Log in

Robust design optimization of laminated plates under uncertain bounded buckling loads

  • Research Paper
  • Published:
Structural and Multidisciplinary Optimization Aims and scope Submit manuscript

Abstract

In this paper, a new systematic approach is suggested for better exploration of given uncertain buckling loads in the problem of optimal designs of hybrid symmetric laminated composites. Laminated composites are made up of 16-layered carbon-epoxy, glass-epoxy, and hybrid carbon-glass plies with discrete ply angles as design variables. In the analysis, the ply angles and the type of constituents in the laminates are varied, and one source of uncertainty, namely, uncertainty in buckling load is incorporated. In order to form nested optimization, a new improved rank-based version of Quantum-inspired Evolutionary Algorithm (QEA) is proposed and different versions of QEA and Genetic Algorithm (GA) are utilized. Using anti-optimization approach, the worst case biaxial compressive loading is obtained by Golden Section Search (GSS) method and the buckling load capacity is maximized. Numerical results of the optimal configurations are obtained under several bi-axial loading cases, panel aspect ratios, and materials. The results are investigated from different perspectives and sensitivity analyses are performed.

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

Access this article

Subscribe and save

Springer+ Basic
EUR 32.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or Ebook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

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

References

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

    Article  Google Scholar 

  • Adali S, Lene F, Duvaut G, Chiaruttini V (2003) Optimization of laminated composites subject to uncertain buckling loads. Compos Struct 62:261–269

    Article  Google Scholar 

  • Akmar AI, Kramer O, Rabczuk T (2017) Probabilistic multi-scale optimization of hybrid laminated composites. Compos Struct 184:1111–1125. https://doi.org/10.1016/j.compstruct.2017.10.032

  • Arora JS (2017) Chapter 17 - nature-inspired search methods. In: Arora JS (ed) Introduction to optimum design, 4th edn. Academic, Boston, pp 739–769. https://doi.org/10.1016/B978-0-12-800806-5.00017-2

    Chapter  Google Scholar 

  • Çarbaş S, Saka MP (2012) Optimum topology design of various geometrically nonlinear latticed domes using improved harmony search method. Struct Multidiscip Optim 45:377–399

    Article  Google Scholar 

  • 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 

  • Elishakoff I, Haftka R, Fang J (1994) Structural design under bounded uncertainty—optimization with anti-optimization. Comput Struct 53:1401–1405

    Article  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Fukunaga H, Sekine H, Sato M, Iino A (1995) Buckling design of symmetrically laminated plates using lamination parameters. Comput Struct 57:643–649. https://doi.org/10.1016/0045-7949(95)00050-Q

    Article  MATH  Google Scholar 

  • 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 

  • 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 

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

    Google Scholar 

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

    Article  Google Scholar 

  • Haftka RT, Gürdal Z (2012) Elements of structural optimization. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2550-5

    MATH  Google Scholar 

  • Han K-H, Kim J-H (2002) Quantum-inspired evolutionary algorithm for a class of combinatorial optimization. IEEE Trans Evol Comput 6:580–593

    Article  Google Scholar 

  • Hey T (1999) Quantum computing: an introduction. Comput Control Eng J 10:105–112

  • Holland JH (1992) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence, 2nd edn. MIT Press, Cambridge

    Book  Google Scholar 

  • Huang J, Haftka R (2005) Optimization of fiber orientations near a hole for increased load-carrying capacity of composite laminates. Struct Multidiscip Optim 30:335–341

    Article  Google Scholar 

  • Hussain K, Salleh MNM, Cheng S, Shi Y (2018) Metaheuristic research: a comprehensive survey. Artif Intell Rev:1–43

  • Kalantari M, Dong C, Davies IJ (2017) Effect of matrix voids, fibre misalignment and thickness variation on multi-objective robust optimization of carbon/glass fibre-reinforced hybrid composites under flexural loading. Compos Part B 123:136–147

    Article  Google Scholar 

  • Kaveh A (2017a) Advances in metaheuristic algorithms for optimal design of structures, 2nd edn. Springer International Publishing, Basel

    Book  MATH  Google Scholar 

  • Kaveh A (2017b) Applications of metaheuristic optimization algorithms in civil engineering Springer, Switzerland

  • Kaveh A, Dadras A (2017) A novel meta-heuristic optimization algorithm: thermal exchange optimization. Adv Eng Softw 110:69–84. https://doi.org/10.1016/j.advengsoft.2017.03.014

  • 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 

  • 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. https://doi.org/10.1007/s00707-017-2068-0

    Article  MathSciNet  Google Scholar 

  • Lee D, Morillo C, Oller S, Bugeda G, Oñate E (2013) Robust design optimisation of advance hybrid (fiber–metal) composite structures. Compos Struct 99:181–192

    Article  Google Scholar 

  • Liu B, Haftka R, Trompette P (2004) Maximization of buckling loads of composite panels using flexural lamination parameters. Struct Multidiscip Optim 26:28–36

    Article  Google Scholar 

  • Liu D, Toropov VV, Barton DC, Querin OM (2015) Weight and mechanical performance optimization of blended composite wing panels using lamination parameters. Struct Multidiscip Optim 52:549–562

    Article  MathSciNet  Google Scholar 

  • Lombardi M, Haftka RT (1998) Anti-optimization technique for structural design under load uncertainties. Comput Methods Appl Mech Eng 157:19–31

    Article  MATH  Google Scholar 

  • Nemeth MP (1986) Importance of anisotropy on buckling of compression-loaded symmetric composite plates. AIAA J 24:1831–1835

    Article  Google Scholar 

  • Reddy JN (2004) Mechanics of laminated composite plates and shells: theory and analysis, 2nd edn. CRC Press, Boca Raton

    Book  MATH  Google Scholar 

  • Reis P, Ferreira J, Antunes F, Costa J (2007) Flexural behaviour of hybrid laminated composites. Compos A Appl Sci Manuf 38:1612–1620

    Article  Google Scholar 

  • Saka M, Erdal F (2009) Harmony search based algorithm for the optimum design of grillage systems to LRFD-AISC. Struct Multidiscip Optim 38:25–41

    Article  Google Scholar 

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

    Article  Google Scholar 

  • Sivanandam S, Deepa S (2007) Introduction to genetic algorithms. Springer Science & Business Media, Berlin

    MATH  Google Scholar 

  • Sivanandam S, Deepa S (2008) Genetic algorithm optimization problems. In: Introduction to genetic algorithms. Springer, Berlin, pp 165–209

    Chapter  Google Scholar 

  • 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 

  • Tejani GG, Savsani VJ, Patel VK (2016) Adaptive symbiotic organisms search (SOS) algorithm for structural design optimization. J Comput Des Eng 3:226–249

    Google Scholar 

  • Venkataraman S, Haftka RT (1999) Optimization of composite panels-a review. In: Proc Amer Soc Compos. pp 479–488

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Kaveh.

Additional information

Responsible Editor: Emilio Carlos Nelli Silva

Publisher’s Note

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

Electronic supplementary material

ESM 1

(DOCX 118 kb)

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kaveh, A., Dadras, A. & Geran Malek, N. Robust design optimization of laminated plates under uncertain bounded buckling loads. Struct Multidisc Optim 59, 877–891 (2019). https://doi.org/10.1007/s00158-018-2106-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00158-018-2106-0

Keywords

Navigation