A New Size-Dependent Cylindrical Shell Element Based on Modified Couple Stress Theory (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, using modified couple stress theory, a new cylindrical shellelement is introduced. Here, using modified couple stress theory in place of classicalcontinuum theory, and using shell model in place of beam model which has beenused in previous research, vibrational behavior and buckling behavior of nanotubesis investigated via the finite element method. In addition, the new cylindrical shellelement is defined, the mass-stiffness matrix is developed, and the use of the superelement and size-dependent finite element formulation together with shell elementis extended to more precisely account for nanotube vibration and buckling. The newcylindrical shell element has been developed based on super element's shape function.In special cases, in order to investigate the application of the equations developed, thecylindrical nano-shell bending displacement is studied using modified couple stresscylindrical shell element and the results are validated using the analytical method. Inaddition, the effects of parameters such as length scale parameter, length, and thicknesson cylindrical shell displacement are investigated. The results have indicated usingthe super element considerably reduces the amount of computations and analysistime in comparison with the use of molecular dynamic simulation.