Skip to main content
SpringerLink
Log in

Hygro-thermal buckling analysis of polymer–CNT–fiber-laminated nanocomposite disk under uniform lateral pressure with the aid of GDQM

  • Original Article
  • Published:
Engineering with Computers Aims and scope Submit manuscript

Abstract

In this research, we study the thermal buckling performance of multi-scale hybrid laminated nanocomposite (MHLC) disk (MHLCD) subjected hygro-mechanical loading. The matrix material is reinforced with carbon nanotubes (CNTs) or carbon fibers (CF) at the nano- or macro-scale, respectively. The disk is modeled based on higher order shear deformation theory. We present a modified Halpin–Tsai model to predict the effective properties of the MHLCD. The minimum total potential energy principle is employed to establish the governing equations of the system, which is finally solved by the generalized differential quadrature method. To validate the approach, numerical results are compared with available results from the literature. Subsequently, a comprehensive parameter study is carried out to quantify the influence of different parameters such as stiffness of the substrate, patterns of temperature increase, moisture coefficient, stacking sequence of the CFs, weight fraction and distribution patterns of CNTs, outer radius to inner radius ratio and inner radius to thickness ratio on the response of the plate. Some new results related to critical buckling of an MHLCD are also presented, which can serve as benchmark solutions for future investigations.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

h, R i, and R o :

Thickness, the inner and outer radius of the disk, respectively

CNTs:

Carbon nanotubes

F and NCM:

Fiber and nanocomposite matrix, respectively

ρ, E, ν and G:

Density, Young’s module, Poisson’s ratio, and shear parameters, respectively

V NCM, V F :

Volume fractions of nanocomposite matrix and fiber, respectively

l CNT, t CNT, d CNT, E CNT and V CNT :

The length, thickness, diameter, Younge’s module, and volume fraction of carbon nanotubes, respectively

V *CNT , W CNT :

Effective volume fraction and weight fraction of the CNTs, respectively

N t, V CNT :

Layer number and volume fraction of CNTs, respectively

α 11 and α 22 :

Thermal expansion coefficients of the multi-scale hybrid nanocomposite

α NCM :

The thermal expansion coefficient of the nanocomposite matrix

\(\beta_{11} \,\,\,{\text{and}}\,\,\,\beta_{22}\) :

The moisture coefficients of the multi-scale hybrid laminated nanocomposite

β M :

The moisture coefficients of the matrix

U, V, W :

Displacement fields of a disk

u, v, w, ØR and Øθ :

The displacements of the mid-surface in R, θ and Z directions and rotations of the transverse normal around R and θ directions, respectively

ɛ RR and ɛ θθ :

The corresponding normal strains in R and θ directions, respectively

γ RZ, γ Rθ and γ θZ :

The shear strain in the R–Z, R–θ and θ –Z plane

U*, W*:

Corresponding strain energy of the system, the work done, respectively

N T :

Applied forces due to variation of temperature

ΔT :

Temperature changes

N H :

Applied forces due to variation of hygro-loading

ΔH :

Moisture changes

K w and K p :

Winkler and Pasternak coefficients of the substrate

Q ij and \(\bar{Q}_{ij}\) :

Stiffness elements, stiffness elements relates to orientation angle and the orientation angle, respectively

θ :

The lamination angle with respect to the disk R-axis

N :

The number of distributed points along the R-axis

d, b, and δ :

d as a subscript stands for the domain grid points, b as subscript stands for boundary grid points and the displacement vector, respectively

F ij and K ij :

Components of force and stiffness matrices, respectively

\(F_{ij}^{*} \,{\text{and}}\,K_{ij}^{*}\) :

Components of force and stiffness matrices in the GDQ method, respectively

References

  1. Chakrapani SK, Barnard DJ, Dayal V (2016) Nonlinear forced vibration of carbon fiber/epoxy prepreg composite beams: theory and experiment. Compos B Eng 91:513–521. https://doi.org/10.1016/j.compositesb.2016.02.009

    Article  Google Scholar 

  2. Emam S, Eltaher MA (2016) Buckling and postbuckling of composite beams in hygrothermal environments. Compos Struct 152:665–675. https://doi.org/10.1016/j.compstruct.2016.05.029

