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Finite element nonlinear transient modelling of carbon nanotubes reinforced fiber/polymer composite spherical shells with a cutout

  • Sang-Youl Lee EMAIL logo and Ji-Gwang Hwang
Published/Copyright: December 18, 2019
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Nanotechnology Reviews
From the journal Nanotechnology Reviews Volume 8 Issue 1

Abstract

This study dealt with geometrically nonlinear transient behaviors of carbon nanotube/fiber/polymer composite (CNTFPC) spherical shells containing a central cutout. A multiscale analysis using the Hewitt and Malherbe model was performed to determine the carbon nanotube (CNT)weight ratios, thickness-radius ratios, thickness-length ratios of CNTs, and cutout sizes. Based on the first-order shear deformation plate theory (FSDT),the Newmark method and Newton-Raphson iteration were used for the nonlinear dynamic solution. The proposed approach in this study has been verified by previous studies. Parametric results showed the significance of a proper CNT ratio and curvature for better structural performance on the nonlinear dynamic behaviors of CNTFPC spherical shells with a cutout.

Keywords: CNTFPC spherical shell; Finite element nonlinear transient modelling; carbon nanotube; multiscale model; CNT weight ratio

1 Introduction

Carbon-based nanomaterials have been applied to various engineering fields because of their excellent mechanical properties. In some of these fields, compound and application technologies of carbon nanotubes (CNTs) have greatly increased the need for multifunctional materials for semiconductors, composites, flexible displays, etc. The reason for this is that CNTs have higher Young’s modulus and tensile strength than those of existing materials. For example, CNTs are a hundred times stronger than steel, but are three to five times lighter. Moreover, the strain at the breaking point of CNTs is about 10%,which is much higher than that of composite materials. For these reasons, theoretical and experimental studies related to CNTs have been performed by a number of investigators. However, most of these studies were focused on dispersion or compound technologies from a micromechanical point of view [1, 2, 3, 4, 5].

The macromechanical performances of CNTs have been studied by several researchers for carbon nanotube reinforced composite (CNTRC) beams or plates. Wattanasakulpong and Ungbhakorn [6] dealt with the closed forms for the bending, buckling, and vibration responses of CNTRC beams resting on an elastic foundation. Zhu et al. [7] studied the static and free vibration of functional graded(FG) CNTRC plates according to the first-order shear deformation theory (FSDT), and the study was extended to the Levy method for the natural frequency analysis of FG-CNT composites under in-plane loads using the higher-order shear deformation plate theory (HSDT) [8]. The multi-scale mechanical behaviors of three-phase CNTs/fiber/polymer laminated composites have also been studied by a few investigators [9]. In the studies, the effective material properties of the CNT/fiber/polymer composite (CNTFPC) structures were computed using a combination of the Halpin–Tsai scheme and a micromechanical approach. However, these studies dealt with CNTRC or CNTFPC rectangular or skew-type structures, which are not considered in geometrical curvature effects.

Recently, structural analyses of cylindrical panels or shells made of CNTRCs or CNTFPCs have been carried out for various parameters. For example, García-Macías et al. [10] performed a buckling analysis of FG-CNT-reinforced cylindrical panels subjected to axial compression and shear. Mirzaeia and Kianib [11] studied the free vibration of FG-CNT-reinforced composite cylindrical panels. Zhang et al. [12] investigated the static and dynamic behaviors of FG-CNT-reinforced cylindrical panels. These studies were further extended to deal with the dynamic instability problems of FG-CNTRC cylindrical panels [13, 14, 15]. However, all of these studies were limited in their coverage of the CNT effects of CNTRC cylindrical panels without a cutout. Cutout in composite structures has significant effects on the dynamic behaviors, especially for the geometrical non-linearity. To the best of this author’s knowledge, a nonlinear transient analysis of CNTFPC laminated spherical shells with a cutout is not yet widely available in the literature. Bhardwaj et al. [16] dealt with the nonlinear static and dynamic analysis of CNT reinforced composite plate-type structures without a cutout. The nonlinear static or dynamic behaviors of laminated composites with a cutout has been studied by other investigators; however, most relevant studies have dealt with the typical composites, which are not reinforced by CNTs [17, 18, 19].

