Amirkabir University of Technology Amirkabir Journal of Mechanical Engineering 2008-6032 47 2 2016 01 21 Application of Strain Gradient Elasticity in Analysis of Elastic Properties of Single Walled Carbon Nanotubes Application of Strain Gradient Elasticity in Analysis of Elastic Properties of Single Walled Carbon Nanotubes 53 62 406 10.22060/mej.2016.406 FA Mahmood Shokrieh Iman Zibaei Journal Article 2012 12 12 In this paper, the size effect on elastic properties of single- walled nanotubes is evaluated via the strain gradient elasticity approach. For this purpose, rod, torsion bar and Euler- Bernoulli beam models are used. The tension rod model is developed in the present study. The Euler- Bernoulli beam model is utilized and the boundary conditions are modified in the present research. In addition, a model for the rod under torsion is developed. Afterwards, by using the constitutive relation in strain gradient elasticity, the size- dependent elastic properties of carbon nanotube are achieved effectively. The results show that the length of the carbon nanotube is more effective on the Young modulus in comparison with that of on shear modulus and when the length of nanotube decreases, the Young modulus decreases similarly. In this paper, the size effect on elastic properties of single- walled nanotubes is evaluated via the strain gradient elasticity approach. For this purpose, rod, torsion bar and Euler- Bernoulli beam models are used. The tension rod model is developed in the present study. The Euler- Bernoulli beam model is utilized and the boundary conditions are modified in the present research. In addition, a model for the rod under torsion is developed. Afterwards, by using the constitutive relation in strain gradient elasticity, the size- dependent elastic properties of carbon nanotube are achieved effectively. The results show that the length of the carbon nanotube is more effective on the Young modulus in comparison with that of on shear modulus and when the length of nanotube decreases, the Young modulus decreases similarly. https://mej.aut.ac.ir/article_406_8cb22bdd0b7ba1ab13d742e22eed8da2.pdf