    Article  Google Scholar 

  3. Maghamikia Sh, Jam JE (2011) Buckling analysis of circular and annular composite plates reinforced with carbon nanotubes using FEM. J Mech Sci Technol 25:2805–2810. https://doi.org/10.1007/s12206-011-0738-8

    Article  Google Scholar 

  4. Tahouneh V, Yas MH (2014) Influence of equivalent continuum model based on the Eshelby-Mori-Tanaka scheme on the vibrational response of elastically supported thick continuously graded carbon nanotube-reinforced annular plates. Polym Compos 35:1644–1661. https://doi.org/10.1002/pc.22818

    Article  Google Scholar 

  5. Tahouneh V, Jam JE (2014) A semi-analytical solution for 3-d dynamic analysis of thick continuously graded carbon nanotube-reinforced annular plates resting on a two-parameter elastic foundation. Mech Adv Compos Struct 1:113–130. https://doi.org/10.22075/macs.2014.286

    Article  Google Scholar 

  6. Ansari R, Torabi J, Shojaei MF (2017) Buckling and vibration analysis of embedded functionally graded carbon nanotube-reinforced composite annular sector plates under thermal loading. Compos B Eng 109:197–213. https://doi.org/10.1016/j.compositesb.2016.10.050

    Article  Google Scholar 

  7. Keleshteri MM, Asadi H, Wang Q (2017) Postbuckling analysis of smart FG-CNTRC annular sector plates with surface-bonded piezoelectric layers using generalized differential quadrature method. Comput Methods Appl Mech Eng 325:689–710. https://doi.org/10.1016/j.cma.2017.07.036

    Article  MathSciNet  MATH  Google Scholar 

  8. Keleshteri MM, Asadi H, Aghdam MM (2017) Geometrical nonlinear free vibration responses of FG-CNT reinforced composite annular sector plates integrated with piezoelectric layers. Compos Struct 171:100–112. https://doi.org/10.1016/j.compstruct.2017.01.048

    Article  Google Scholar 

  9. Keleshteri MM, Asadi H, Wang Q (2017) Large amplitude vibration of FG-CNT reinforced composite annular plates with integrated piezoelectric layers on elastic foundation. Thin-Walled Struct 120:203–214. https://doi.org/10.1016/j.tws.2017.08.035

    Article  Google Scholar 

  10. Torabi J, Ansari R (2017) Nonlinear free vibration analysis of thermally induced FG-CNTRC annular plates: asymmetric versus axisymmetric study. Comput Methods Appl Mech Eng 324:327–347. https://doi.org/10.1016/j.cma.2017.05.025

    Article  MathSciNet  MATH  Google Scholar 

  11. Pang F, Li H, Du Y et al (2018) Free vibration of functionally graded carbon nanotube reinforced composite annular sector plate with general boundary supports. Curved Layer Struct 5:49–67. https://doi.org/10.1515/cls-2018-0005

    Article  Google Scholar 

  12. Ansari R, Torabi J, Hassani R (2018) In-plane and shear buckling analysis of FG-CNTRC annular sector plates based on the third-order shear deformation theory using a numerical approach. Comput Math Appl 75:486–502. https://doi.org/10.1016/j.camwa.2017.09.022

    Article  MathSciNet  MATH  Google Scholar 

  13. Gholami R, Ansari R (2018) Geometrically nonlinear resonance of higher-order shear deformable functionally graded carbon-nanotube-reinforced composite annular sector plates excited by harmonic transverse loading. Eur Phys J Plus 133:56. https://doi.org/10.1140/epjp/i2018-11874-6

    Article  Google Scholar 

  14. Mercan K, Baltacıoglu AK, Civalek Ö (2018) Free vibration of laminated and FGM/CNT composites annular thick plates with shear deformation by discrete singular convolution method. Compos Struct 186:139–153. https://doi.org/10.1016/j.compstruct.2017.12.008

