• Structural Engineering and Mechanics
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• v.68 no.3
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• pp.313-323
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• 2018

A numerical study is performed to investigate the impacts of thermal loading on the vibration and buckling of functionally graded carbon nanotube-reinforced composite (FG-CNTRC) conical shells. Thermo-mechanical properties of constituents are considered to be temperature-dependent. Considering the shear deformation theory, the energy functional is derived, and applying the variational differential quadrature (VDQ) method, the mass and stiffness matrices are obtained. The shear correction factors are accurately calculated by matching the shear strain energy obtained from an exact three-dimensional distribution of the transverse shear stresses and shear strain energy related to the first-order shear deformation theory. Numerical results reveal that considering temperature-dependent material properties plays an important role in predicting the thermally induced vibration of FG-CNTRC conical shells, and neglecting this effect leads to considerable overestimation of the stiffness of the structure.

• Steel and Composite Structures
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• v.31 no.3
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• pp.243-259
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• 2019

This study deals with the nonlinear static analysis of functionally graded carbon nanotubes reinforced composite (FG-CNTRC) truncated conical shells subjected to axial load based on the classical shell theory. Detailed studies for both nonlinear buckling and post-buckling behavior of truncated conical shells. The truncated conical shells are reinforced by single-walled carbon nanotubes which alter according to linear functions of the shell thickness. The nonlinear equations are solved by both the Airy stress function and Galerkin method based on the classical shell theory. In numerical results, the influences of various types of distribution and volume fractions of carbon nanotubes, geometrical parameters, elastic foundations on the nonlinear buckling and post-buckling behavior of FG-CNTRC truncated conical shells are presented. The proposed results are validated by comparing with other authors.

• Steel and Composite Structures
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• v.44 no.2
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• pp.155-169
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• 2022

In the present paper an analytical model was developed to study the non-linear vibrations of Functionally Graded Carbon Nanotube (FG-CNT) reinforced doubly-curved shallow shells using the Multiple Scales Method (MSM). The nonlinear partial differential equations of motion are based on the FGM shallow shell hypothesis, the non-linear geometric Von-Karman relationships, and the Galerkin method to reduce the partial differential equations associated with simply supported boundary conditions. The novelty of the present model is the simultaneous prediction of the natural frequencies and their mode shapes versus different curvatures (cylindrical, spherical, conical, and plate) and the different types of FG-CNTs. In addition to combining the vibration analysis with optimization algorithms based on the genetic algorithm, a design optimization methode was developed to maximize the natural frequencies. By considering the expression of the non-dimensional frequency as an objective optimization function, a genetic algorithm program was developed by valuing the mechanical properties, the geometric properties and the FG-CNT configuration of shallow double curvature shells. The results obtained show that the curvature, the volume fraction and the types of NTC distribution have considerable effects on the variation of the Dimensionless Fundamental Linear Frequency (DFLF). The frequency response of the shallow shells of the FG-CNTRC showed two types of nonlinear hardening and softening which are strongly influenced by the change in the fundamental vibration mode. In GA optimization, the mechanical properties and geometric properties in the transverse direction, the volume fraction, and types of distribution of CNTs have a considerable effect on the fundamental frequencies of shallow double-curvature shells. Where the difference between optimized and not optimized DFLF can reach 13.26%.