In this study, the multi-scale nonlinear dynamic behaviors of CNTFPC laminated spherical shells with a central cutout was investigated. The multiscale analysis using the modified Halpin-Tsai model were performed on the basis of the FSDT. Parametric examples were focused on the correlation between radius-length ratios, cutout sizes, and CNT weight ratios. The interactions between the parameters also showed different trends for the cutout sizes, which are difficult to predict. The significance of each parameter in predicting the geometrically dynamic non-linearity of CNTFPC spherical shells with a cutout is investigated.

2 Theoretical formulation

2.1 Multiscale formulation for CNTFPC shells

To perform a multiscale analysis of CNT/fiber/polymer multi-phase composites (referred to as CNTFPC), we used the modified Halpin-Tsai model (refferred as Hewitt and Malherbe model) and micromechanical approaches. CNTFPC shells were dealt with in this study as they were assumed to have a perfect distribution of CNTs and to be impregnated with polymer. First, the effective elastic modulus of CNT-reinforced resins (referred to as CNTRC) can be determined using the Halpin-Tsai equation as [20]

(1)Ecnr=Ere381+2(lcnt/dcnt)γdlVcnt1−γdlVcnt+581+2γddVcnt1−γddVcnt,

where,

(2)γdd=(E11cnt/Ere)−(dcnt/4tcnt)(E11cnt/Ere)+(dcnt/2tcnt),γdl=(E11cnt/Ere)−(dcnt/4tcnt)(E11cnt/Ere)+(lcnt/2tcnt),

where, Ecnr is the effective elastic modulus of CNT-reinforced resins, and EreandE11cntare Young’s modulus of resin and single-walled carbon nanotubes (SWCNTs) or multi-walled carbon nanotubes (MWCNTs), respectively. dcnt, lcnt, and tcnt are the diameter, length, and thickness of SWCNTs or MWCNTs. The Possion’s ratio (νcnr12 ) and mass density (ρcnr) are determined from the rule of mixture as

(3)ν12cnr=νcntVcnt+νreVre
(4)ρcnr=ρcntVcnt+ρreVre

where, νcnt and νre are Possion’s ratios of CNTs and resin, and ρcnt and ρre are mass densities of CNTs and resin, and Vre is the volume fraction of resin, respectively. In Eqs. (9)–(10), the volume fraction (Vcnt) of CNTs can be determined as

(5)Vcnt=wcntwcnt+(ρcnt/ρre)−(ρcnt/ρre)wcnt ,

where, wcnt denotes the weight ratio of the SWCNTs or MWCNTs.

Next, the CNT-reinforced resins are reinforced again with fibers, which are the CNTFPC. The effective longitudinal Young’s modulus (E11) and the Poisson’s ratio (ν12) of the CNTFPC spherical shells are written using the rule of mixture as

(6)E11=EfVf+Ecnr(1−Vf),
(7)ν12=ν12fVf+ν12cnr(1−Vf).

where, Ef , νf12 and Vf mean the Young’s modulus, Poisson’s ratio and the volume fraction of the fiber, respectively. The transverse Young’s modulus (E22) is given by

(8)E22=Ere1+χ1η1Vf1−η1Vf,η1=(Ef/Ecnr)−1(Ef/Ecnr)+χ1.

The in-plane shear modulus (G12) determined from Halphin–Tsai formulation is the similar form as that obtained using Eq. (8).

(9)G12=Gre1+χ2η2Vf1−η2Vf, η2=(Gf/Gcnr)−1(Gf/Gcnr)+χ2,

where, Gre and Gcnr are the shear modulus of the resin and CNT-reinforced resins, and Gf is the shear modulus of the fiber. Hewitt and Malherbe proposed a modified equation for the calibration of χ2 and χ2 for a high volume fraction,

(10)χ1=2.0+40(Vf)10,  χ2=1.0+40(Vf)10

It should be noted that the results obtained from Eq. (9) were in good agreement with the experimental data from Hashin (1970) [21]. For this reason, this study applied the modified Halpin-Tsai equation from Hewitt and Malherbe for the effective in-plane shear modulus.

