The current trend in microelectronics towards miniaturization has pushed for an interest in theories intended to explain the behavior of materials at small scales. In particular, an increase in yield strength with decreasing size has been experimentally observed in several materials and under different loading conditions. A class of non-classical continuum mechanics theories has been recently e...

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...

Atomic-like systems in which electronic motion is two dimensional are now realizable as " quantum dots ". In place of the attraction of a nucleus there is a confining potential, usually assumed to be quadratic. Additionally, a perpendicular magnetic field B may be present. We review some recent rigorous results for these systems. We have shown that a Thomas-Fermi type theory for the ground stat...

deflection analysis of a simply supported microbeam subjected to a concentrated load at the middle is investigated on the basis of a shear deformable beam theory and non-classical theory. effects of shear deformation and small size are taken into consideration by hyperbolic shear deformable beam theory and modified strain gradient theory, respectively. the governing differential equations and c...

In this paper the nano conical shell model is developed based on modified strain gradient theory. The governing equations of the nano truncated conical shell are derived using the FSDT, and the size parameters through modified strain gradient theory have been taken into account. Hamilton’s principle is used to obtain the governing equations, and the shell’s equations of motion are derived with ...

In the present study, the buckling analysis of the rectangular nanoplate under biaxial non-uniform compression using the modified couple stress continuum theory with various boundary conditions has been considered. The simplified first order shear deformation theory (S-FSDT) has been employed and the governing differential equations have been obtained using the Hamilton’s principle. An analytic...

Non invasive ultrasound-based imaging systems are being more commonly used in clinical bio-microscopy applications for both ex vivo and in vivo analysis of tissue pathological and physiological states. These modalities usually employ high-frequency ultrasound systems to overcome spatial resolution limits of conventional clinical diagnostic approaches. Biological tissues are non continuous, non ...

We develop a point-free construction of the classical onedimensional continuum, with an interval structure based on mereology and either a weak set theory or logic of plural quanti…cation. In some respects this realizes ideas going back to Aristotle, although, unlike Aristotle, we make free use of classical "actual in…nity". Also, in contrast to intuitionistic, Bishop, and smooth in…nitesimal a...

The Cosserat continuum is used in this paper to regularize the ill-posed governing equations of Cauchy/Maxwell continuum. Most available constitutive models adopt yield and plastic potential surfaces with a circular deviatoric section. This too crude an approximation which hinders application into practice, particularly geotechnical domain. An elasto-plastic model for linear formulation here pr...