An Innovative Optimized Design for Laminated Composites in terms of a Proposed Bi-Objective Technique

Document Type: Regular Article


1 Professor, Department of Mechanical and Aerospace Engineering, Aeronautical University of Science and Technology, Tehran, Iran

2 Graduate Student, Center for Postgraduate Studies, Aeronautical University of Science and Technology, Tehran, Iran

3 Ph.D. Student, Department of Mechanical Engineering, University of Manitoba, Winnipeg, Canada



The article proposes a bi-objective optimization approach for layup design of laminates. The optimization method combines the Particle Swarm Optimization (PSO) heuristics and Simulated Annealing (SA) optimization method. The minimum weight optimization is subjected to design constraints such as strength, stiffness, layup blending continuity, and several manufacturing design rules, which are combined as a single function and included within the bi-objective formulation. Several composite materials design problems are included to show the capabilities and usefulness of the proposed method. The optimization analysis has also been connected to the finite element analysis to solve the problem of composite plate optimization with blending constraints. The plate is divided into some regions, and the blending constraints are imposed globally by using the concepts of the greater-than-or-equal-to blending to achieve continuity of laminate layups across the regions. The results generally showed that the proposed method led to excellent results, representing a promising approach for the design of laminated composite materials.


Main Subjects

[1]     Soutis C. Introduction: engineering requirements for aerospace composite materials. Polym. Compos. Aerosp. Ind., Elsevier; 2015, p. 1–18. doi:10.1016/B978-0-85709-523-7.00001-3.

[2]     Javidrad F, Nouri R. A simulated annealing method for design of laminates with required stiffness properties. Compos Struct 2011;93:1127–35. doi:10.1016/j.compstruct.2010.10.011.

[3]     Kaveh A, Dadras A, Geran Malek N. Optimum stacking sequence design of composite laminates for maximum buckling load capacity using parameter-less optimization algorithms. Eng Comput 2019;35:813–32. doi:10.1007/s00366-018-0634-2.

[4]     Deveci HA, Artem HS. Optimum design of fatigue-resistant composite laminates using hybrid algorithm. Compos Struct 2017;168:178–88. doi:10.1016/j.compstruct.2017.01.064.

[5]     Li X, Wang H, Li G. Reanalysis assisted metaheuristic optimization for free vibration problems of composite laminates. Compos Struct 2018;206:380–91. doi:10.1016/j.compstruct.2018.08.028.

[6]     Reguera F, Cortínez VH. Optimal design of composite thin-walled beams using simulated annealing. Thin-Walled Struct 2016;104:71–81. doi:10.1016/j.tws.2016.03.001.

[7]     Barbero EJ. Introduction to composite materials design. CRC press; 2017.

[8]     Belardi VG, Fanelli P, Vivio F. First-order shear deformation analysis of rectilinear orthotropic composite circular plates undergoing transversal loads. Compos Part B Eng 2019;174:107015. doi:10.1016/j.compositesb.2019.107015.

[9]     Adhikari B, Singh BN. An efficient higher order non-polynomial Quasi 3-D theory for dynamic responses of laminated composite plates. Compos Struct 2018;189:386–97. doi:10.1016/j.compstruct.2017.10.044.

[10]    Khandan R, Noroozi S, Sewell P, Vinney J. The development of laminated composite plate theories: a review. J Mater Sci 2012;47:5901–10. doi:10.1007/s10853-012-6329-y.

[11]    Guo Y, Nagy AP, Gürdal Z. A layerwise theory for laminated composites in the framework of isogeometric analysis. Compos Struct 2014;107:447–57. doi:10.1016/j.compstruct.2013.08.016.

[12]    Carrera E. CZ° requirements—models for the two dimensional analysis of multilayered structures. Compos Struct 1997;37:373–83. doi:10.1016/S0263-8223(98)80005-6.

[13]    Arora JS. Introduction to optimum design. (4th ed.). 707-738. Academic Press, (Chapter 18). Elsevier; 2018.

[14]    Guenin B, Könemann J, Tuncel L. A gentle introduction to optimization. Cambridge University Press; 2014.

[15]    An H, Chen S, Huang H. Laminate stacking sequence optimization with strength constraints using two-level approximations and adaptive genetic algorithm. Struct Multidiscip Optim 2015;51:903–18. doi:10.1007/s00158-014-1181-0.