    Article  Google Scholar 

  15. Ansari R, Torabi J, Faghih Shojaei M (2018) Free vibration analysis of embedded functionally graded carbon nanotube-reinforced composite conical/cylindrical shells and annular plates using a numerical approach. J Vib Control 24:1123–1144. https://doi.org/10.1177/1077546316659172

    Article  MathSciNet  MATH  Google Scholar 

  16. Ansari R, Torabi J, Hasrati E (2018) Axisymmetric nonlinear vibration analysis of sandwich annular plates with FG-CNTRC face sheets based on the higher-order shear deformation plate theory. Aerosp Sci Technol 77:306–319. https://doi.org/10.1016/j.ast.2018.01.010

    Article  Google Scholar 

  17. Zhong R, Wang Q, Tang J et al (2018) Vibration analysis of functionally graded carbon nanotube reinforced composites (FG-CNTRC) circular, annular and sector plates. Compos Struct 194:49–67. https://doi.org/10.1016/j.compstruct.2018.03.104

    Article  Google Scholar 

  18. Civalek Ö, Baltacıoğlu AK (2018) Vibration of carbon nanotube reinforced composite (CNTRC) annular sector plates by discrete singular convolution method. Compos Struct 203:458–465. https://doi.org/10.1016/j.compstruct.2018.07.037

    Article  Google Scholar 

  19. Yang B, Kitipornchai S, Yang Y-F, Yang J (2017) 3D thermo-mechanical bending solution of functionally graded graphene reinforced circular and annular plates. Appl Math Model 49:69–86. https://doi.org/10.1016/j.apm.2017.04.044

    Article  MathSciNet  MATH  Google Scholar 

  20. Malekzadeh P, Setoodeh AR, Shojaee M (2018) Vibration of FG-GPLs eccentric annular plates embedded in piezoelectric layers using a transformed differential quadrature method. Comput Methods Appl Mech Eng 340:451–479. https://doi.org/10.1016/j.cma.2018.06.006

    Article  MathSciNet  MATH  Google Scholar 

  21. Gholami R, Ansari R (2019) Asymmetric nonlinear bending analysis of polymeric composite annular plates reinforced with graphene nanoplatelets. JMC. https://doi.org/10.1615/IntJMultCompEng.2019029156

    Article  Google Scholar 

  22. Mishra BP, Barik M (2019) NURBS-augmented finite element method for stability analysis of arbitrary thin plates. Eng Comput 35:351–362. https://doi.org/10.1007/s00366-018-0603-9

    Article  Google Scholar 

  23. Akgoz B, Civalek O (2011) Nonlinear vibration analysis of laminated plates resting on nonlinear two-parameters elastic foundations. Steel Compos Struct 11:403–421. https://doi.org/10.12989/scs.2011.11.5.403

    Article  Google Scholar 

  24. Katariya PV, Hirwani CK, Panda SK (2019) Geometrically nonlinear deflection and stress analysis of skew sandwich shell panel using higher-order theory. Eng Comput 35:467–485. https://doi.org/10.1007/s00366-018-0609-3

    Article  Google Scholar 

  25. Katariya PV, Panda SK (2019) Numerical evaluation of transient deflection and frequency responses of sandwich shell structure using higher order theory and different mechanical loadings. Eng Comput 35:1009–1026. https://doi.org/10.1007/s00366-018-0646-y

    Article  Google Scholar 

  26. Civalek Ö, Acar MH (2007) Discrete singular convolution method for the analysis of Mindlin plates on elastic foundations. Int J Press Vessels Pip 84:527–535. https://doi.org/10.1016/j.ijpvp.2007.07.001

    Article  Google Scholar 

  27. Yang X, Sahmani S, Safaei B (2020) Postbuckling analysis of hydrostatic pressurized FGM microsized shells including strain gradient and stress-driven nonlocal effects. Eng Comput. https://doi.org/10.1007/s00366-019-00901-2

    Article  Google Scholar 

  28. Akgöz B, Civalek Ö (2017) Effects of thermal and shear deformation on vibration response of functionally graded thick composite microbeams. Compos B Eng 129:77–87. https://doi.org/10.1016/j.compositesb.2017.07.024

