Advertisement

Structural and Multidisciplinary Optimization

, Volume 57, Issue 4, pp 1507–1521 | Cite as

A novel technique for the design of hybrid composite laminates based on dynamic programming and dynamic tree trimming

  • Javier Sanz-Corretge
  • Mikel Echeverría
RESEARCH PAPER
  • 119 Downloads

Abstract

This paper proposes a novel technique for the design of hybrid composite laminates. The method explores design space with several implicit decision trees in order to obtain the Pareto front, applying a number of manufacturing and structural considerations. The research is carried out using a parallelized breadth first search algorithm aided by dynamic programming and dynamic tree trimming; as a consequence the searching process is significantly accelerated. This novel procedure is applied to a well-known design case, where it identifies the best carbon-epoxy and glass-epoxy laminate combinations in terms of weight versus cost, and finds the Pareto front with less computational effort than alternative methods used in the past to solve the same problem. Since a full set of feasible solutions is produced with this new methodology, some important conclusions are obtained regarding hybrid laminate design criteria.

Keywords

Discrete multi-objective optimization Hybrid laminate design Dynamic programming Pareto front Optimum laminate stacking sequence Decision trees Graph theory 

Abbreviations

BB

Building block

BFS

Breadth-first search

CFRP

Carbon fiber reinforced plastic

COV

Covariance operator

CLT

Classical laminate theory

DTT

Dynamic tree trimming

FSD

Fully stressed design

GA

Genetic algorithm

GFRP

Glass fiber reinforced plastic

OT

Order tree

OOP

Object oriented programming

NSGA

Non-sorted dominated GA

PDP

Parallel dynamic programming

RHS

Right-hand side

SF

Structural safety factor

VAR

Variance operator

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.  https://doi.org/10.1007/s00158-008-0235-6 CrossRefGoogle Scholar
  2. Ahrari A, Atai A (2013) A fully stressed design evolution strategy for shape and size optimization of truss structures. Comput Struct 123:58–67CrossRefGoogle Scholar
  3. Altair HyperStudy (2017) Users manual. Altair Engineering, Inc, TroyGoogle Scholar
  4. Bailie JA, Ley RP, Pasricha A (1997) A summary and review of composite laminate design guidelines. Technical report NASA, NAS1–19347. Northrop Grumman-Military Aircraft Systems Division.Google Scholar
  5. Barroso ES, Parente E, Cartaxo de Melo AM (2017) A hybrid PSO-GA algorithm for optimization of laminated composites. Struct Multidiscip Optim 55:2111.  https://doi.org/10.1007/s00158-016-1631-y MathSciNetCrossRefGoogle Scholar
  6. Bednárek D, Brabec M, Kruliš M (2017) Improving matrix-based dynamic programming on massively parallel accelerators. Inf Syst 64:175–193CrossRefGoogle Scholar
  7. Clerc, M (2013) Particle swarm optimization. Wiley-ISTE; 1 edition (4 Mar. 2013). ISBN 10: 1–905209–04-5Google Scholar
  8. Conceição António CA (2006) A hierarchical genetic algorithm with age structure for multimodal optimal design of hybrid composites. Struct Multidiscip Optim 31:280.  https://doi.org/10.1007/s00158-005-0570-9 CrossRefGoogle Scholar
  9. Eckold G. 1994 Design and manufacture of composite structures. Woodhead Publishing. ISBN: 978-1-845-69856-0Google Scholar
  10. Farshi B, Rabiei R (2007) Optimum design of composite laminates for frequency constraints. Compos Struct 81(4):587–597CrossRefGoogle Scholar
  11. Goldberg DE (1989). Genetic algorithms in search, optimization and machine learning. Addison Wesley Longman. Inc. ISBN 0-201-15767-5Google Scholar
  12. Guttag JV (2013). Introduction to computation and programming using Python. MIT PressGoogle Scholar
  13. Hunter JD (2012) Matplotlib: a 2D graphics environment. Computing In Science & Engineering 9(3):90–95CrossRefGoogle Scholar
  14. Jones RM (1999) Mechanics of composite materials. Taylor & Francis (Materials Science & Engineering Series)Google Scholar
  15. Karakaya Ş, Soykasap (2011) Natural frequency and buckling optimization of laminated hybrid composite plates using genetic algorithm and simulated annealing. Struct Multidiscip Optim 43:61.  https://doi.org/10.1007/s00158-010-0538-2 CrossRefGoogle Scholar
  16. Kim IY, de Weck OL (2005) Adaptive weighted-sum method for bi-objective optimization: Pareto front generation. Struct Multidiscip Optim 29(2):149–158CrossRefGoogle Scholar
  17. Kim IY, de Weck O (2006) Adaptive weighted sum method for multi-objective optimization: a new method for Pareto front generation. Struct Multidiscip Optim 31(2):105–116MathSciNetCrossRefzbMATHGoogle Scholar
  18. Koenig S, Likhachev M, Liu Y, Furcy D (2004) Incremental heuristic search in AI. AI Mag 25(2):99–112Google Scholar
  19. Kollár LP (2003) Springer GS. Mechanics of composite structures. Cambridge University Press. ISBN 978-0-521-80165-2Google Scholar
  20. Lopez RH, Luersen MA, Cursi ES (2009) Optimization of laminated composites considering different failure criteria. Compos Part B 40(8):731–740CrossRefGoogle Scholar
  21. Mohammadi M, Forghani K (2017) A hybrid method based on genetic algorithm and dynamic programming for solving a bi-objective cell formation problem considering alternative process routings and machine duplication. Appl Soft Comput 53:97–110CrossRefGoogle Scholar
  22. Montemurro M, Koutsawa Y, Belouettar S, Vincenti A, Vannucci P (2012) Design of damping properties of hybrid laminates through a global optimisation strategy. Compos Struct 94(11):3309–3320CrossRefGoogle Scholar
  23. Sanz-Corretge J (2017) A procedure to Design Optimum Composite Plates Using Implicit Decision Trees. Struct Multidiscip Optim.  https://doi.org/10.1007/S00158-017-1711-7
  24. Stenz A (1994) Optimal and efficient planning for partially-known environments. Proceedings of the international Conference on Robotic and AutomationGoogle Scholar
  25. Todoroki A, Haftka RT (1998) Stacking sequence optimization by a genetic algorithm with a new recessive gene like repair strategy. Compos Part B 29(3):277–285CrossRefGoogle Scholar
  26. West DB (2001). Introduction to graph theory. TBS; 2002. ISBN: 8120321421. Prentice hallGoogle Scholar
  27. Zhang J, Chaisombat K, He S, Wang HC (2012) Hybrid composite laminates reinforced with glass/carbon woven fabrics for lightweight load bearing structures. Mater Des 36:75–80CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany 2017

Authors and Affiliations

  1. 1.Meletea EngineeringPamplonaSpain

Personalised recommendations