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Optimum stacking sequence design of composite laminates for maximum buckling load capacity using parameter-less optimization algorithms

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Abstract

This paper presents a comparative study of the application of parameter-less meta-heuristic algorithms in optimum stacking sequence design of com of composite laminates for maximum buckling load capacity. Here, JAYA algorithm, along with Salp Swarm Algorithm, Colliding Bodies Optimization, Grey Wolf Optimizer, and Genetic Algorithm with standard setting and self-adaptive version are implemented to the problem of composite laminates with 64 graphite/epoxy plies with conventional ply angles, under several bi-axial cases and panel aspect ratios. Optimization objective is to maximize the buckling load of symmetric and balanced laminated plate. Statistical analysis are performed for six cases and the results are compared in terms of mean, standard deviation, the coefficient of variation, best and worst solutions, accompanied by the percentage of the independent runs that found the global optimum \(\left( {{R_{{\text{op}}}}} \right)\) and near global optimum \(\left( {{R_{{\text{no}}}}} \right)\). The Kruskal–Wallis nonparametric test is also utilized to make further confidence in the examinations. Numerical results show the high capability of the JAYA algorithm for maximizing the buckling capacity of composite plates.

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References

  1. Abachizadeh M, Tahani M (2009) An ant colony optimization approach to multi-objective optimal design of symmetric hybrid laminates for maximum fundamental frequency and minimum cost. Struct Multidiscip Optim 37:367–376

    Article  Google Scholar 

  2. Abhishek K, Kumar VR, Datta S, Mahapatra SS (2017) Application of JAYA algorithm for the optimization of machining performance characteristics during the turning of CFRP (epoxy) composites: comparison with TLBO, GA and ICA. Eng Comput 33:457–475

    Article  Google Scholar 

  3. Abrate S (1994) Optimal design of laminated plates and shells. Compos Struct 29:269–286

    Article  Google Scholar 

  4. Almeida F, Awruch A (2009) Design optimization of composite laminated structures using genetic algorithms and finite element analysis. Compos Struct 88:443–454

    Article  Google Scholar 

  5. Attaran A, Majid DL, Basri S, Mohd Rafie AS, Abdullah EJ (2008) Structural optimization of an aeroelastically tailored composite flat plate made of woven fiberglass/epoxy. Acta Mech 196:161–173. https://doi.org/10.1007/s00707-007-0488-y

    Article  MATH  Google Scholar 

  6. Bäck T, Fogel DB, Michalewicz Z (2000) Evolutionary computation 1: Basic algorithms and operators. vol 1. CRC press, Boca Raton

    Book  MATH  Google Scholar 

  7. de Almeida FS (2016) Stacking sequence optimization for maximum buckling load of composite plates using harmony search algorithm. Compos Struct 143:287–299

    Article  Google Scholar 

  8. De Jong KA (1975) Analysis of the behavior of a class of genetic adaptive systems. Ph.D. Thesis, University of Michigan, USA

  9. Du D-C, Vinh H-H, Trung V-D, Hong Quyen N-T, Trung N-T (2017) Efficiency of Jaya algorithm for solving the optimization-based structural damage identification problem based on a hybrid objective function. Eng Optim 50:1–19

    MathSciNet  Google Scholar 

  10. Erdal O, Sonmez FO (2005) Optimum design of composite laminates for maximum buckling load capacity using simulated annealing. Compos Struct 71:45–52

    Article  Google Scholar 

  11. Fang C, Springer GS (1993) Design of composite laminates by a Monte Carlo method. J Compos Mater 27:721–753

    Article  Google Scholar 

  12. García S, Molina D, Lozano M, Herrera F (2009) A study on the use of non-parametric tests for analyzing the evolutionary algorithms’ behaviour: a case study on the CEC’2005 special session on real parameter optimization. J Heuristics 15:617

    Article  MATH  Google Scholar 

  13. Ghavidel S, Azizivahed A, Li L (2018) A hybrid Jaya algorithm for reliability–redundancy. allocation problems. Eng Optim 50:698–715

    Article  MathSciNet  Google Scholar 

  14. Ghiasi H, Fayazbakhsh K, Pasini D, Lessard L (2010) Optimum stacking sequence design of composite materials Part II: variable stiffness design. Compos Struct 93:1–13

    Article  Google Scholar 

  15. Ghiasi H, Pasini D, Lessard L (2009) Optimum stacking sequence design of composite materials Part I: constant stiffness design. Compos Struct 90:1–11. https://doi.org/10.1016/j.compstruct.2009.01.006

    Article  Google Scholar 

  16. Goldberg DE (2006) Genetic algorithms. Pearson Education India, Noida

    Google Scholar 

  17. Goldberg DE, Deb K (1991) A comparative analysis of selection schemes used in genetic algorithms. In: Foundations of genetic algorithms, vol 1. Elsevier, Amsterdam, pp 69–93