2.2 Nonlinear transient modelling for CNTFPC spherical shells

In this study, we developed a finite element nonlinear dynamic model based on the FSDT. For the sake of completeness, nonlinear transient formulations are presented here. Figure 1 shows the geometry and coordinate system (ξ1, ξ, ζ ) of the laminated CNTFPC spherical shell containing a central cutout. Based on the shell theory of Sanders [22], the strain components for the spherical shells with the principal radii of curvature R1 and R2 can be written as [23]

Figure 1 A laminated CNTFPC spherical shell with a central cutout
Figure 1

A laminated CNTFPC spherical shell with a central cutout

(11)ϵξ1ξ1ϵξ2ξ2γξ2ξ3γξ1ξ3γξ1ξ2=u0,ξ1+w0,R1+12(w0,ξ1)2+ζϕξ1,ξ1v0,ξ2+w0,R2+12(w0,ξ2)2+ζϕξ2,ξ2w0,ξ2+ϕξ2w0,ξ1+ϕξ1u0,ξ2+v0,ξ1+w0,ξ1w0,ξ2+ζϕξ1,ξ2ϕξ2,ξ1

where (u0, v0, w0) denote the displacements of a point (ξ1, ξ, 0) on the mid-surface of the shell, and ϕξ1 and ϕξ2 denote the rotations of a normal to the reference surface, respectively. From the nonlinear strain-displacement relationship, the stress resultants and the equations of motion of the CNTFPC spherical shell. The additional details consult the reference by Sanders [22].

The nonlinear equation of motion at time p + 1 can be reduced to the fully discretized from using Newmark’s scheme:

(12)K~({δ}p+1){δ}p+1={F~}p,p+1,

where,

(13)[K~({δ}p+1)]=[K({δ}p+1)]+κ1M({δ}p+1)
(14){F~}p,p+1={F}p+1+[M]p+1(κ1{δ}s+κ2{δ˙}s+κ3{δ¨}s)

where, [K({δ}p+1)], [M({δ}p+1)], and {F}p+1 denote the element stiffness matrix, the element mass matrix, and the external force vector at time tp+1, respectively. The parameters k1–k3 are used to compute the effective stiffness matrix [K̃K({δ}p+1)] and the effective force vector {F̃F}p,p+1. At the end of each time step, the new velocity vector {δ}s+1 and acceleration vector {δ¨}s+1are determined using the Newmark’s scheme [24]. Using the Newton-Raphon iterative method, the solution at the sth iteration, {δ}p+1scan be expressed as

(15){R^}({δ}p+1)≡K~({δ}p+1){δ}p+1−{F~}p,p+1=0,

where, {R} is a nonlinear function of {δ}p+1. Expanding {R} in Taylor’s series about {δ}sp+1, the following ^iterative equation is obtained:

(16)0={R^}p+1s+[K~T({δ}p+1s)]{δ¯}+O({δ¯}2),
(17)K~T({δ}p+1s)≡∂{R}∂{δ}p+1s,{R^}p+1s=K~({δ}p+1s){δ}p+1s−{F~}p,p+1

where, O(·) and [K̃KT] are the higher-order terms and the tangent stiffness matrix. The assembled equations are solved for the incremental displacement vector after imposing the boundary and initial conditions.

3 Parametric results and discussion

3.1 Verification

Table 1 shows the detailed properties of the CNTs, resins, and fibers used for parametric examples. Figure 2 shows the comparisons of non-dimensionalized nonlinear transient displacement of composite spherical shells under uniformly distributed load. It can be observed from the figure that the present results agreed well with those reported by other investigators. Figure 2 shows non-dimensionalized nonlinear transient displacements of SWCNTs reinforced composite plates for different length-diameter ratios and weight ratios of SWCNTs. It is evident that the induced displacements agreed well with those reported by Bhardwaj et al. [16].

Figure 2 Non-dimensionalized nonlinear transient displacement (w/q) of composite spherical shells under uniformly distributed load ([0/90], Material I)
Figure 2

Non-dimensionalized nonlinear transient displacement (w/q) of composite spherical shells under uniformly distributed load ([0/90], Material I)

