Buckling Analysis of a Double-Walled Carbon Nanotube Embedded in an Elastic Medium Using the Energy Method

The axially compressed buckling of a double-walled carbon nanotabe surrounded by an elasticmedium using the energy and the rayleigh-ritz methods is investigated in this paper. in thisresearch, based on the elastic shell models at nano scale, the effects of the van der waals forcesbetween the inner and the outer tubes, the small scale and the surrounding elastic medium on thecritical buckling load are considered. normal stresses at the outer tube medium interface are alsoincluded in the current analysis. an expression is derived relating the external pressure to thebuckling mode number, from which the critical pressure can be obtained. it is seen from theresults that the critical pressure is dependent on the outer radius to thickness ratio, the materialparameters of the surrounding elastic medium such as young’s modulus and poisson’s ratio.moreover, it is shown that the critical pressure descend very quickly with increasing the half axialwave numbers.