    Article  Google Scholar 

  29. Demir Ç, Civalek Ö (2017) A new nonlocal FEM via Hermitian cubic shape functions for thermal vibration of nano beams surrounded by an elastic matrix. Compos Struct 168:872–884. https://doi.org/10.1016/j.compstruct.2017.02.091

    Article  Google Scholar 

  30. Civalek O, Demir C (2011) Buckling and bending analyses of cantilever carbon nanotubes using the Euler-Bernoulli beam theory based on non-local continuum model. Tech Note 651–661

  31. Thangaratnam KR, Palaninathan Ramachandran J (1989) Thermal buckling of composite laminated plates. Comput Struct 32:1117–1124. https://doi.org/10.1016/0045-7949(89)90413-6

    Article  MATH  Google Scholar 

  32. Sarma MS, Venkateshwar Rao A, Pillai SRR, Nageswara Rao B (1992) Large amplitude vibrations of laminated hybrid composite plates. J Sound Vib 159:540–545. https://doi.org/10.1016/0022-460X(92)90758-P

    Article  Google Scholar 

  33. Walker M, Reiss T, Adali S (1997) A procedure to select the best material combinations and optimally design hybrid composite plates for minimum weight and cost. Eng Optim 29:65–83. https://doi.org/10.1080/03052159708940987

    Article  Google Scholar 

  34. Karakaya Ş, Soykasap Ö (2011) Natural frequency and buckling optimization of laminated hybrid composite plates using genetic algorithm and simulated annealing. Struct Multidisc Optim 43:61–72. https://doi.org/10.1007/s00158-010-0538-2

    Article  Google Scholar 

  35. Thostenson ET, Li WZ, Wang DZ et al (2002) Carbon nanotube/carbon fiber hybrid multiscale composites. J Appl Phys 91:6034–6037. https://doi.org/10.1063/1.1466880

    Article  Google Scholar 

  36. Song YS (2007) Multiscale fiber-reinforced composites prepared by vacuum-assisted resin transfer molding. Polym Compos 28:458–461. https://doi.org/10.1002/pc.20301

    Article  Google Scholar 

  37. Bekyarova E, Thostenson ET, Yu A et al (2007) Multiscale carbon nanotube–carbon fiber reinforcement for advanced epoxy composites. Langmuir 23:3970–3974. https://doi.org/10.1021/la062743p

    Article  Google Scholar 

  38. Bekyarova E, Thostenson ET, Yu A et al (2007) Functionalized single-walled carbon nanotubes for carbon fiber–epoxy composites. J Phys Chem C 111:17865–17871. https://doi.org/10.1021/jp071329a

    Article  Google Scholar 

  39. Jiang S, Li Q, Wang J et al (2016) Multiscale graphene oxide–carbon fiber reinforcements for advanced polyurethane composites. Compos A Appl Sci Manuf 87:1–9. https://doi.org/10.1016/j.compositesa.2016.04.004

    Article  Google Scholar 

  40. dos Cougo CM, S, Pezzin SH, Pachekoski WM, Amico SC, (2019) Multiscale hybrid composites with carbon-based nanofillers. Nanocarbon and its composites. 21:449–470. https://doi.org/10.1016/B978-0-08-102509-3.00014-6

    Article  Google Scholar 

  41. Kim M, Park Y-B, Okoli OI, Zhang C (2009) Processing, characterization, and modeling of carbon nanotube-reinforced multiscale composites. Compos Sci Technol 69:335–342. https://doi.org/10.1016/j.compscitech.2008.10.019

    Article  Google Scholar 

  42. Inam F, Wong DWY, Kuwata M, Peijs T (2010) Multiscale hybrid micro-nanocomposites based on carbon nanotubes and carbon fibers. J Nanomater 2010:9. https://doi.org/10.1155/2010/453420

    Article  Google Scholar 

  43. Wang B-C, Zhou X, Ma K-M (2013) Fabrication and properties of CNTs/carbon fabric hybrid multiscale composites processed via resin transfer molding technique. Compos B Eng 46:123–129. https://doi.org/10.1016/j.compositesb.2012.10.022

