The present work is aimed at analyzing free longitudinal vibrations of nanorods composed a functionally graded (FG) material with deformable boundaries within hardening nonlocal elasticity approach. For this purpose, FG nanorod the ceramic and metal constituents considered to be elastically supported by means axial springs both ends. Then analytical method based on association Fourier sine seri...

A mode III crack problem in a functionally graded material (FGM) modeled by anisotropic strain gradient elasticity theory is solved by the integral equation method. The gradient elasticity theory has two material characteristic lengths ` and `′, which are responsible for volumetric and surface strain-gradient terms, respectively. The governing differential equation of the problem is derived ass...

The nanostructures under rotation have high promising future to be used in nano-machines, nano-motors and nano-turbines. They are also one of the topics of interests and it is new in designing of rotating nano-systems. In this paper, the scale-dependent vibration analysis of a nanoplate with consideration of the axial force due to the rotation has been investigated. The governing equation and b...

In this article, small scale effects on free vibration analysis of non-uniform nanobeams is discussed. Small scale effects are modelled after Eringen’s nonlocal elasticity theory while the non-uniformity is presented by exponentially varying width among the beams length with constant thickness. Analytical solution is achieved for free vibration with different boundary conditions. It is shown th...

The interrelations between weight-function upscaling (measurement) and the definition of various nonlocal operators is explored. Let < f > = f∗g where f∗g is the convolution product which represents the effect of upscaling via an instrument (defined by g) on a field variable f and its localized counterpart. Nonlocal field variables are defined and employed for upscaling. In this talk it will be...

The multi-mode propagation and diffusion properties are crucial informations when studying complex waveguides. In this paper, firstly, the three-dimensional modeling of micro-sized structures is introduced by using second strain gradient theory. constitutive relation deduced while six quintic Hermite polynomial shape functions employed for displacement field. weak formulations including element...

We derive strain-gradient plasticity from a nonlocal phase-field model of dislocations in plane. After scaling, the elastic interaction we continuous energy with linear growth depending on measure which characterizes macroscopic dislocation density as well effective representing far-field between dislocations. Relaxation and formation microstructures at intermediate scales are automatically inc...