Table 1

Material and geometrical properties of the materials used in this study

MaterialSourceSymbolValueDefinition
Material I[18]E1125E22Longitudinal Young’s modulus
E22106 N/cm2Transverse Young’s modulus
G120.5E22In-plane shear modulus
ρ1Ns2/cm4Mass density
ν120.25Possion’s ratio
Epoxy resin[25]Eep2.72 GPaYoung’s modulus of epoxy resin
ρpm1, 200 kg/m3Mass density of epoxy resin
νpm0.33Possion’s ratio of epoxy resin
SWCNT[3]Ecnt11640 GPaYoung’s modulus of SWCNT
ρcnt1, 350 kg/m3Mass density of SWCNT
νcnt0.33Possion’s ratio of SWCNT
tcnt0.34 nmThickness of SWCNT
dcnt1.4 nmDiameter of SWCNT
lcnt25 μmLength of SWCNT
MWCNT[3]Ecnt11400.0 GPaYoung’s modulus of MWCNT
ρcnt1, 350 kg/m3Mass density of MWCNT
νcnt0.33Possion’s ratio of MWCNT
tcnt0.34 nmThickness of MWCNT
dcnt20.0 nmDiameter of MWCNT
lcnt50 μmLength of MWCNT
E-Glass fiber[25]Ef69.0 GPaYoung’s modulus of E-Glass fiber
ρf1, 200 kg/m3Mass density of E-Glass fiber
νf0.2Possion’s ratio of E-Glass fiber

Figure 4 shows the comparisons of nonlinear transient displacements of SWCNT reinforced composite spherical shells (R/a = 10) for different multiscale models. The CNTFPC spherical shells with all simply supported edges were laminated as [0/90]s, and the results determined from different multi-scale formulations were compared. It may be noted that only the Halpin-Tsai model was corrected for a volume fraction of less than 0.5. For this reason, we used the multi-scale model modified from Hewitt and Malherbe equation as presented in Eqs.(8)–(9) for E22 and G12. For Vf = 0.8, the maximum displacement using the conventional Halpin-Tsai equation was about 22% higher than those obtained using the modified equation by Hewitt and Malherbe. Therefore, for greater accuracy, all the subsequent induced results were based on the modified Halpin-Tsai equation.

Figure 3 Non-dimensionalized nonlinear transient displacement (w/h) of SWCNT reinforced composite plates for different length-diameter ratios of SWCNT ([0/90/90/0])
Figure 3

Non-dimensionalized nonlinear transient displacement (w/h) of SWCNT reinforced composite plates for different length-diameter ratios of SWCNT ([0/90/90/0])

Figure 4 Comparison of nonlinear transient displacements (w/h) of SWCNT reinforced composite spherical shells (R/a = 10) for different multiscale models (q = 1.0MPa, [0/90]s, Vf = 0.8, wcnt = 1.0% no cutout).
Figure 4

Comparison of nonlinear transient displacements (w/h) of SWCNT reinforced composite spherical shells (R/a = 10) for different multiscale models (q = 1.0MPa, [0/90]s, Vf = 0.8, wcnt = 1.0% no cutout).

3.2 CNTFPC spherical shells without a cutout

Figure 5 represents nonlinear transient displacements of [0/90]s SWCNT reinforced composite flat plates and spherical shells for different the SWCNT weight ratios. All parameters were compared for shells without a cutout. The maximum displacements occurred at earlier time and dereased as the SWCNT ratios increased. For both plates and shells, the trends were similar to each other. This is clearly due to increased stiffness effects as the SWCNT weight ratio increases. The SWCNT reinforcement plays a role in increased stiffness and lead to the higher frequency of plates and shells. Nonlinear transient displacement for shells are lower than those of plates because of membrane force effects resulted from the curvature of the shell. It can be also be seen from the figure that small SWCNT weight ratios of 1 − 2% resulted in the noticeable reduction of nonlinear dynamic displacements. On the other hand, the differences in induced displacements for increased MWCNT ratios are negligible for flat plates as shown in Figure 6. For the shell with R/a = 5.0, the induced displacement for the MWCNT weight ratio of 1.0% is extremely lower than that for the shell without MWCNT reinforcement. For the MWCNT weight ratio of more than 1.0%, the induced displacements are close to each other as shown in Figure 6(b). It can be concluded from the results that small MWCNT ratios result in better rigidity against dynamic loading, especially for the spherical shell.

Figure 5 Nonlinear transient displacements (w/h) of SWCNT reinforced composite flat plates and spherical shells (q = 1.0MPa, [0/90]s, Vf = 0.8, no cutout)
Figure 5

Nonlinear transient displacements (w/h) of SWCNT reinforced composite flat plates and spherical shells (q = 1.0MPa, [0/90]s, Vf = 0.8, no cutout)

Figure 6 Nonlinear transient displacements (w/h) of MWCNT reinforced composite flat plates and spherical shells (q = 1.0MPa, [0/90]s, Vf = 0.8, no cutout)
Figure 6

Nonlinear transient displacements (w/h) of MWCNT reinforced composite flat plates and spherical shells (q = 1.0MPa, [0/90]s, Vf = 0.8, no cutout)

Figure 7 shows induced nonlinear transient displacements of [0/90]s CNTFPC spherical shells with 1.0% SWCNT reinforcement for different radius-length ratios. The maximum displacement occurred at earlier time as the radius-length ratios decreased. As mentioned earlier, this is due to curvature effects such as the occurrence of membrane forces as the radius-length decreases. In this case, the membrane force effects also play a role in increased stiffness and lead to the higher frequency of spherical shells.

