Nonlinear bending of porous curved beams reinforced by functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach

Anirudh, B.; Zineb, Tarak Ben; Polit, O.; Ganapathi, M.; Prateek, G.

doi:10.1016/j.ijnonlinmec.2019.103346

Cited by 26 publications

(6 citation statements)

References 40 publications

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“…The primary objective of this section is to verify the effectiveness of the established FG-GPLRC beam model through numerical cases and to discuss the impact of structural-, material-, and foundation-related parameters on the nonlinear vibration characteristics of the beam. For the sake of simplicity and clarity of presentation, the details of the arithmetic examples are standardized in advance as: B=0.1m, H=0.1m, L/H=20 (structural parameters); KW=10 6 , KP=10 6 , CD=10 8 (viscoelastic foundation parameters); the base material is set to Epoxy and the reinforcing phase is set to GPL, whose material properties are referenced in Table 1; Nl=30, fg*=1%, and FG-GPLRC distribution type is FG-X (FG-GPLRC material parameters); lGPL=2.5μm, wGPL=1.5μm, hGPL=1.5nm…”

Section: Numerical Results and Analysismentioning

confidence: 99%

“…In accordance with the third-order shear deformation theory and the Gram-Schmidt-Ritz method, Songsuwan et al [7] developed the nonlinear governing equations for FG-GPLRC beams, then compared the linear and nonlinear bending vibration results under a variety of external excitations. Based on the developed finite element analysis model, Anirudh et al [8] discussed the nonlinear bending vibration behavior for curved beams made of FG-GPLRC depending on the load-deflection curve, where the curvature degree and the slenderness ratio of the structure have a strong combined impact on the nonlinear hardening characteristics. Chen et al [9] derived the nonlinear control differential equations for the pore-containing FG-GPLRC beams and solved their free vibration and post-buckling characteristics in the framework of the energy method.…”

Section: Introductionmentioning

confidence: 99%

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A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Wang,

Zhong,

Wang

2024

Preprint

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Combining the spectral geometry method and the incremental harmonic balance method (IHB), the nonlinear analytical model of functionally graded graphene platelet reinforced composite (FG-GPLRC) beams is developed in this paper. Nonlinear free and forced vibration characteristics are studied based on this model containing viscoelastic foundation and geometric nonlinear factors. Geometric nonlinear strain-displacement relationship and Lagrangian energy generalization for the FG-GPLRC beam structure are derived according to the Von-Kármán and Timoshenko theories. The IHB method is applied to track the nonlinear vibration response solution of the reduced-order model, which is constructed by introducing linear modal components into the overall nonlinear dynamic equation of the FG-GPLRC beam. Through comparison of the present solution with those from numerical method and literature, the correctness of the established nonlinear analytical model is evidenced. Further, the influence of material-, geometry-, foundation-related parameters and boundary constraints on the nonlinear frequency parameter and amplitude-frequency response of FG-GPLRC beams rested on viscoelastic foundation is analyzed, which can serve as a theoretical guide for designing and evaluating the dynamic environment adaptation of FG-GPLRC beams.

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Section: Numerical Results and Analysismentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Wang,

Zhong,

Wang

2024

Preprint

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“…On the other hand, extraordinary properties of nanocomposites have made them excellent choices for the design of advanced structural elements in the recent years [ 23 ]. Such ultra-stiff nanomaterials are able to provide big natural frequencies [ 24 , 25 , 26 , 27 ], bear against extreme compressive stimulations [ 28 , 29 , 30 , 31 , 32 , 33 ], and lessen the deflection amplitude [ 34 , 35 , 36 , 37 ] of continuous systems. Lately, investigation of the elastic performance of auxetic nanocomposite-made structures has attracted the attention of the academics.…”

Section: Introductionmentioning

confidence: 99%

Porosity Effects on Static Performance of Carbon Nanotube-Reinforced Meta-Nanocomposite Structures