[16]    Li K, Liu X, Jin Y, Qi H, Liu X, Xu S. Structural Strength and Laminate Optimization of Composite Connecting Bracket in Manned Spacecraft Using a Genetic Algorithm. Appl Compos Mater 2019;26:591–604. doi:10.1007/s10443-018-9736-7.

[17]    Wang W, Guo S, Chang N, Zhao F, Yang W. A modified ant colony algorithm for the stacking sequence optimisation of a rectangular laminate. Struct Multidiscip Optim 2010;41:711–20. doi:10.1007/s00158-009-0447-4.

[18]    Zadeh PM, Fakoor M, Mohagheghi M. Bi-level optimization of laminated composite structures using particle swarm optimization algorithm. J Mech Sci Technol 2018;32:1643–52. doi:10.1007/s12206-018-0319-1.

[19]    Kathiravan R, Ganguli R. Strength design of composite beam using gradient and particle swarm optimization. Compos Struct 2007;81:471–9. doi:10.1016/j.compstruct.2006.09.007.

[20]    Javidrad F, Nazari M, Javidrad HR. Optimum stacking sequence design of laminates using a hybrid PSO-SA method. Compos Struct 2018;185:607–18. doi:10.1016/j.compstruct.2017.11.074.

[21]    Barroso ES, Parente E, Cartaxo de Melo AM. A hybrid PSO-GA algorithm for optimization of laminated composites. Struct Multidiscip Optim 2017;55:2111–30. doi:10.1007/s00158-016-1631-y.

[22]    Javidrad F, Nazari M. A new hybrid particle swarm and simulated annealing stochastic optimization method. Appl Soft Comput 2017;60:634–54. doi:10.1016/j.asoc.2017.07.023.

[23]    Halpin JC. Primer on Composite Materials Analysis. Technomic Publishinf Company, Inc., USA. 1984.

[24]    Sun CT, Tao QJ, Oplinger DW, J. HW. Comparative evaluation of failure analysis methods for composite laminates. In DOT/FAA/AR-95/109, Office of Aviation Research, Washington. 1996.

[25]    Daniel IM. Constitutive behavior and failure criteria for composites under static and dynamic loading. Meccanica 2015;50:429–42. doi:10.1007/s11012-013-9829-1.

[26]    Tsai SW, Wu EM. A General Theory of Strength for Anisotropic Materials. J Compos Mater 1971;5:58–80. doi:10.1177/002199837100500106.

[27]    Kim CW, Song SR, Hwang W, Park HC, Han KS. On the failure indices of quadratic failure criteria for optimal stacking sequence design of laminated plate. Appl Compos Mater 1994;1:81–5. doi:10.1007/BF00567214.

[28]    Tsai SW. Strength Characteristics of Composite Materials. . NASA CR-224, USA. 1965.

[29]    Hoffman O. The Brittle Strength of Orthotropic Materials. J Compos Mater 1967;1:200–6. doi:10.1177/002199836700100210.

[30]    Dong H, Wang J, Karihaloo BL. An improved Puck’s failure theory for fibre-reinforced composite laminates including the in situ strength effect. Compos Sci Technol 2014;98:86–92. doi:10.1016/j.compscitech.2014.04.009.

[31]    Rohwer K. Predicting fiber composite damage and failure. J Compos Mater 2015;49:2673–83. doi:10.1177/0021998314553885.

[32]    Akbulut M, Sonmez FO. Design optimization of laminated composites using a new variant of simulated annealing. Comput Struct 2011;89:1712–24. doi:10.1016/j.compstruc.2011.04.007.

[33]    Zhu H, Sankar B V., Marrey R V. Evaluation of Failure Criteria for Fiber Composites Using Finite Element Micromechanics. J Compos Mater 1998;32:766–82. doi:10.1177/002199839803200804.

[34]    Bailie JA, Ley RP, Pasricha A. A summary and review of composite laminate design guidelines. NASA contract final report NAS1-19347, National Aeronautics and Space Administration, Langley Research Center, USA. 1997.

[35]    Kim J-S, Kim N-P, Han S-H. Optimal stiffness design of composite laminates for a train carbody by an expert system and enumeration method. Compos Struct 2005;68:147–56. doi:10.1016/j.compstruct.2004.03.009.

[36]    Vannucci P, Verchery G. A special class of uncoupled and quasi-homogeneous laminates. Compos Sci Technol 2001;61:1465–73. doi:10.1016/S0266-3538(01)00039-2.