Figure 7 Nonlinear transient displacements (w/h) of SWCNT reinforced composite spherical shells for different radius-length ratios (q = 1.0MPa, [0/90]s, Vf = 0.8, wcnt = 1.0%, no cutout)
Figure 7

Nonlinear transient displacements (w/h) of SWCNT reinforced composite spherical shells for different radius-length ratios (q = 1.0MPa, [0/90]s, Vf = 0.8, wcnt = 1.0%, no cutout)

3.3 CNTFPC spherical shells with a cutout

Figure 8 represents nonlinear dynamic behaviors of [45/−45]s SWCNT reinforced composite spherical shells for different cutout sizes. A distributed step loading of loading of magnitude q = 1.0MPa is applied at time t = 0.

Figure 8 Nonlinear dynamic behaviors (w/h) of SWCNT reinforced composite spherical shells for different cutout sizes (q = 1.0MPa, [45/−45]s, Vf = 0.8, wcnt = 1.0%)
Figure 8

Nonlinear dynamic behaviors (w/h) of SWCNT reinforced composite spherical shells for different cutout sizes (q = 1.0MPa, [45/−45]s, Vf = 0.8, wcnt = 1.0%)

The deformed shape of CNTFPC spherical shells for the different cutout sizes is a dominant factor in identifying dynamic characteristics of SWCNT reinforced laminates under a suddenly applied distributed load. It can be observed from the figure that the deformed shapes at different time steps are significantly different for the cutout size of more than c/a=0.6. The amplitude of overall displacements for bigger cutout size is larger than that of small cutout size due to the mass loss.

Figures 9 shows the interactions of maximum nonlinear displacements between the cutout sizes, SWCNT weight ratios, and radius-length ratios of CNTFPC spherical shells. For increased SWCNT weight ratios, the maximum nonlinear transient displacements sharply decreased as radius-length ratios (R/a) decreased, especially for R/a < 5.0. The SWCNT reinforcements showed greater enhancement to the nonlinear dynamic flexural rigidity, especially for shells with large curvatures. On the other hand, effects on cutout areas were relatively small for the flat panels. For spherical shells with R/a=5.0 and c/a = 0.4 cutout area, the induced nonlinear displacements were similar to that of shells with c/a = 0.4 cutout area. On the other hand, the nonlinear transient displacements of shells with R/a > 5.0 asymptotically approached a fixed value for increased the SWCNT weight ratios(> 2.0%). These results lead us to conclude that spherical shells with R/a > 5.0 can be considered as having similar nonlinear dynamic rigidity regardless of the CNT weight ratio. Therefore, we may pay attention to the radius-length effects

Figure 9 Maximum nonlinear dynamic displacements of [45/−45/45/−45] CNTFPC spherical shells for increased cutout sizes and SWCNT weight ratios, and radius-length ratios
Figure 9

Maximum nonlinear dynamic displacements of [45/−45/45/−45] CNTFPC spherical shells for increased cutout sizes and SWCNT weight ratios, and radius-length ratios

of spherical CNTFPC shells because the various geometrical nonlinear dynamic behaviors made by the cutout area could be significant to the curvature of spherical shells containing a cutout.

4 Summary and conclusion

In this study, we performed a nonlinear transient analysis of laminated CNTFPC spherical shells containing a central cutout according to the FSDT model. Multi-scale formulations of SWCNT or MWCNT reinforced three-phase composites were investigated by comparison with the conventional and modified Halpin-Tsai models. From the numerical results, the following significant observations and conclusions were drawn:

  1. For volume fractions of more than 0.6, the differences in induced natural frequencies between the conventional and the modified Halpin-Tasi models were significant for increased SWCNT or MWCNT weight ratios. Therefore, the modified Halpin-Tsai model is recommended for greater accuracy, especially for the high volume fractions.

