Analytical investigation on the buckling and free vibration of porous laminated FG-CNTRC plates

  • Tahir Ghazoul University of Djillali Liabes, Structures and Advanced Materials in Civil Engineering and Public Works Laboratory, Sidi Bel Abbes, People's Democratic Republic of Algeria https://orcid.org/0009-0006-9869-4339
  • Mohamed Atif Benatta University of Djillali Liabes, Structures and Advanced Materials in Civil Engineering and Public Works Laboratory, Sidi Bel Abbes, People's Democratic Republic of Algeria https://orcid.org/0009-0007-5854-9054
  • Abdelwahhab Khatir Polytechnic University of Marche, Structural Section DICEA, Ancona, Italian Republic https://orcid.org/0000-0003-4920-5165
  • Youcef Beldjelili University of Djillali Liabes, Structures and Advanced Materials in Civil Engineering and Public Works Laboratory, Sidi Bel Abbes, People's Democratic Republic of Algeria https://orcid.org/0000-0003-3877-9665
  • Baghdad Krour University of Djillali Liabes, Structures and Advanced Materials in Civil Engineering and Public Works Laboratory, Sidi Bel Abbes, People's Democratic Republic of Algeria https://orcid.org/0000-0002-8265-9807
  • Mohamed Bachir Bouiadjra University of Djillali Liabes, Structures and Advanced Materials in Civil Engineering and Public Works Laboratory, Sidi Bel Abbes, People's Democratic Republic of Algeria; Thematic Agency for Research in Science and Technology, Algiers, People's Democratic Republic of Algeria https://orcid.org/0009-0008-4814-6187
Keywords: buckling, free vibration, laminated composite plate, porosity, functionally graded material, carbon nanotubes

Abstract


Introduction/purpose: The aim of this study is to examine the buckling and free vibration behavior of laminated composite plates reinforced with carbon nanotubes when various sources of uncertainty are taken into account with the main focus being the existence of porosity.

Methods: A porous laminated plate model is developed using a  high order shear deformation theory. Different configurations of functionally graded aligned single-walled carbon nanotubes throughout the thickness of each layer are being investigated. The effective properties of materials are evaluated through the extended rule of mixture while considering an upper bound for the effect of porosity. The governing equations are derived and solved using the virtual work principle and Navier's approach. The validity of the current formulation is confirmed by comparing the results with the existing data from literature sources. The impact of numerous parameters such as porosity, carbon nanotube volume fraction, reinforcement distribution types, lamination scheme, and the number of layers on the buckling and free vibration responses is investigated in detail.

Results: A key finding of this study is the significant reduction in buckling resistance of laminated FG-CNTRC plates due to porosity, contrasting with the minor impact on the free vibration response. 

Conclusion: The results of this paper emphasize the critical role of porosity in structural integrity and provide novel insights into the behaviour of advanced composite materials.

References

Alimoradzadeh, M., Heidari, H., Tornabene, F. & Dimitri, R. 2023. Thermo-Mechanical Buckling and Non-Linear Free Oscillation of Functionally Graded Fiber-Reinforced Composite Laminated (FG-FRCL) Beams. Applied Sciences, 13(8), art.number:4904. Available at: https://doi.org/10.3390/app13084904.

Arani, A.G., Kiani, F. & Afshari, H. 2021. Free and forced vibration analysis of laminated functionally graded CNT-reinforced composite cylindrical panels. Journal of Sandwich Structures & Materials, 23(1), pp.255-278. Available at: https://doi.org/10.1177/1099636219830787.

Chiker, Y., Bachene, M., Attaf, B., Hafaifa, A. & Guemana, M. 2023. Uncertainty influence of nanofiller dispersibilities on the free vibration behavior of multi-layered functionally graded carbon nanotube-reinforced composite laminated plates. Acta Mechanica, 234(4), pp.1687-1711. Available at: https://doi.org/10.1007/s00707-022-03438-6.

Ciriscioli, P.R., Springer, G.S. & Lee, W.I. 1991. An Expert System for Autoclave Curing of Composites. Journal of Composite Materials, 25(12), pp.1542-1587. Available at: https://doi.org/10.1177/002199839102501201.

Daikh, A.A., Belarbi, M.-O., Salami, S.J., Ladmek, M., Belkacem, A., Houari, M.S.A., Ahmed, H.M. & Eltaher, M.A. 2023. A three-unknown refined shear beam model for the bending of randomly oriented FG-CNT/fiber-reinforced composite laminated beams rested on a new variable elastic foundation. Acta Mechanica, 234(10), pp.5171-5186. Available at: https://doi.org/10.1007/s00707-023-03657-5.

