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Structural Engineering and Mechanics
  Volume 65, Number 1, January10 2018 , pages 033-41

Finite element vibration analysis of nanoshell based on new cylindrical shell element
Iman Soleimani, Yaghoub T. Beni and Mohsen B. Dehkordi

    In this paper, using modified couple stress theory in place of classical continuum theory, and using shell model in place of beam model, vibrational behavior of nanotubes is investigated via the finite element method. Accordingly classical continuum theory is unable to correctly compute stiffness and account for size effects in micro/nanostructures, higher order continuum theories such as modified couple stress theory have taken on great appeal. In the present work the mass-stiffness matrix for cylindrical shell element is developed, and by means of size-dependent finite element formulation is extended to more precisely account for nanotube vibration. In addition to modified couple stress cylindrical shell element, the classical cylindrical shell element can also be defined by setting length scale parameter to zero in the equations. The boundary condition were assumed simply supported at both ends and it is shown that the natural frequency of nano-scale shell using the modified coupled stress theory is larger than that using the classical shell theory and the results of Ansys. The results have indicated using the modified couple stress cylindrical shell element, the rigidity of the nano-shell is greater than that in the classical continuum theory, which results in increase in natural frequencies. Besides, in addition to reducing the number of elements required, the use of this type of element also increases convergence speed and accuracy.
Key Words
    modified couple stress theory; FEM; cylindrical shell element; size dependent; Thin Shell Theory
Iman Soleimani: Mechanical Engineering Department, Shahrekord University, Shahrekord, Iran
Yaghoub T. Beni and Mohsen B. Dehkordi: Faculty of Engineering, Shahrekord University, Shahrekord, Iran

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