Stacking-Sequence Optimization and Buckling Analysis of Graphene/Fiber-Reinforced Laminated Plates

Document Type : Special Issue: Mechanics of Advanced Fiber Reinforced Composite Structures

Authors

1 Department of Mechanical Engineering, Durban University of Technology, Durban, 4001, South Africa

2 Department of Mechanical Engineering and Institute for Systems Science, Durban University of Technology, Durban, 4001, South Africa

Abstract

The use of graphene-based composites, particularly in aerospace and structural applications, has received extensive attention in recent years. Graphene nanoplatelets are normally used to enhance composite materials' mechanical, thermal, and electrical properties. The present research investigates the biaxial buckling of two- and three-phase angle ply laminated plates reinforced with carbon or glass fibers.  The simply supported plate in this study is defined as a 16-ply symmetric and balanced laminate with uniform distribution of the fiber and graphene content through the thickness. The objective of this work is to produce a cost-effective design using the minimum amount of expensive reinforcement while maximizing the compressive buckling load. The desired results are achieved by finding the optimal stacking sequence of reinforcement fibers, as well as selecting an optimal amount of graphene nanoplatelets and fiber volume content. Numerical results are first obtained for two-phase laminates with different ratios of applied loads. Further, three-phase laminates are studied and, among other things, the relationship between the fiber and graphene content is analyzed. The optimization procedures were performed by particle swarm optimization (PSO) for continuous optimization and genetic algorithm (GA) for integer optimization. The software applications were written by the authors and proved to be very fast and efficient.