    Article  Google Scholar 

  44. Lee S-B, Choi O, Lee W et al (2011) Processing and characterization of multi-scale hybrid composites reinforced with nanoscale carbon reinforcements and carbon fibers. Compos A Appl Sci Manuf 42:337–344. https://doi.org/10.1016/j.compositesa.2010.10.016

    Article  Google Scholar 

  45. Guo J, Lu C, An F, He S (2012) Preparation and characterization of carbon nanotubes/carbon fiber hybrid material by ultrasonically assisted electrophoretic deposition. Mater Lett 66:382–384. https://doi.org/10.1016/j.matlet.2011.09.022

    Article  Google Scholar 

  46. Thostenson ET, Gangloff JJ, Li C, Byun J-H (2009) Electrical anisotropy in multiscale nanotube/fiber hybrid composites. Appl Phys Lett 95:073111. https://doi.org/10.1063/1.3202788

    Article  Google Scholar 

  47. Qin FX, Brosseau C, Peng HX (2013) Microwave properties of carbon nanotube/microwire/rubber multiscale hybrid composites. Chem Phys Lett 579:40–44. https://doi.org/10.1016/j.cplett.2013.06.021

    Article  Google Scholar 

  48. Pal G, Kumar S (2016) Multiscale modeling of effective electrical conductivity of short carbon fiber-carbon nanotube-polymer matrix hybrid composites. Mater Des 89:129–136. https://doi.org/10.1016/j.matdes.2015.09.105

    Article  Google Scholar 

  49. Sung DH, Kim M, Park Y-B (2018) Prediction of thermal conductivities of carbon-containing fiber-reinforced and multiscale hybrid composites. Compos B Eng 133:232–239. https://doi.org/10.1016/j.compositesb.2017.09.032

    Article  Google Scholar 

  50. Rodriguez AJ, Guzman ME, Lim C-S, Minaie B (2011) Mechanical properties of carbon nanofiber/fiber-reinforced hierarchical polymer composites manufactured with multiscale-reinforcement fabrics. Carbon 49:937–948. https://doi.org/10.1016/j.carbon.2010.10.057

    Article  Google Scholar 

  51. Rahmanian S, Suraya AR, Shazed MA et al (2014) Mechanical characterization of epoxy composite with multiscale reinforcements: carbon nanotubes and short carbon fibers. Mater Des 60:34–40. https://doi.org/10.1016/j.matdes.2014.03.039

    Article  Google Scholar 

  52. Radue MS, Odegard GM (2018) Multiscale modeling of carbon fiber/carbon nanotube/epoxy hybrid composites: comparison of epoxy matrices. Compos Sci Technol 166:20–26. https://doi.org/10.1016/j.compscitech.2018.03.006

    Article  Google Scholar 

  53. Li W, Dichiara A, Zha J et al (2014) On improvement of mechanical and thermo-mechanical properties of glass fabric/epoxy composites by incorporating CNT–Al2O3 hybrids. Compos Sci Technol 103:36–43. https://doi.org/10.1016/j.compscitech.2014.08.016

    Article  Google Scholar 

  54. Hadden CM, Klimek-McDonald DR, Pineda EJ et al (2015) Mechanical properties of graphene nanoplatelet/carbon fiber/epoxy hybrid composites: multiscale modeling and experiments. Carbon 95:100–112. https://doi.org/10.1016/j.carbon.2015.08.026

    Article  Google Scholar 

  55. Aluko O, Gowtham S, Odegard GM (2017) Multiscale modeling and analysis of graphene nanoplatelet/carbon fiber/epoxy hybrid composite. Compos B Eng 131:82–90. https://doi.org/10.1016/j.compositesb.2017.07.075

    Article  Google Scholar 

  56. Al Mahmud H, Radue M, Chinkanjanarot S et al (2018) Predicting the effective mechanical properties of graphene nanoplatelet-carbon fiber-epoxy hybrid composites using ReaxFF: a multiscale modeling. Earth Space 556:556–569. https://doi.org/10.1061/9780784481899.053