[37]    Montemurro M. An extension of the polar method to the First-order Shear Deformation Theory of laminates. Compos Struct 2015;127:328–39. doi:10.1016/j.compstruct.2015.03.025.

[38]    Middleton TH. Composite Materials in Aircraft Structures. John Wiley and Sons. 1990.

[39]    Niu MC-Y. Composite Airframe Structures, Third edition. Hong Kong Conmilit Press Ltd. 2010.

[40]    Todoroki A, Sasada N, Miki M. Object-Oriented Approach to Optimize Composite Laminated Plate Stiffness with Discrete Ply Angles. J Compos Mater 1996;30:1020–41. doi:10.1177/002199839603000904.

[41]    Wang D, Tan D, Liu L. Particle swarm optimization algorithm: an overview. Soft Comput 2018;22:387–408. doi:10.1007/s00500-016-2474-6.

[42]    Kennedy J, Eberhart R. Particle swarm optimization. Proc. IEEE Int. Conf. Neural Netw. IV, 1942–1948., vol. 4, IEEE; 1995, p. 1942–8. doi:10.1109/ICNN.1995.488968.

[43]    Taherkhani M, Safabakhsh R. A novel stability-based adaptive inertia weight for particle swarm optimization. Appl Soft Comput 2016;38:281–95. doi:10.1016/j.asoc.2015.10.004.

[44]    Schneider JJ, Puchta M. Investigation of acceptance simulated annealing — A simplified approach to adaptive cooling schedules. Phys A Stat Mech Its Appl 2010;389:5822–31. doi:10.1016/j.physa.2010.08.045.

[45]    Atiqullah MM. An Efficient Simple Cooling Schedule for Simulated Annealing, 2004, p. 396–404. doi:10.1007/978-3-540-24767-8_41.

[46]    Xia W, Wu Z. A hybrid particle swarm optimization approach for the job-shop scheduling problem. Int J Adv Manuf Technol 2006;29:360–6. doi:10.1007/s00170-005-2513-4.

[47]    Xi-Huai Wang, Jun-Jun Li. Hybrid particle swarm optimization with simulated annealing. Proc. 2004 Int. Conf. Mach. Learn. Cybern. (IEEE Cat. No.04EX826), vol. 4, IEEE; n.d., p. 2402–5. doi:10.1109/ICMLC.2004.1382205.

[48]    Shieh H-L, Kuo C-C, Chiang C-M. Modified particle swarm optimization algorithm with simulated annealing behavior and its numerical verification. Appl Math Comput 2011;218:4365–83. doi:10.1016/j.amc.2011.10.012.

[49]    Javidrad F, Nazari M, Javidrad HR. A variable Markov chain length strategy for improving simulated annealing convergence behavior: An experimental verification. In A. Scollen & T. Hargraves (Eds.), Simulated Annealing, Introduction, Applications and Theory n.d.:221–68.

[50]    Grosset L, LeRiche R, Haftka RT. A double-distribution statistical algorithm for composite laminate optimization. Struct Multidiscip Optim 2006;31:49–59. doi:10.1007/s00158-005-0551-z.

[51]    Venter G, Haftka RT. Constrained particle swarm optimization using a bi-objective formulation. Struct Multidiscip Optim 2010;40:65–76. doi:10.1007/s00158-009-0380-6.

[52]    Kristinsdottir BP, Zabinsky ZB, Tuttle ME, Neogi S. Optimal design of large composite panels with varying loads. Compos Struct 2001;51:93–102. doi:10.1016/S0263-8223(00)00128-8.

[53]    Liu D, Toroporov V V., Querin OM, Barton DC. Bilevel Optimization of Blended Composite Wing Panels. J Aircr 2011;48:107–18. doi:10.2514/1.C000261.

[54]    Adams DB, Watson LT, Gürdal Z, Anderson-Cook CM. Genetic algorithm optimization and blending of composite laminates by locally reducing laminate thickness. Adv Eng Softw 2004;35:35–43. doi:10.1016/j.advengsoft.2003.09.001.

[55]    Irisarri F-X, Lasseigne A, Leroy F-H, Le Riche R. Optimal design of laminated composite structures with ply drops using stacking sequence tables. Compos Struct 2014;107:559–69. doi:10.1016/j.compstruct.2013.08.030.

[56]    Jong-Hwan Kim, Hyun Myung. Evolutionary programming techniques for constrained optimization problems. IEEE Trans Evol Comput 1997;1:129–40. doi:10.1109/4235.687880.