Journal of Theoretical
and Applied Mechanics

56, 4, pp. 1153-1162, Warsaw 2018
DOI: 10.15632/jtam-pl.56.4.1153

Mechanical nature of a single walled carbon nanotube using Legendre’s polynomials

Parul Tiwari, Priyanka Nagar
This paper is concerned with the mechanical response of a single-walled carbon nanotube.
Euler-Bernoulli’s beam theory and Hamilton’s principle are employed to derive the set of
governing differential equations. An efficient variational method is used to determine the
solution of the problem and Legendre’s polynomials are used to define basis functions. Significance
of using these polynomials is their orthonormal property as these shape functions
convert mass and stiffness matrices either to zero or one. The impact of various parameters
such as length, temperature and elastic medium on the buckling load is observed and the
results are furnished in a uniform manner. The degree of accuracy of the obtained results
is verified with the available literature, hence illustrates the validity of the applied method.
Current findings show the usage of nanostructures in vast range of engineering applications.
It is worth mentioning that completely new results are obtained that are in validation with
the existing results reported in literature.
Keywords: Euler-Bernoulli’s beam theory, nonlocal elasticity theory, Legendre’s polynomial, aspect ratio, critical buckling load, Winkler and Pasternak elastic constants


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