Fu, T., Chen, Z., Yu, H., Wang, Z. & Liu, X. 2019. Mechanical behavior of laminated functionally graded carbon nanotube reinforced composite plates resting on elastic foundations in thermal environments. Journal of Composite Materials, 53(9), pp.1159-1179. Available at: https://doi.org/10.1177/0021998318796170.

Guessas, H., Zidour, M., Meradjah, M. & Tounsi, A. 2018. The critical buckling load of reinforced nanocomposite porous plates. Structural Engineering and Mechanics, 67(2), pp.115-123. Available at: https://doi.org/10.12989/sem.2018.67.2.115.

Hagstrand, P.-O., Bonjour, F. & Månson, J.-A.E. 2005. The influence of void content on the structural flexural performance of unidirectional glass fibre reinforced polypropylene composites. Composites Part A: Applied Science and Manufacturing, 36(5), pp.705-714. Available at: https://doi.org/10.1016/j.compositesa.2004.03.007.

Hayashi, T. & Takahashi, J. 2017. Influence of void content on the flexural fracture behaviour of carbon fiber reinforced polypropylene. Journal of Composite Materials, 51(29), pp.4067-4078. Available at: https://doi.org/10.1177/0021998317698215.

Hernández, S., Sket, F., Molina-Aldareguı´a, J.M., González, C. & LLorca, J. 2011. Effect of curing cycle on void distribution and interlaminar shear strength in polymer-matrix composites. Composites Science and Technology, 71(10), pp.1331-1341. Available at: https://doi.org/10.1177/0021998317698215.

Huang, B., Guo, Y., Wang, J., Du, J., Qian, Z., Ma, T. & Yi, L. 2017. Bending and free vibration analyses of antisymmetrically laminated carbon nanotube-reinforced functionally graded plates. Journal of Composite Materials, 51(22), pp.3111-3125. Available at: https://doi.org/10.1177/0021998316685165.

Kirchhoff, G. 1850. Über das Gleichgewicht und die Bewegung einer elastischen Scheibe. Journal für die reine und angewandte Mathematik (Crelles Journal), 1850(40), pp.51-88. Available at: https://doi.org/10.1515/crll.1850.40.51.

Kwon, H., Bradbury, C.R. & Leparoux, M. 2011. Fabrication of Functionally Graded Carbon Nanotube-Reinforced Aluminum Matrix Composite. Advanced Engineering Materials, 13(4), pp.325-329. Available at: https://doi.org/10.1002/adem.201000251.

Lee, J., Kim, J. & Hyeon, T. 2006. Recent Progress in the Synthesis of Porous Carbon Materials. Advanced Materials, 18(16), pp.2073-2094. Available at: https://doi.org/10.1002/adma.200501576.

Lei, Z.X., Liew, K.M. & Yu, J.L. 2013. Buckling analysis of functionally graded carbon nanotube-reinforced composite plates using the element-free kp-Ritz method. Composite Structures, 98, pp.160-168. Available at: https://doi.org/10.1016/j.compstruct.2012.11.006.

Lei, Z.X., Zhang, L.W. & Liew, K.M. 2018. Modeling large amplitude vibration of matrix cracked hybrid laminated plates containing CNTR-FG layers. Applied Mathematical Modelling, 55, pp.33-48. Available at: https://doi.org/10.1016/j.apm.2017.10.032.

Liew, K.M., Lei, Z.X. & Zhang, L.W. 2015. Mechanical analysis of functionally graded carbon nanotube reinforced composites: A review. Composite Structures, 120, pp.90-97. Available at: https://doi.org/10.1016/j.compstruct.2014.09.041.

Ma, R. & Jin, Q. 2023. Free Vibration Analysis of Functionally Graded Graphene-Reinforced Composite-Laminated Plates. Journal of Aerospace Engineering, 36(3), art.ID:04023016. Available at: https://doi.org/10.1061/JAEEEZ.ASENG-4657.

Madsen, B. & Lilholt, H. 2003. Physical and mechanical properties of unidirectional plant fibre composites—an evaluation of the influence of porosity. Eco-Composites, 63(9), pp.1265-1272. Available at: https://doi.org/10.1016/S0266-3538(03)00097-6.

Madsen, B., Thygesen, A. & Lilholt, H. 2009. Plant fibre composites – porosity and stiffness. Composites Science and Technology, 69(7), pp.1057-1069. Available at: https://doi.org/10.1016/j.compscitech.2009.01.016.

Malekzadeh, P. & Shojaee, M. 2013. Buckling analysis of quadrilateral laminated plates with carbon nanotubes reinforced composite layers. Thin-Walled Structures, 71, pp.108-118. Available at: https://doi.org/10.1016/j.tws.2013.05.008.