  2. The maximum nonlinear dynamic displacement occurred at lower disturbing frequencies as the radius-thickness ratios decreased. The membrane effects in the spherical shell led to increased stiffness and resulted in higher excitation frequency. For shells with a cutout, the excitation frequencies were lower than those for shells without a cutout, because the area of the shells decreased. Small SWCNT weight ratios of 1 − 2% play a significant role in the downward shift of the nonlinear dynamic displacement.

  3. Maximum displacements increased as the cutout areas increased because of the effects of the reduced stiffness. On the other hand, the SWCNT reinforcement produced higher nonlinear frequencies for increased curvature effects. Only 2% of the CNT-reinforcement for shells with 40% cutout areas affected the nonlinear dynamic rigidity similarly to that for panels with 10% cutout areas. The SWCNT reinforcement enables the nonlinear dynamic rigidity of spherical CNTFPC shells with a cutout to be enhanced.

  4. From the parametric results, spherical shells with R/a > 5.0 can be considered as a similar nonlinear dynamic flexural rigidity regardless of the CNT weight ratios. However, we cannot neglect the effect of the thickness-length ratio in analyzing the spherical CNTFPC shells because the various effects of the cutout area could be significant to the thickness or length of spherical shells containing a cutout.

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Acknowledgement

This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIP – Korea) (No. 2018R1D1A1B07050080).

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Received: 2019-03-18
Accepted: 2019-08-22
Published Online: 2019-12-18

© 2019 Sang-Youl Lee, Ji-Gwang Hwang published by De Gruyter

This work is licensed under the Creative Commons Attribution 4.0 Public License.

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  13. Experimental study on the existence of nano-scale pores and the evolution of organic matter in organic-rich shale
  14. Mechanical characterizations of braided composite stents made of helical polyethylene terephthalate strips and NiTi wires
  15. Mechanical properties of boron nitride sheet with randomly distributed vacancy defects
  16. Fabrication, mechanical properties and failure mechanism of random and aligned nanofiber membrane with different parameters
  17. Micro- structure and rheological properties of graphene oxide rubber asphalt
  18. First-principles calculations of mechanical and thermodynamic properties of tungsten-based alloy
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  20. Preparation of spherical aminopropyl-functionalized MCM-41 and its application in removal of Pb(II) ion from aqueous solution
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  23. Electric-field assisted growth and mechanical bactericidal performance of ZnO nanoarrays with gradient morphologies
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  26. Surface modification of nano-sized carbon black for reinforcement of rubber
  27. Temperature-dependent negative Poisson’s ratio of monolayer graphene: Prediction from molecular dynamics simulations
  28. Finite element nonlinear transient modelling of carbon nanotubes reinforced fiber/polymer composite spherical shells with a cutout
  29. Preparation of low-permittivity K2O–B2O3–SiO2–Al2O3 composites without the addition of glass
  30. Large amplitude vibration of doubly curved FG-GRC laminated panels in thermal environments
  31. Enhanced flexural properties of aramid fiber/epoxy composites by graphene oxide
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  35. Test on axial compression performance of nano-silica concrete-filled angle steel reinforced GFRP tubular column
  36. Multi-scale modeling of the lamellar unit of arterial media
  37. The multiscale enhancement of mechanical properties of 3D MWK composites via poly(oxypropylene) diamines and GO nanoparticles
  38. Mechanical properties of circular nano-silica concrete filled stainless steel tube stub columns after being exposed to freezing and thawing
  39. Arc erosion behavior of TiB2/Cu composites with single-scale and dual-scale TiB2 particles
  40. Yb3+-containing chitosan hydrogels induce B-16 melanoma cell anoikis via a Fak-dependent pathway
  41. Template-free synthesis of Se-nanorods-rGO nanocomposite for application in supercapacitors
  42. Effect of graphene oxide on chloride penetration resistance of recycled concrete
  43. Bending resistance of PVA fiber reinforced cementitious composites containing nano-SiO2
  44. Review Articles
  45. Recent development of Supercapacitor Electrode Based on Carbon Materials
  46. Mechanical contribution of vascular smooth muscle cells in the tunica media of artery
  47. Applications of polymer-based nanoparticles in vaccine field
  48. Toxicity of metallic nanoparticles in the central nervous system
  49. Parameter control and concentration analysis of graphene colloids prepared by electric spark discharge method
  50. A critique on multi-jet electrospinning: State of the art and future outlook
  51. Electrospun cellulose acetate nanofibers and Au@AgNPs for antimicrobial activity - A mini review
  52. Recent progress in supercapacitors based on the advanced carbon electrodes
  53. Recent progress in shape memory polymer composites: methods, properties, applications and prospects
  54. In situ capabilities of Small Angle X-ray Scattering
  55. Review of nano-phase effects in high strength and conductivity copper alloys
  56. Progress and challenges in p-type oxide-based thin film transistors
  57. Advanced materials for flexible solar cell applications
  58. Phenylboronic acid-decorated polymeric nanomaterials for advanced bio-application
  59. The effect of nano-SiO2 on concrete properties: a review
  60. A brief review for fluorinated carbon: synthesis, properties and applications
  61. A review on the mechanical properties for thin film and block structure characterised by using nanoscratch test
  62. Cotton fibres functionalized with plasmonic nanoparticles to promote the destruction of harmful molecules: an overview
https://doi.org/10.1515/ntrev-2019-0039
Keywords for this article
CNTFPC spherical shell; Finite element nonlinear transient modelling; carbon nanotube; multiscale model; CNT weight ratio
Creative Commons
BY 4.0

