Stochastic modelling of nanostructures: An engineering perspective

Scarpa, F., and Adhikari, S.,
Fourth International Workshop on Functional and Nanostructured Materials, Gdansk, Poland, September 2007.

Over the past five years there has been extensive research in the reduced mechanical modelling of multiwalled and singlewalled carbon nanotubes. Majority of the proposed modelling techniques are dominated by determinist approaches. However, significant uncertainties have been reported in the measured materials and geometric properties of carbon nanotubes. In this paper, perhaps for the first time, we propose a probabilistic mechanics approach to take account of these uncertainties at the nanoscale. It is considered that the mechanics of a nominally identical set of carbon nanotubes are governed by stochastic partial differential equations. Two approaches, namely a Stochastic Finite Element (SFE) based method and a stochastic beam model have been investigated. The probability density function of the natural frequencies of singlewalled carbon nanotubes is derived in closed-form for three different physically realistic cases. The analytical results are compared with high-fidelity stochastic finite element simulations and available experimental results. The studies taken in the paper indicate that stochastic approach can significantly enhance the applicability of the mechanistic modelling at the nanoscale.
BiBTeX Entry
@INPROCEEDINGS{cp48,
    AUTHOR={F. Scarpa and S. Adhikari},
    TITLE={Stochastic modelling of nanostructures: an engineering perspective},
    BOOKTITLE={Fourth International Workshop on Functional and Nanostructured Materials},
    YEAR={2007},
    Address={Gdansk, Poland},
    Month={September}
}
by Sondipon Adhikari