Ebrahimi

Dabbagh

2023

Micromachines

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A mixture of outstanding merits of polymer nanocomposites (PNCs) and metamaterials can lead to the development of ultra-light meta-nanomaterials whose high sensitivity can be efficiently used in wearable strain sensors. Thus, reliable data about the performance of structural elements manufactured from such meta-nanomaterials are needed before implementing their design. Motivated by this issue, the negative impacts of pores in the microstructure and carbon nanotubes’ (CNTs’) wavy configuration on the nonlinear bending features of thick beams consisted of auxetic CNT-reinforced (CNTR) polymers are probed for the first time. The impacts of distinct porosity distributions on the mechanical reaction of the system are covered in this article. In addition, a very low computationally cost homogenization is implemented herein to consider the waviness’ influence on the reinforcement mechanism in the auxetic PNC material. Moreover, higher-order shear deformation theory (HSDT) is followed and merged with non-linear definition of strain tensor with the aid of von Kármán’s theory to gather the equations describing the problem. Thereafter, the famous Navier’s exact solution is employed towards solving the problem for thick beams with simple supports at both ends. A comparison of our data with those existing in the literature certifies the accuracy of the presented modeling. The outcomes indicate on the remarkable rise in the flexural deformation of the auxetic PNC beam while the coefficient of porosity is raised. It is also shown that utilization of thick-walled cells in the re-entrant lattice can help to control the system’s total deflection. In addition, if the non-ideal shape of the nanofillers is ignored, the deflection of the meta-nanomaterial beam will be much larger than that of ideal calculations.

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“…Notwithstanding a number of studies have been carried out on the mechanical behavior of macroscopical structures like beams [14][15][16][17][18][19][20], plates and shells [21][22][23][24][25], made of functionally graded carbon nanotubes (FG-CNTRC) or graphene nanoplatelets reinforced -A slender and perfectly straight nano-beam of a Euler-Bernoulli type, with a rectangular cross-section, is considered; hence, the influence of thickness stretching and shear deformation are neglected; -…”

Section: Introductionmentioning

confidence: 99%

“…Notwithstanding a number of studies have been carried out on the mechanical behavior of macroscopical structures like beams [ 14 , 15 , 16 , 17 , 18 , 19 , 20 ], plates and shells [ 21 , 22 , 23 , 24 , 25 ], made of functionally graded carbon nanotubes (FG-CNTRC) or graphene nanoplatelets reinforced composites (FG-GNPRC), there is relatively little scientific knowledge about their size-dependent mechanical response at small scale. The FG-CNTRC nano-beam has become a potential candidate for a wide variety of nanosystems and the size effects on their statical and dynamic response should be further developed.…”

Section: Introductionmentioning

confidence: 99%

Dynamic Response of Multilayered Polymer Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) Nano-Beams in Hygro-Thermal Environment

2021

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This work studies the dynamic response of Bernoulli–Euler multilayered polymer functionally graded carbon nanotubes-reinforced composite nano-beams subjected to hygro-thermal environments. The governing equations were derived by employing Hamilton’s principle on the basis of the local/nonlocal stress gradient theory of elasticity (L/NStressG). A Wolfram language code in Mathematica was written to carry out a parametric investigation on the influence of different parameters on their dynamic response, such as the nonlocal parameter, the gradient length parameter, the mixture parameter and the hygro-thermal loadings and the total volume fraction of CNTs for different functionally graded distribution schemes. It is shown how the proposed approach is able to capture the dynamic behavior of multilayered polymer FG-CNTRC nano-beams under hygro-thermal environments.

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Nonlinear bending of porous curved beams reinforced by functionally graded nanocomposite graphene platelets applying an efficient shear flexible finite element approach

Cited by 26 publications

References 40 publications

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

A SGM-IHB approach for nonlinear free and forced vibration analysis of FG-GPLRC beams rested on viscoelastic foundation

Porosity Effects on Static Performance of Carbon Nanotube-Reinforced Meta-Nanocomposite Structures

Dynamic Response of Multilayered Polymer Functionally Graded Carbon Nanotube Reinforced Composite (FG-CNTRC) Nano-Beams in Hygro-Thermal Environment

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