A method has been proposed for developing structure-property relationships of nano-structured materials. This method serves as a link between computational chemistry and solid mechanics by substituting discrete molecular structures with equivalent-continuum models. It has been shown that this substitution may be accomplished by equating the molecular potential energy of a nano-structured materi...

In the present study, small scale effect on critical buckling loads of triangular nano- composite plates under uniform in-plane compression is studied. Since at nano-scale the structure of the plate is discrete, the size dependent nonlocal elasticity theory is employed to develop an equivalent continuum plate model for this nanostructure incorporating the changes in its mechanical behavior. The...

Let 8 denote the real line. If TQ& and r £ 8 , we set {t+r: / £ J H } = r [ r ] . In [ l ] we have proved these two theorems: (BK) Let S C S , T C 8 , S be at most enumerable and T be of first category. Then 8 contains a residual subset R such that SC\T\r\ is empty for every rÇzR. (BM) Let S C S , 2"C8, S be at most enumerable and T be of measure zero. Then 8 contains a subset R such that 8— Ri...

the the main objective of this research paper is to present 3-d elasticity solution for free vibration analysis of elastically supported continuously graded carbon nanotube-reinforced (cgcntr) annular plates. the volume fractions of oriented, straight single-walled carbon nanotubes (swcnts) are assumed to be graded in the thickness direction. an equivalent continuum model based on the eshelby-m...

This study presents a modified continuum model to investigate the vibration behavior of single and multi-carbon nanotubes (CNTs). Two parameters are exploited to consider size dependence; one derived from the energy equivalent model and the other from the modified couple stress theory. The energy equivalent model, derived from the basis of molecular mechanics, is exploited to describe size-depe...

It has long been argued that the continuum limit of the 3D Ising model is equivalent to a string theory. Unfortunately, in the usual starting point for this equivalence – a certain lattice theory of surfaces – it is not at all obvious how to take the continuum limit. In this note, I reformulate the lattice theory of surfaces in a fashion such that the continuum limit is straightforward. I go on...