    Article  Google Scholar 

  57. Al Mahmud H, Radue MS, Chinkanjanarot S et al (2019) Multiscale modeling of carbon fiber- graphene nanoplatelet-epoxy hybrid composites using a reactive force field. Compos B Eng 172:628–635. https://doi.org/10.1016/j.compositesb.2019.05.035

    Article  Google Scholar 

  58. Zhang X, Yang W, Zhang J et al (2019) Multiscale graphene/carbon fiber reinforced copper matrix hybrid composites: microstructure and properties. Mater Sci Eng A 743:512–519. https://doi.org/10.1016/j.msea.2018.11.117

    Article  Google Scholar 

  59. Ebrahimi F, Habibi S (2018) Thermal effects on nonlinear dynamic characteristics of polymer-CNT-fiber multiscale nanocomposite structures. Struct Eng Mech 67:403–415. https://doi.org/10.12989/sem.2018.67.4.403

    Article  Google Scholar 

  60. Ebrahimi F, Habibi S (2018) Nonlinear eccentric low-velocity impact response of a polymer-carbon nanotube-fiber multiscale nanocomposite plate resting on elastic foundations in hygrothermal environments. Mech Adv Mater Struct 25:425–438. https://doi.org/10.1080/15376494.2017.1285453

    Article  Google Scholar 

  61. Ahmadi M, Ansari R, Rouhi H (2018) Studying buckling of composite rods made of hybrid carbon fiber/carbon nanotube reinforced polyimide using multiscale FEM. Scientia Iranica. https://doi.org/10.24200/sci.2018.5722.1444

    Article  Google Scholar 

  62. Ahmadi M, Ansari R, Rouhi H (2019) Free and forced vibration analysis of rectangular/circular/annular plates made of carbon fiber-carbon nanotube-polymer hybrid composites. Sci Eng Compos Mater 26:70–76. https://doi.org/10.1515/secm-2017-0279

    Article  Google Scholar 

  63. Ebrahimi F, Dabbagh A (2019) On thermo-mechanical vibration analysis of multi-scale hybrid composite beams. J Vib Control 25:933–945. https://doi.org/10.1177/1077546318806800

    Article  MathSciNet  Google Scholar 

  64. Karimiasl M, Ebrahimi F, Vinyas M (2019) Nonlinear vibration analysis of multiscale doubly curved piezoelectric composite shell in hygrothermal environment. J Intell Mater Syst Struct 30:1594–1609. https://doi.org/10.1177/1045389X19835956

    Article  Google Scholar 

  65. Karimiasl M, Ebrahimi F, Mahesh V (2019) Nonlinear free and forced vibration analysis of multiscale composite doubly curved shell embedded in shape-memory alloy fiber under hygrothermal environment. J Vib Control 25:1945–1957. https://doi.org/10.1177/1077546319842426

    Article  MathSciNet  Google Scholar 

  66. Karimiasl M, Ebrahimi F, Akgöz B (2019) Buckling and post-buckling responses of smart doubly curved composite shallow shells embedded in SMA fiber under hygro-thermal loading. Compos Struct 223:110988. https://doi.org/10.1016/j.compstruct.2019.110988

    Article  Google Scholar 

  67. Ebrahimi F, Dabbagh A (2019) Vibration analysis of multi-scale hybrid nanocomposite plates based on a Halpin-Tsai homogenization model. Compos B Eng 173:106955. https://doi.org/10.1016/j.compositesb.2019.106955

    Article  Google Scholar 

  68. Ebrahimi F, Dabbagh A (2019) An analytical solution for static stability of multi-scale hybrid nanocomposite plates. Eng Comput. https://doi.org/10.1007/s00366-019-00840-y

    Article  Google Scholar 

  69. Shen H-S (2009) A comparison of buckling and postbuckling behavior of FGM plates with piezoelectric fiber reinforced composite actuators. Compos Struct 91:375–384

    Article  Google Scholar 

  70. Rafiee M, Liu X, He X, Kitipornchai S (2014) Geometrically nonlinear free vibration of shear deformable piezoelectric carbon nanotube/fiber/polymer multiscale laminated composite plates. J Sound Vib 333:3236–3251