Keywords

Main Subjects


[1]    Fu, S.Y., Lauke, B. and Mai, Y.W., 2009. Science and Engineering of Short Fiber-Reinforced Polymer Composites. Woodhead Publishing.
[2]    Parveen, S., Rana, S. and Fangueiro, R., 2017. Advanced Composite Materials: Properties and Applications. De Gruyter Brill.
[3]    Rafiee, M., Nitzsche, F. and Labrosse, M., 2018. Modeling and mechanical analysis of multiscale fiber-reinforced graphene composites: Nonlinear bending, thermal post-buckling and large amplitude vibration. International Journal of Non-Linear Mechanics, 103(1), pp.104-112. doi.org/10.1016/j.ijnonlinmec.2018.05.004.
[4]    Rafiee, M.A., Rafiee, J., Wang, Z., Song, H., Yu, Z.Z. and Koratkar, N., 2009. Enhanced mechanical properties of nanocomposites at low graphene content. ACS Nano, 3(12), pp.3884-3890. doi.org/10.1021/nn9010472. 
[5]    Kim, H., Abdala, A.A. and Macosko, C. W., 2010. Graphene/polymer nanocomposites. Macromolecules, 43(16), pp.6515-6530. doi.org/10.1021/ma100572e.
[6]    Safaei, B. and Fattahi, A., 2017. Free vibrational response of single-layered graphene sheets embedded in an elastic matrix using different non-local plate models. Mechanics, 23(5), pp.678-687. doi.org/10.5755/j01.mech.23.5.14883.
[7]    Su, X., Wang, R., Li, X., Araby, S., Kuan, H.C., Naeem, M. and Ma, J., 2022. A comparative study of polymer nanocomposites containing multi-walled carbon nanotubes and graphene nanoplatelets. Nano Materials Science, 4(3), pp.185-204. doi.org/10.1016/j.nanoms.2021.08.003.
[8]    Shokrieh, M., Ghoreishi, S., Esmkhani, M. and Zhao, Z., 2014. Effects of graphene nanoplatelets and graphene nanosheets on fracture toughness of epoxy nanocomposites. Fatigue & Fracture of Engineering Materials & Structures, 37(10), pp.1116-1123. doi.org/10.1111/ffe.12191.
[9]    Ebrahimi, F. and Dabbagh, A., 2021. An analytical solution for static stability of multi-scale hybrid nanocomposite plates. Engineering with Computers, 37(1), pp.545-559. doi.org/10.1007/s00366-019-00840-y.
[10]    Song, M., Yang, J., Kitipornchai, S. and Zhu W., 2017. Buckling and post-buckling of biaxially compressed functionally graded multilayer graphene nanoplatelet-reinforced polymer composite plates. International Journal of Mechanical Sciences, 131(1), pp.345-355. doi.org/10.1016/j.ijmecsci.2017.07.017.
[11]    Radebe, I.S., Drosopoulos, G.A. and Adali, S., 2019. Buckling of non-uniformly distributed graphene and fiber-reinforced multiscale angle-ply laminates. Meccanica, 54(14), pp. 2263-2279. doi.org/10.1007/s11012-019-01067-3.
[12]    Radebe, I.S., Drosopoulos, G.A. and Adali, S., 2022. Effect of Non-Uniform Fiber Distribution along Thickness and Non-Uniform Ply Thicknesses on Frequencies of Symmetric Angle-Ply Laminates. Fibers and Polymers, 23(8), pp.2250-2260. doi.org/10.1007/s12221-022-4440-5.
[13]    Georgantzinos, S.K., Giannopoulos, G. I. and Markolefas, S. I., 2020. Vibration analysis of carbon fiber-graphene-reinforced hybrid polymer composites using finite element techniques. Materials, 13(19), p.4225. doi.org/10.3390/ma13194225.
[14]    Jeawon, Y., Drosopoulos, G., Foutsitzi, G., Stavroulakis, G. and Adali, S., 2021. Optimization and analysis of frequencies of multi-scale graphene/fiber reinforced nanocomposite laminates with non-uniform distributions of reinforcements. Engineering Structures, 228(2). p.111525. doi.org/10.1016/j.engstruct.2020.111525.
[15]    Chao, C., Koh, S. and Sun, C., 1975. Optimization of buckling and yield strengths of laminated composites. AIAA Journal, 13(9), pp.1131-1132. doi.org/10.2514/3.60515.
[16]    Chen, T.L., 1976. Design of composite-material plates for maximum uniaxial compressive buckling load. Proceedings of the Oklahoma Academy of Science, 56 (1976), pp.104-107. 
[17]    Schmit Jr, L. and Farshi, B., 1977. Optimum design of laminated fiber composite plates. International Journal for Numerical Methods in Engineering, 11(4), pp.623-640, doi.org/10.1002/nme.1620110403.
[18]    Hirano, Y., 1979. Optimum design of laminated plates under axial compression. AIAA Journal, 17(9), pp.1017-1019. doi.org/10.2514/3.61269.
[19]    Haftka, R.T. and Walsh, J.L., 1992. Stacking-sequence optimization for buckling of laminated plates by integer programming. AIAA Journal, 30(3), pp.814-819. doi.org/10.2514/3.10989.
[20]    Chai, G. and Hoon, K., 1992. Buckling of generally laminated composite plates. Composites Science and Technology, 45(2), pp.125-133. doi.org/10.1016/0266-3538(92)90035-2.
[21]    Kicher, T. and Mandell, J., 1971.  A study of the buckling of laminated composite plates.  AIAA Journal, 9(4), pp.605-613. doi.org/10.2514/3.6237.
