4K stiffness matrix. Keyword: plane elasticity problem, natural integral equation, Shannon wavelet, Galerkin-wavelet method.

Article history: Received 20 September 2016 Received in revised form 11 May 2017 Accepted 14 May 2017 Available online 10 June 2017 In this paper, free longitudinal vibration of nanorods is investigated from the wave viewpoint. The Eringen’s nonlocal elasticity theory is used for nanorods modelling. Wave propagation in a medium has a similar formulation as vibrations and thus, it can be used to...

In this paper, we study a nonlocal parabolic problem arising in the study of microelectro mechanical system. The nonlocal nonlinearity involved is related to an integral over the spatial domain. We first give the structure of stationary solutions. Then we derive the convergence of global (in time) solution to the maximal solution as the time tends to infinity. Finally, we provide some quenching...

We give an overview on existence results in nonlinear peridynamics, a nonlocal elasticity theory, and compare these results with those known for classical nonlinear elastodynamics. In peridynamics, it is possible to obtain stronger results under equal or even less restrictive assumptions on the stress.