Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element

Frikha, Ahmed; Zghal, Souhir; Dammak, Fakhreddine

doi:10.1016/j.ast.2018.04.048

Cited by 98 publications

(24 citation statements)

References 88 publications

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“…25 Frikha et al. 26 studied the dynamic behavior of FG-CNTRC plates and shells using a double directors finite shell element, and Tornabene et al. 27 applied GDQ solution for free vibrations of FG and laminated doubly curved shells and panels of revolution with a free-form meridian.…”

Section: Introductionmentioning

confidence: 99%

Vibration and stability analysis of functionally graded CNT-reinforced composite beams with variable thickness on elastic foundation

Mohseni

Shakouri

2019

Proceedings of the IMechE

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The free vibration and buckling of functionally graded carbon nanotube reinforced composite beams with variable thickness resting on elastic foundations are investigated in the present paper. To account rotary inertia and transverse shear deformation effects, the Timoshenko beam theory is employed and governing equations are derived using Hamilton's principle. The obtained equations are solved using generalized differential quadrature method. Different carbon nanotube distributions through the thickness are considered, and the rule of mixture is used to describe the effective material properties of the functionally graded reinforced beams. The results are validated with available investigations, and the effects of boundary conditions, nanotube volume fraction and distribution, foundation and thickness ratio on both natural frequency and buckling load are studied. Finally, due to the weight optimization in aerospace and turbomachinery applications, the optimum beam shape and nanotube distribution are suggested to achieve the most capacity of bearing axial loads with fixed weight.

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Section: Introductionmentioning

confidence: 99%

Vibration and stability analysis of functionally graded CNT-reinforced composite beams with variable thickness on elastic foundation

Mohseni

Shakouri

2019

Proceedings of the IMechE

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“…The functionally graded material (FGM) is a novel type of composite material whose mechanical properties smoothly and continuously vary in a preferred direction [11][12][13][14]. To better use the superior mechanical properties of carbon-based nanofillers and inspire from the concept of FGM, the functionally graded carbon nanotube-reinforced composite (FG-CNTRC) [15][16][17] and functionally graded graphene nanoplatelet reinforced composite (FG-GPLRC) [18][19][20] have been introduced, where the weight fractions of the CNTs and GPLs vary in the thickness direction.…”

Section: Introductionmentioning

confidence: 99%

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

Wang

Xie

et al. 2019

Nanomaterials

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A novel functionally graded (FG) polymer-based nanocomposite reinforced by graphene nanoplatelets is proposed based on a new distribution law, which is constructed by the error function and contains a gradient index. The variation of the gradient index can result in a continuous variation of the weight fraction of graphene nanoplatelets (GPLs), which forms a sandwich structure with graded mechanical properties. The modified Halpin–Tsai micromechanics model is used to evaluate the effective Young’s modulus of the novel functionally graded graphene nanoplatelets reinforced composites (FG-GPLRCs). The bending and elastic vibration behaviors of the novel nanocomposite beams are investigated. An improved third order shear deformation theory (TSDT), which is proven to have a higher accuracy, is implemented to derive the governing equations related to the bending and vibrations. The Chebyshev–Ritz method is applied to describe various boundary conditions of the beams. The bending displacement, stress state, and vibration frequency of the proposed FG polymer-based nanocomposite beams under uniformly distributed loads are provided in detail. The numerical results show that the proposed distributions of GPL nanofillers can lead to a more effective pattern of improving the mechanical properties of GPL-reinforced composites than the common ones.

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“…Shao et al (2017a) adopted an enhanced reverberation ray matrix approach to assess the transient response of composite laminated shallow shells with general boundary conditions based on the first-order shear deformation shallow shell theory and the classical shallow shell theory. Frikha et al (2018) used a linear discrete double directors finite element model and Newmark's algorithm to study the dynamic behavior of functionally graded carbon nanotubes-reinforced shells. incorporated the Bubnov-Galerkin method and Runge-Kutta method to evaluate the nonlinear transient response of imperfect shallow shells.…”

Section: Introductionmentioning

confidence: 99%

A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries

et al. 2019

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The dynamic behavior of cylindrical shells with arbitrary boundaries is studied in this paper. Love's shell theory and Hamilton's principle are employed to derive the motion equations for cylindrical shells. A semi-analytical methodology, which incorporates Durbin's inverse Laplace transform, differential quadrature method and Fourier series expansion technique, is proposed to investigate this phenomenon. The use of the differential quadrature method provides a solution in terms of the axial direction whereas the use of Durbin's numerical inversion method generates a solution in the time domain. Comparison of calculated frequency parameters to that derived from the literature illustrates the effectiveness of the method. Specifically, convergence tests indicate that the present approach has a rapid convergence, the time-history response and the Navier's solution are in great agreement. Comparisons between time-history responses derived by two shell theories show that the results fit well with each other when the thickness-radius ratios are small enough. An analysis of the influences of boundaries on the time-history response of cylindrical shells indicates that the peak displacement is closely related to the degrees of freedom of boundaries. The influences of the length-radius ratios and the thickness-radius ratios on the peak displacement are further investigated.

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Dynamic analysis of functionally graded carbon nanotubes-reinforced plate and shell structures using a double directors finite shell element

Cited by 98 publications

References 88 publications

Vibration and stability analysis of functionally graded CNT-reinforced composite beams with variable thickness on elastic foundation

Vibration and stability analysis of functionally graded CNT-reinforced composite beams with variable thickness on elastic foundation

Bending and Elastic Vibration of a Novel Functionally Graded Polymer Nanocomposite Beam Reinforced by Graphene Nanoplatelets

A semi-analytical method for the dynamic analysis of cylindrical shells with arbitrary boundaries

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