[22]    Chattopadhyay, A. and Gu, H., 1994. New higher-order plate theory in modeling delamination buckling of composite laminates. AIAA Journal, 32(8), pp.1709-1716. doi.org/10.2514/3.12163.
[23]    Jane, K., Liao, H. and Hong, W., 2003. Validation of the Rayleigh–Ritz method for the post-buckling analysis of rectangular plates with application to delamination growth. Mechanics Research Communications, 30(6), pp.531-538. doi.org/10.1016/S00936413(03)00060-0.
[24]    Darvizeh, M., Darvizeh, A., Ansari, R. and Sharma, C., 2004.  Buckling analysis of generally laminated composite plates (generalized differential quadrature rules versus Rayleigh–Ritz method). Composite Structures, 63(1), pp.69-74. doi.org/10.1016/S0263-8223(03)00133-8.
[25]    Karakaya, Ş. and Soykasap, Ö., 2009. Buckling optimization of laminated composite plates using genetic algorithm and generalized pattern search algorithm. Structural and Multidisciplinary Optimization, 39(3), pp.477-486. doi.org/10.1007/s00158-008-0344-2.
[26]    Nikbakt, S., Kamarian, S. and Shakeri, M., 2018. A review on optimization of composite structures Part I: Laminated composites. Composite Structures, 195(1), pp.158-185. doi.org/10.1016/j.compstruct.2018.03.063.
[27]    Vosoughi, A., Darabi, A., Anjabin, N. and Topal, U., 2017. A mixed finite element and improved genetic algorithm method for maximizing buckling load of stiffened laminated composite plates. Aerospace Science and Technology, 70(4), pp.378-387. doi.org/10.1016/j.ast.2017.08.022.
[28]    Keshtegar, B., Nguyen-Thoi, T., Truong, T.T. and Zhu, S.P., 2021. Optimization of buckling load for laminated composite plates using adaptive Kriging-improved PSO: A novel hybrid intelligent method. Defense Technology, 17(1), pp.85-99. doi.org/10.1016/j.dt.2020.02.020.
[29]    Kaveh, A., Dadras, A. and Malek, N.G., 2019. Optimum stacking sequence design of composite laminates for maximum buckling load capacity using parameter-less optimization algorithms. Engineering with Computers, 35(1), pp.813-832. doi.org/10.1007/s00366-018-0634-2.
[30]    Fakoor, M., Ghoreishi, S.M.N. and Aminjafari, M., 2019. Multi-objective optimization of buckling load for a laminated composite plate by coupling genetic algorithm and FEM. Journal of Aerospace Science and Technology, 12(1), pp.27-37.
[31]    Leissa, A.W., 1987. A review of laminated composite plate buckling. Applied Mechanics Reviews, 40(5), pp. 575-591. doi.org/10.1115/1.3149534.
[32]    Baba, B.O., 2007. Buckling behavior of laminated composite plates. Journal of Reinforced Plastics and Composites, 26(16), pp.1637-1655. doi.org/10.1177/0731684407079515.
[33]    El-Sawy, K.M. and Nazmy, A.S., 2001. Effect of aspect ratio on the elastic buckling of uniaxially loaded plates with eccentric holes. Thin-Walled Structures, 39(12), pp.983-998. doi.org/10.1016/S0263-8231(01)00040-4.
[34]    Soden, P.D., Hinton, M.J. and Kaddour, A., 1998. Lamina properties, lay-up configurations, and loading conditions for a range of fiber reinforced composite laminates. Failure Criteria in Fiber-Reinforced-Polymer Composites: Elsevier, 58(17) pp.1011-1022. doi.org/10.1016/S0266-3538(98)00078-5.
[35]    Ren, J., 2021. Handbook of Ceramics and Composites. CRC Press. 
[36]    Aslan, Z. and Şahin, M., 2009. Buckling behavior and compressive failure of composite laminates containing multiple large delaminations. Composite Structures, 89(3), pp.382-390. doi.org/10.1016/j.compstruct.2008.08.011.
[37]    Vosoughi, A., Darabi, A. and Forkhorji, H.D., 2017. Optimum stacking sequences of thick laminated composite plates for maximizing buckling load using FE-GAs-PSO. Composite Structures, 159(1), pp.361-367. doi.org/10.1016/j.compstruct.2016.09.085.
[38]    Ehsani, A. and Rezaeepazhand, J., 2016. Stacking sequence optimization of laminated composite grid plates for maximum buckling load using genetic algorithm. International Journal of Mechanical Sciences, 119(1), pp.97-106. doi.org/10.1016/j.ijmecsci.2016.09.028.
[39]    Chen, Q. and Qiao, P., 2021. Buckling and post-buckling of rotationally restrained laminated composite plates under shear. Thin-Walled Structures, 161(1), p.107435. doi.org/10.1016/j.tws.2021.107435.
[40]    Bert, C.W. and Malik, M., 1997. On the buckling characteristics of symmetrically laminated cross-ply plates. Mechanics of Composite Materials and Structures, 4(1), pp. 39-67. doi.org/10.1080/10759419708945874.
[41]    Weaver, P.M. and Nemeth, M.P., 2007. Bounds on flexural properties and buckling response for symmetrically laminated composite plates. Journal of Engineering Mechanics, 133(11), pp.1178-1191. doi.org/10.1061/(ASCE)07339399(2007)133:11(1178).