Abstract We develop a theory of existence minimizers energy functionals in vectorial problems based on nonlocal gradient under Dirichlet boundary conditions. The model shares many features with the peridynamics and is also applicable to solid mechanics, especially nonlinear elasticity. This was introduced an earlier work, inspired by Riesz’ fractional gradient, but suitable for bounded domains....

In this article free vibration of a Timoshenko nanobeam with variable cross-section is investigated using nonlocal elasticity theory within the scope of continuum mechanics. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width through the beam length with constant thickness. Analytical solution is achiev...

A two-dimensional model composite with elastic reinforcements in a crystalline matrix subject to macroscopic shear is considered using both discrete dislocation plasticity and a nonlocal continuum crystal plasticity theory. Only single slip is permitted in the matrix material. The discrete dislocation results are used as numerical experiments and we explore the extent to which the nonlocal crys...

abstract: in this paper, nonlocal euler–bernoulli beam theory is employed for transverse vibration analysis of an initially pre-stressed size-dependent rotating nanotube. the nonlocal eringen theory takes into account the effect of small size, which enables the present model to become effective in the analysis and design of nanosensors and nanoactuators. governing equations are derived through ...

1. Abdelrahman A.A., Esen I., Özarpa C., Eltaher M.A., 2021, Dynamics of perforated nanobeams subject to moving mass using the nonlocal strain gradient theory, Applied Mathematical Modelling, 96, 215-235. CrossRef Google Scholar

In many practical applications of nanotechnology and in microelectromechanical devices, typical structural components are in the form of beams, plates, shells and membranes. When the scale of such components is very small, the material microstructural lengths become important and strain gradient elasticity can provide useful material modelling. In addition, small scale beams and bars can be use...

In this article, eigenfrequencies of nano-beams under axial loads are assessed by making recourse to the well-posed stress-driven nonlocal model (SDM) and strain-driven two-phase local/nonlocal formulation (NstrainG) elasticity Bernoulli-Euler kinematics. The developed methodology is applicable a wide variety nano-engineered materials, such as carbon nanotubes, modern small-scale beam-like devi...

Recent developments in modeling and analysis of nanostructures are illustrated discussed this paper. Starting with the early theories nonlocal elastic continua, a thorough investigation continuum nano-mechanics is provided. Two-phase local/nonlocal models shown as possible to recover consistency strain-driven purely integral theory, provided that mixture parameter not vanishing. Ground-breaking...

in this article, an analytical solution is developed to study the free vibration analysis offunctionally graded rectangular nanoplates. the governing equations of motion are derived basedon second order shear deformation theory using nonlocal elasticity theory. it is assumed that thematerial properties of nanoplate vary through the thickness according to the power lawdistribution. our numerical...