    Google Scholar 

  18. Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning 3:95–99

  19. Gürdal Z, Haftka RT (1993) Optimization of composite laminates. In: Rozvany GIN (ed) Optimization of large structural systems. Springer Netherlands, Dordrecht, pp 623–648. https://doi.org/10.1007/978-94-010-9577-8_31

    Chapter  Google Scholar 

  20. Haftka RT, Gürdal Z (2012) Elements of structural optimization, vol 11. Springer Science & Business Media, Dordrecht

    MATH  Google Scholar 

  21. Haftka RT, Walsh JL (1992) Stacking-sequence optimization for buckling of laminated plates by integer programming. AIAA J 30:814–819

    Article  Google Scholar 

  22. Harik GR, Lobo FG (1999) A parameter-less genetic algorithm. In: Proceedings of the 1st Annual conference on genetic and evolutionary computation, Vol. 1. Morgan Kaufmann Publishers Inc., pp 258–265

  23. Hollander M, Wolfe A, Chicken DE (2014) Nonparametric statistical methods. 3edn. John Wiley, New York, USA

  24. Jacoby SL, Kowalik J, Pizzo JT (1972) Iterative methods for nonlinear optimization problems, Prentice Hall series in automatic computation

  25. Jones RM (1998) Mechanics of composite materials. CRC press, Boca Raton

    Google Scholar 

  26. Karakaya Ş, Soykasap Ö (2009) Buckling optimization of laminated composite plates using genetic algorithm and generalized pattern search algorithm. Struct Multidiscip Optim 39:477–486

    Article  Google Scholar 

  27. Kaveh A (2017) Advances in metaheuristic algorithms for optimal design of structures. 2 edn. Springer, Berlin. https://doi.org/10.1007/978-3-319-46173-1

    Book  MATH  Google Scholar 

  28. Kaveh A (2017) Applications of metaheuristic optimization algorithms in civil engineering. Springer, Berlin

    Book  MATH  Google Scholar 

  29. Kaveh A, Dadras A, Malek NG (2018) Buckling load of laminated composite plates using three variants of the biogeography-based optimization algorithm. Acta Mech 229:1551–1566

    Article  MathSciNet  Google Scholar 

  30. Kaveh A, Ilchi Ghazaan M (2015) A comparative study of CBO and ECBO for optimal design of skeletal structures. Comput Struct 153:137–147

    Article  Google Scholar 

  31. Kaveh A, Mahdavi VR (2014) Colliding bodies optimization method for optimum design of truss structures with continuous variables. Adv Eng Softw 70:1–12

    Article  Google Scholar 

  32. Kaveh A, Mahdavi VR (2014) Colliding bodies optimization: a novel meta-heuristic method. Comput Struct 139:18–27

    Article  Google Scholar 

  33. Kaw AK (2005) Mechanics of composite materials. CRC press, Boca Raton

    Book  MATH  Google Scholar 

  34. Kogiso N, Watson LT, Gürdal Z, Haftka RT (1994) Genetic algorithms with local improvement for composite laminate design. Struct Multidiscip Optim 7:207–218

    Article  Google Scholar 

  35. Le Riche R, Haftka RT (1993) Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm. AIAA J 31:951–956

    Article  MATH  Google Scholar 

  36. Lin C-C, Lee Y-J (2004) Stacking sequence optimization of laminated composite structures using genetic algorithm with local improvement. Compos Struct 63:339–345

    Article  Google Scholar 

  37. Liu B, Haftka RT, Akgün MA, Todoroki A (2000) Permutation genetic algorithm for stacking sequence design of composite laminates. Comput Methods Appl Mech Eng 186:357–372

    Article  MathSciNet  MATH  Google Scholar 

  38. Lobo FG, Goldberg DE (2004) The parameter-less genetic algorithm in practice. Inf Sci 167:217–232

    Article  MATH  Google Scholar 

  39. Matsuzaki R, Todoroki A (2007) Stacking-sequence optimization using fractal branch-and-bound method for unsymmetrical laminates. Compos Struct 78:537–550. https://doi.org/10.1016/j.compstruct.2005.11.015

    Article  Google Scholar 

  40. McMahon MT, Watson LT, Soremekun GA, Gürdal Z, Haftka RT (1998) A Fortran 90 genetic algorithm module for composite laminate structure design. Eng with Comput 14:260–273

    Article  Google Scholar 

  41. Mirjalili S, Gandomi AH, Mirjalili SZ, Saremi S, Faris H, Mirjalili SM (2017) Salp Swarm algorithm: a bio-inspired optimizer for engineering design problems. Adv Eng Softw

