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 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...

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...

Abstract A challenging task in nonlocal continuum mechanics consists formulating constitutive relations leading to well-posed structural problems. Several strategies have been adopted overcome issues inherent applicability of Eringen’s pure theory nanostructures, such as local/nonlocal mixtures elasticity and integral models involving modified averaging kernels. These can be applied the ill-pos...

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...

In this paper, buckling and free vibration analysis of a circular tapered nanoplate subjected to in-plane forces were studied. The linear variation of the plate thickness was considered in radial direction. Nonlocal elasticity theory was employed to capture size-dependent effects. The Raleigh-Ritz method and differential transform method were utilized to obtain the frequency equations for simpl...

In this paper, axisymmetric free vibration analysis of a circular Nano-plate having variable thickness was studied. The variation in thickness of plate was considered as a linearly in radial direction. Nonlocal elasticity theory was utilized to take into account size-dependent effects. Ritz functions was utilized to obtain the frequency equations for simply supported and clamped boundary. To ve...