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**Large deflection response-based geometrical nonlinearity of nanocomposite structures reinforced with carbon nanotubes.**
*(English)*
Zbl 1457.74159

Summary: This paper deals with the nonlinear large deflection analysis of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) plates and panels using a finite element method. Based on the first-order shear deformation theory (FSDT), the proposed model takes into account the transverse shear deformations and incorporates the geometrical nonlinearity type. A \(C^0\) isoparametric finite shell element is developed for the present nonlinear model with the description of large displacements and finite rotations. By adopting the extended rule of mixture, the effective material properties of FG-CNTRCs are approximated with the introduction of some efficiency parameters. Four carbon nanotube (CNT) distributions, labeled uniformly distributed (UD)-CNT, FG-V-CNT, FG-O-CNT, and FG-X-CNT, are considered. The solution procedure is carried out via the Newton-Raphson incremental technique. Various numerical applications in both isotropic and CNTRC composite cases are performed to trace the potential of the present model. The effects of the CNT distributions, their volume fractions, and the geometrical characteristics on the nonlinear deflection responses of FG-CNTRC structures are highlighted via a detailed parametric study.

### MSC:

74M25 | Micromechanics of solids |

74A40 | Random materials and composite materials |

74S05 | Finite element methods applied to problems in solid mechanics |

### Keywords:

carbon nanotube (CNT); functionally graded material (FGM); geometrical nonlinearity; large deflection
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\textit{S. Zghal} et al., AMM, Appl. Math. Mech., Engl. Ed. 41, No. 8, 1227--1250 (2020; Zbl 1457.74159)

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### References:

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