Mantari, J.L., Oktem, A.S. & Guedes Soares, C. 2012. A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. International Journal of Solids and Structures, 49(1), pp.43-53. Available at: https://doi.org/10.1016/j.ijsolstr.2011.09.008.

Medani, M., Benahmed, A., Zidour, M., Heireche, H. & Tounsi, A. 2019. Static and dynamic behavior of (FG-CNT) reinforced porous sandwich plate using energy principle. Steel and Composite Structures, 32(5), pp.595-610. Available at: https://doi.org/10.12989/scs.2019.32.5.595.

Mehdikhani, M., Gorbatikh, L., Verpoest, I. & Lomov, S.V. 2019. Voids in fiber-reinforced polymer composites: A review on their formation, characteristics, and effects on mechanical performance. Journal of Composite Materials, 53(12), pp.1579-1669. Available at: https://doi.org/10.1177/0021998318772152.

Mindlin, R.D. 1951. Influence of rotatory inertia and shear on flexural motions of isotropic, elastic plates. Journal of Applied Mechanics, 18(1), pp.31-38. Available at: https://doi.org/10.1115/1.4010217.

Phani, K.K. & Niyogi, S.K. 1987. Young’s modulus of porous brittle solids. Journal of Materials Science, 22(1), pp.257-263. Available at: https://doi.org/10.1007/BF01160581.

Reddy, J.N. 1984. A Simple Higher-Order Theory for Laminated Composite Plates. Journal of Applied Mechanics, 51(4), pp.745-752. Available at: https://doi.org/10.1115/1.3167719.

Sayyad, A.S. & Ghugal, Y.M. 2015. On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results. Composite Structures, 129, pp.177-201. Available at: https://doi.org/10.1016/j.compstruct.2015.04.007.

Shen, H.S. 2009. Nonlinear bending of functionally graded carbon nanotube-reinforced composite plates in thermal environments. Composite Structures, 91(1), pp.9-19. Available at: https://doi.org/10.1016/j.compstruct.2009.04.026.

Shimpi, R.P., Arya, H. & Naik, N.K. 2003. A Higher Order Displacement Model for the Plate Analysis. Journal of Reinforced Plastics and Composites, 22(18), pp.1667-1688. Available at: https://doi.org/10.1177/073168403027618.

Stamopoulos, A.G., Tserpes, K.I., Průcha, P. & Vavřík, D. 2016. Evaluation of porosity effects on the mechanical properties of carbon fiber-reinforced plastic unidirectional laminates by X-ray computed tomography and mechanical testing. Journal of Composite Materials, 50, pp.2087-2098. Available at: https://doi.org/10.1077/0021998315602049.

Thai, H.-T. & Choi, D.-H. 2011. A refined plate theory for functionally graded plates resting on elastic foundation. Composites Science and Technology, 71(16), pp.1850-1858. Available at: https://doi.org/10.1016/j.compscitech.2011.08.016.

Thai, H.-T. & Vo, T.P. 2013. A new sinusoidal shear deformation theory for bending, buckling, and vibration of functionally graded plates. Applied Mathematical Modelling, 37(5), pp.3269–3281. Available at: https://doi.org/10.1016/j.apm.2012.08.008.

Tran, H.Q., Vu, V.T., Tran, M.T. & Nguyen-Tri, P. 2020. A new four-variable refined plate theory for static analysis of smart laminated functionally graded carbon nanotube reinforced composite plates. Mechanics of Materials, 142, art.number:103294. Available at: https://doi.org/10.1016/j.mechmat.2019.103294.

Wattanasakulpong, N. & Chaikittiratana, A. 2015. Exact solutions for static and dynamic analyses of carbon nanotube-reinforced composite plates with Pasternak elastic foundation. Applied Mathematical Modelling, 39(18), pp.5459-5472. Available at: https://doi.org/10.1016/j.apm.2014.12.058.

Zhang, L.W. & Selim, B.A. 2017. Vibration analysis of CNT-reinforced thick laminated composite plates based on Reddy’s higher-order shear deformation theory. Composite Structures, 160, pp.689-705. Available at: https://doi.org/10.1016/j.compstruct.2016.10.102.

Zhu, P., Lei, Z.X. & Liew, K.M. 2012. Static and free vibration analyses of carbon nanotube-reinforced composite plates using finite element method with first order shear deformation plate theory. Composite Structures, 94(4), pp.1450-1460. Available at: https://doi.org/10.1016/j.compstruct.2011.11.010.

Published
2024/09/28
Section
Original Scientific Papers