This paper addresses the influence of boundary conditions and small-scale effect on the free vibration of nano-plates using molecular dynamics (MD) and nonlocal elasticity theory. Based on the MD simulations, Large-scale Atomic/Molecular Massively Parallel Simulator (LAMMPS) is used to obtain fundamental frequencies of single layered graphene sheets (SLGSs) which modeled in this paper as the mo...

bending analysis of multilayer graphene sheets (mlgss) subjected to non-uniform shear and normal tractions is presented. the constitutive relations are considered to be non-classical based on nonlocal theory of elasticity. based on the differential transformation method, numerical illustrations are carried out for circular and annular geometries. the effects of nano scale parameter, radius of c...

In this paper, we study the correlation of tissue (i.e. prostate) elasticity with the spread and aggression of prostate cancers. We describe an improved, in-vivo method that estimates the individualized, relative tissue elasticity parameters directly from medical images. Although elasticity reconstruction, or elastograph, can be used to estimate tissue elasticity, it is less suited for in-vivo ...

In present study, thermo-elastic buckling analysis of multi-layer orthotropic annular/circular graphene sheets is investigated based on Eringen’s theory. The moderately thick and also thick nano-plates are considered. Using the non-local first and third order shear deformation theories, the governing equations are derived. The van der Waals interaction between the layers is simulated for multi-...

Carnegie Mellon University, Pittsburgh, PA, USA. E-:mail: [email protected] . Abstract. In finite elasticity, the traditional local boundary-value problems are rarely appropriate. More often one has to consider non-local environmental loads. This paper gives a general description of schemes for formulating such non-local problems. Interesting examples are cavity problems, special cases of whi...

We initiate the development of a theory of the elasticity of nanoscale objects based upon new physical concepts which remain properly defined on the nanoscale. This theory provides a powerful way of understanding nanoscale elasticity in terms of local group contributions and gives insight into the breakdown of standard continuum relations. We also give two applications. In the first, we show ho...

For certain a, b ∈ N, the Arithmetic Congruence Monoid M(a, b) is a multiplicatively closed subset of N given by {x ∈ N : x ≡ a (mod b)}∪{1}. An irreducible in this monoid is any element that cannot be factored into two elements, each greater than 1. Each monoid element (apart from 1) may be factored into irreducibles in at least one way. The elasticity of a monoid element (apart from 1) is the...

Abstract Two nonlocal approaches are applied to the borehole geometry, herein simply modelled as a circular hole in an infinite elastic medium, subjected remote biaxial loading and/or internal pressure. The former approach lies within framework of Gradient Elasticity (GE). Its characteristic is material behaviour and local failure criterion, hence related stress concentration factor. latter Fin...