  42. Mirjalili S, Mirjalili SM, Lewis A (2014) Grey wolf optimizer. Adv Eng Softw 69:46–61

    Article  Google Scholar 

  43. Omkar S, Senthilnath J, Khandelwal R, Naik GN, Gopalakrishnan S (2011) Artificial Bee Colony (ABC) for multi-objective design optimization of composite structures. Appl Soft Comput 11:489–499

    Article  Google Scholar 

  44. Omkar SN, Khandelwal R, Ananth TVS, Narayana Naik G, Gopalakrishnan S (2009) Quantum behaved Particle Swarm Optimization (QPSO) for multi-objective design optimization of composite structures. Expert Syst Appl 36:11312–11322. https://doi.org/10.1016/j.eswa.2009.03.006

    Article  Google Scholar 

  45. Omkar SN, Mudigere D, Naik GN, Gopalakrishnan S (2008) Vector evaluated particle swarm optimization (VEPSO) for multi-objective design optimization of composite structures. Comput Struct 86:1–14. https://doi.org/10.1016/j.compstruc.2007.06.004

    Article  Google Scholar 

  46. Pai N, Kaw A, Weng M (2003) Optimization of laminate stacking sequence for failure load maximization using. Tabu Search Compos Part B Eng 34:405–413. https://doi.org/10.1016/S1359-8368(02)00135-X

    Article  Google Scholar 

  47. Rao ARM, Arvind N (2005) A scatter search algorithm for stacking sequence optimisation of laminate composites. Compos Struct 70:383–402

    Article  Google Scholar 

  48. Rao R (2016) Jaya: A simple and new optimization algorithm for solving constrained and unconstrained optimization problems. Int J Ind Eng Comput 7:19–34

    Google Scholar 

  49. Rao RV, Waghmare G (2017) A new optimization algorithm for solving complex constrained design optimization problems. Eng Optim 49:60–83

    Article  Google Scholar 

  50. Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis. CRC press, Boca raton

    Book  MATH  Google Scholar 

  51. Rnndles RH (1986) Nonparametric statistical inference. Taylor & Francis, Routledge

    Book  Google Scholar 

  52. Sargent PM, Ige DO, Ball NR (1995) Design of laminate composite layups using genetic algorithms. Eng Comput 11:59–69

    Article  Google Scholar 

  53. Sebaey T, Lopes C, Blanco N, Costa J (2011) Ant colony optimization for dispersed laminated composite panels under biaxial loading. Compos Struct 94:31–36

    Article  Google Scholar 

  54. Setoodeh A, Shojaee M (2017) Critical buckling load optimization of functionally graded carbon nanotube-reinforced laminated composite quadrilateral plates. Polym Compos 39:853–868

    Google Scholar 

  55. Setoodeh S, Abdalla MM, Gürdal Z (2006) Design of variable–stiffness laminates using lamination Parameters. Compos Part B Eng 37:301–309

    Article  Google Scholar 

  56. Soremekun G, Gürdal Z, Haftka R, Watson L (2001) Composite laminate design optimization by genetic algorithm with generalized elitist selection. Comput struct 79:131–143

    Article  Google Scholar 

  57. Talbi E-G (2009) Metaheuristics: from design to implementation vol 74. Wiley, Hoboken

    Book  MATH  Google Scholar 

  58. Venkataraman S, Haftka RT (1999) Optimization of composite panels—a review. Proc Am Soc Compos 195:479–488

    Google Scholar 

  59. Vosoughi A, Darabi A, Forkhorji HD (2017) Optimum stacking sequences of thick laminated composite plates for maximizing buckling load using FE-GAs-. PSO Compos Struct 159:361–367

    Article  Google Scholar 

  60. Yang X-S (2010) Nature-inspired metaheuristic algorithms. Luniver press

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  1. Centre of Excellence for Fundamental Studies in Structural Engineering, Iran University of Science and Technology, Tehran, Iran

    A. Kaveh, A. Dadras & N. Geran Malek

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  1. A. Kaveh
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Supplementary material 1 Appendix A: Supplementary material of Case 1 Supplementary data containing all optimal design variables of GWO, SSA, CBO, Standard-GA and Self-adaptive GA for Case 1 can be found in the online version. Appendix B: Supplementary material of Case 6. Supplementary data associated with solutions provided by different algorithms for Case 6 can be found in the online version (DOCX 51 KB)

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Kaveh, A., Dadras, A. & Geran Malek, N. Optimum stacking sequence design of composite laminates for maximum buckling load capacity using parameter-less optimization algorithms. Engineering with Computers 35, 813–832 (2019). https://doi.org/10.1007/s00366-018-0634-2

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