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  13. Experimental study on the existence of nano-scale pores and the evolution of organic matter in organic-rich shale
  14. Mechanical characterizations of braided composite stents made of helical polyethylene terephthalate strips and NiTi wires
  15. Mechanical properties of boron nitride sheet with randomly distributed vacancy defects
  16. Fabrication, mechanical properties and failure mechanism of random and aligned nanofiber membrane with different parameters
  17. Micro- structure and rheological properties of graphene oxide rubber asphalt
  18. First-principles calculations of mechanical and thermodynamic properties of tungsten-based alloy
  19. Adsorption performance of hydrophobic/hydrophilic silica aerogel for low concentration organic pollutant in aqueous solution
  20. Preparation of spherical aminopropyl-functionalized MCM-41 and its application in removal of Pb(II) ion from aqueous solution
  21. Electrical conductivity anisotropy of copper matrix composites reinforced with SiC whiskers
  22. Miniature on-fiber extrinsic Fabry-Perot interferometric vibration sensors based on micro-cantilever beam
  23. Electric-field assisted growth and mechanical bactericidal performance of ZnO nanoarrays with gradient morphologies
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  25. Synthesis of nano zirconium oxide and its application in dentistry
  26. Surface modification of nano-sized carbon black for reinforcement of rubber
  27. Temperature-dependent negative Poisson’s ratio of monolayer graphene: Prediction from molecular dynamics simulations
  28. Finite element nonlinear transient modelling of carbon nanotubes reinforced fiber/polymer composite spherical shells with a cutout
  29. Preparation of low-permittivity K2O–B2O3–SiO2–Al2O3 composites without the addition of glass
  30. Large amplitude vibration of doubly curved FG-GRC laminated panels in thermal environments
  31. Enhanced flexural properties of aramid fiber/epoxy composites by graphene oxide
  32. Correlation between electrochemical performance degradation and catalyst structural parameters on polymer electrolyte membrane fuel cell
  33. Materials characterization of advanced fillers for composites engineering applications
  34. Humic acid assisted stabilization of dispersed single-walled carbon nanotubes in cementitious composites
  35. Test on axial compression performance of nano-silica concrete-filled angle steel reinforced GFRP tubular column
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  38. Mechanical properties of circular nano-silica concrete filled stainless steel tube stub columns after being exposed to freezing and thawing
  39. Arc erosion behavior of TiB2/Cu composites with single-scale and dual-scale TiB2 particles
  40. Yb3+-containing chitosan hydrogels induce B-16 melanoma cell anoikis via a Fak-dependent pathway
  41. Template-free synthesis of Se-nanorods-rGO nanocomposite for application in supercapacitors
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  43. Bending resistance of PVA fiber reinforced cementitious composites containing nano-SiO2
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  47. Applications of polymer-based nanoparticles in vaccine field
  48. Toxicity of metallic nanoparticles in the central nervous system
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  50. A critique on multi-jet electrospinning: State of the art and future outlook
  51. Electrospun cellulose acetate nanofibers and Au@AgNPs for antimicrobial activity - A mini review
  52. Recent progress in supercapacitors based on the advanced carbon electrodes
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