Free high-frequency longitudinal vibrations of an inhomogeneous nanosized rod are studied on the basis nonlocal theory elasticity. The upper part spectrum with wavelength comparable to internal characteristic dimension a nanorod is examined. An equations in integral form Helmholtz kernel, incorporating both local and phases, used as constitutive one. original integro-differential equation reduc...

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.

This study presents the analytical formulation and finite element solution of a fractional-order nonlocal plate under both Mindlin Kirchhoff formulations. By employing consistent definitions for kinematic relations, governing equations associated boundary conditions are derived based on variational principles. Remarkably, model gives rise to self-adjoint positive-definite system that accepts un...

We derive, in path integral approach, the (anomalous) master Ward identity associated with an infinite set of nonlocal conservation laws in two-dimensional principal chiral models.

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, the numerical technique based on hybrid bernoulli and block-pulse functions has been developed to approximate the solution of system of linear volterra integral equations. system of volterra integral equations arose in many physical problems such as elastodynamic, quasi-static visco-elasticity and magneto-electro-elastic dynamic problems. these functions are formed by the hybridi...

In this paper, we present an exact, infinite-series solution to Lorentz nonlocal continuum electrostatics for an arbitrary charge distribution in a spherical solute. Our approach relies on two key steps: (1) re-formulating the PDE problem using boundary-integral equations, and (2) diagonalizing the boundary-integral operators using the fact that their eigenfunctions are the surface spherical ha...

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...

in this paper, on the basis of a new strain gradient elasticity theory, wave propagation in rectangular nanoplates by considering in-plane magnetic field is studied. this strain gradient theory has two gradient parameters and has the ability to compare with the nonlocal elasticity theory. from the best knowledge of author, it is the first time that this theory is used for investigating wave pro...