    Article  Google Scholar 

  71. Rafiee M, Yang J, Kitipornchai S (2013) Large amplitude vibration of carbon nanotube reinforced functionally graded composite beams with piezoelectric layers. Compos Struct 96:716–725

    Article  Google Scholar 

  72. Wu H, Kitipornchai S, Yang J (2017) Imperfection sensitivity of thermal post-buckling behaviour of functionally graded carbon nanotube-reinforced composite beams. Appl Math Model 42:735–752

    Article  MathSciNet  Google Scholar 

  73. Reddy JN (2003) Mechanics of laminated composite plates and shells: theory and analysis. CRC Press

  74. Chen D, Yang J, Kitipornchai S (2017) Nonlinear vibration and postbuckling of functionally graded graphene reinforced porous nanocomposite beams. Compos Sci Technol 142:235–245

    Article  Google Scholar 

  75. Safarpour H, Pourghader J, Habibi M (2019) Influence of spring-mass systems on frequency behavior and critical voltage of a high-speed rotating cantilever cylindrical three-dimensional shell coupled with piezoelectric actuator. J Vib Control 25:1543–1557

    Article  MathSciNet  Google Scholar 

  76. Na K-S, Kim J-H (2004) Three-dimensional thermal buckling analysis of functionally graded materials. Compos B Eng 35:429–437

    Article  Google Scholar 

  77. Zeighampour H, Beni YT, Dehkordi MB (2018) Wave propagation in viscoelastic thin cylindrical nanoshell resting on a visco-Pasternak foundation based on nonlocal strain gradient theory. Thin-Walled Struct 122:378–386

    Article  Google Scholar 

  78. Guo H, Zhuang X, Rabczuk T (2019) A deep collocation method for the bending analysis of Kirchhoff Plate. CMC-Comput Mater Contin 59:433–456

    Article  Google Scholar 

  79. Bellman R, Casti J (1971) Differential quadrature and long-term integration. J Math Anal Appl 34:235–238

    Article  MathSciNet  Google Scholar 

  80. Bellman R, Kashef BG, Casti J (1972) Differential quadrature: a technique for the rapid solution of nonlinear partial differential equations. J Comput Phys 10:40–52. https://doi.org/10.1016/0021-9991(72)90089-7

    Article  MathSciNet  MATH  Google Scholar 

  81. Shu C (2012) Differential quadrature and its application in engineering. Springer Science & Business Media

  82. Shu C, Richards BE (1992) Application of generalized differential quadrature to solve two-dimensional incompressible Navier-Stokes equations. Int J Numer Meth Fluids 15:791–798

    Article  Google Scholar 

  83. Shu C (2012) Differential quadrature and its application in engineering. Springer Science & Business Media

  84. Shi-rong L, Chang-jun C (1991) Thermal-buckling of thin annular plates under multiple loads. Appl Math Mech 12:301–308

    Article  Google Scholar 

  85. Tani J (1981) Elastic instability of a heated annular plate under lateral pressure. J Appl Mech (Trans ASME) 48:399–403

    Article  Google Scholar 

  86. Kiani Y, Eslami M (2013) An exact solution for thermal buckling of annular FGM plates on an elastic medium. Compos B Eng 45:101–110

    Article  Google Scholar 

Download references

Acknowledgements

Shandong University Science and Technology Project (J18KB163).

Author information

Authors and Affiliations

  1. Qingdao Huanghai University, Shandong Qingdao, 266427, China

    Huiwei Chen, Hui Song & Yuanyuan Li

  2. Department of Mechanical Engineering, Faculty of Engineering, Tarbiat Modares University, Tehran, 14115-143, Iran

    Mehran Safarpour

Authors
  1. Huiwei Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hui Song
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Yuanyuan Li
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Mehran Safarpour
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Huiwei Chen or Mehran Safarpour.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Chen, H., Song, H., Li, Y. et al. Hygro-thermal buckling analysis of polymer–CNT–fiber-laminated nanocomposite disk under uniform lateral pressure with the aid of GDQM. Engineering with Computers 38, 1793–1817 (2022). https://doi.org/10.1007/s00366-020-01102-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00366-020-01102-y

Keywords

Search

Navigation