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Analytical assessment of the axisymmetric snap-through behaviour of FG_CNTRC spherical shells under uniform external pressure incorporating the CNTs agglomeration effects

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Abstract

In the present paper, the geometrical nonlinear behaviour of the sandwich shallow spherical shells made of the functionally graded carbon nanotube-reinforced composites is assessed. In order to solve the proposed problem, the equilibrium, compatibility and constitutive equations are extended based on the first-order shear deformation theory. The obtained system of nonlinear differential equations is solved by employing an analytical approach based on the modified interactions method, which results a closed-form relationship between external load and deformation of the shell. Firstly, the obtained closed-form formula is validated by comparing the corresponding results with those obtained by other methods such as finite element method. After the validation procedure, the mentioned closed-form solution is employed to perform a comprehensive parametric study incorporating the mechanical and geometrical properties, such as the effects of CNTs agglomerating, depth and boundary conditions of the shell. The obtained results in the parametric studies show that all of the parameters can affect the buckling load, stability region and intensity of the instability (difference of upper and lower limit loads).

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Authors and Affiliations

  1. Department of Civil Engineering, Isfahan University of Technology, Isfahan, Iran

    Mohammad Amin Shahmohammadi & Sayed Mohamad Mirfatah

  2. School of Engineering, Apadana Higher Education Institute, Shiraz, Iran

    Alireza Houshmand-Sarvestani

  3. Department of Mechanical Engineering, Ilam University, Ilam, 69315-516, Iran

    Hamzeh Salehipour

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  1. Mohammad Amin Shahmohammadi
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  2. Sayed Mohamad Mirfatah
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  3. Alireza Houshmand-Sarvestani
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Correspondence to Hamzeh Salehipour.

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Shahmohammadi, M.A., Mirfatah, S.M., Houshmand-Sarvestani, A. et al. Analytical assessment of the axisymmetric snap-through behaviour of FG_CNTRC spherical shells under uniform external pressure incorporating the CNTs agglomeration effects. Eur. Phys. J. Plus 136, 748 (2021). https://doi.org/10.1140/epjp/s13360-021-01724-1

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