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. We conclude that even though peridynamics was developed in the beginning of the current century, it is possible to obtain stronger results under equal or even less restrictive assumptions on the stress. Etienne Emmri...

in this paper, eringen’s nonlocal elasticity and timoshenko beam theories are implemented to analyze the bending vibration for non-uniform nano-beams.  the governing equations and the boundary conditions are derived using hamilton’s principle. a generalized differential quadrature method (gdqm) is utilized for solving the governing equations of non-uniform timoshenko nano-beam for pinned-pinned...

Abstract In this paper vibrations of the isotropic micro/nanoplates subjected to transverse and in-plane excitation are investigated. The governing equations problem based on von Kármán plate theory Kirchhoff–Love hypothesis. small-size effect is taken into account due nonlocal elasticity theory. formulation mixed employs Airy stress function. two-mode approximation deflection application Bubno...

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...

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 article, the nonlocal biaxial buckling load and bending analysis of polymeric piezoelectric nanoplate reinforced by carbon nanotube (CNT) considering the surface stress effect is presented. This plate is subjected to electro-magneto-mechanical loadings. Eshelby-Mori-Tanaka approach is used for defining the piezoelectric nanoplate material properties. Navier’s type solution is employed t...

Abstract The geometrically nonlinear vibrations of simply supported double-layer graphene sheet systems under in-plane magnetic field are considered in the presented manuscript. interaction between layers is taken into account due to van der Waals forces. investigation based on nonlocal elasticity theory, Kirchhoff plate theory and von Kármán theory. effect Lorentz force Maxwell’s equations. go...