Applied Composite Materials

, Volume 26, Issue 2, pp 663–681 | Cite as

Support for Decision Making in Design of Composite Laminated Structures. Part 2: Reduced Parametric Model-Based Optimization

  • Gilberto Fontecha Dulcey
  • Xavier FischerEmail author
  • Pierre Joyot
  • Georges Fadel


The design process of laminated composites faces two challenges: the engineer designs the product and its morphology, but also, simultaneously, the material. The number of design solutions can be huge since the solution space is very large. Standard CAE systems (CAD, Finite Element Simulation) do not offer to the designer an approach to explore these solution spaces efficiently and interactively. This paper provides a possible procedure for engineers having a laminated composite product to create: it presents an approach that allows combining to usual morphological design parameters, specific variables that are typically the domain of composite experts, and manufacturing experts. Using an optimization approach based on an evolutionary algorithm coupled to a reduced order analysis, a decision support solution is detailed. The numerical approach allows the engineer to explore interactively design spaces. Our approach is consisting in processing a Knowledge Model having a reduced and separated form [9]. We present a decision support method that allow designers to have, both, a multiscale and a multiphysical view on the laminated structures that they are creating. Two design problems are presented to illustrate the relevance of the approach when designing composite structures: one under a static load and the having a dynamic behavior.


Decision support system Design of laminated composite structure Separated model based optimization Layer-by-layer design Qualification of optimization 



Young’s modulus (MPa)


Fiber Young’s modulus (MPa)


Matrix Young’s modulus (MPa)


Young’s modulus of the ply in the direction of the fibers (MPa)


Young’s modulus of the ply in a direction transversal to the fiber direction (MPa)


External forces (N)


Force as a function of frequency (N)


Body force


Shear modulus (MPa)


Poisson’s ratio


Length (mm)


Height (mm)


Width (mm)


Displacement in direction x


Displacement in direction y


Displacement in direction z


Strain tensor


Stress Tensor (Pa)


Stress tensor element (Pa)


Objective function

ς, ξ, ψ


\( {\mathbf{\mathcal{L}}}_{\boldsymbol{max}} \)

Maximum deformation to the direction y

\( {\boldsymbol{U}}_{\boldsymbol{x},\boldsymbol{y},\boldsymbol{z},{\boldsymbol{p}}_{\mathbf{1}},{\boldsymbol{p}}_{\mathbf{2}},\bullet \bullet \bullet, {\boldsymbol{p}}_{\boldsymbol{d}}} \)

Approximation of displacement field (mm)

U(x, y, z, p1, p1, , pd)

Displacement field as a function of given parameters (mm)


Tensor of material properties in local coordinates


Number of enrichment modes in PGD sense

\( \overline{\boldsymbol{C}} \)

Tensor of material properties in global coordinates

\( \overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{1}}\right),\overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{2}}\right),\overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{3}}\right),\overline{\boldsymbol{C}}\left({\boldsymbol{p}}_{\mathbf{4}}\right) \)

Tensor of material properties at plies 1, 2, 3, 4 in global coordinates


Tensor of material properties at the interfaces


Transformation matrix


Density (kg/m3)


Fiber density


Resin density


Geometric domain


Fiber orientation of ply i (degrees)


Fiber volume fraction (%)


Short term shear modulus (GPa)


Long-term shear modulus (GPa)


Fractional derivative order


Decay time (s)

X, Y, Z, P1, P2, P3, P4, P5, P6, P7

PGD functions


PGD domains


Maximum twist



The research was supported by the Colciencias (Colombia) and the Universidad Pontificia Bolivariana (Bucaramanga, Colombia).


  1. 1.
    Almeida, J.H.S., Ribeiro, M.L., Tita, V., Amico, S.C.: Stacking sequence optimization in composite tubes under internal pressure based on genetic algorithm accounting for progressive damage. Compos. Struct. 178, 20–26 (2017). CrossRefGoogle Scholar
  2. 2.
    Bouyssou D. Ed: Decision-making process: concepts and methods. ISTE [u.a.], London (2009)Google Scholar
  3. 3.
    Calado, E.A., Leite, M., Silva, A.: Selecting composite materials considering cost and environmental impact in the early phases of aircraft structure design. J. Clean. Prod. 186, 113–122 (2018). CrossRefGoogle Scholar
  4. 4.
    Carrera, E.: Theories and finite elements for multilayered, anisotropic, composite plates and shells. Arch. Comput. Methods Eng. 9, 87–140 (2002). CrossRefGoogle Scholar
  5. 5.
    Corona, A., Madsen, B., Hauschild, M.Z., Birkved, M.: Natural fibre selection for composite eco-design. CIRP Ann. 65, 13–16 (2016). CrossRefGoogle Scholar
  6. 6.
    Coronado Mondragon, A.E., Coronado Mondragon, C.E., Hogg, P.J., Rodríguez-López, N.: A design process for the adoption of composite materials and supply chain reconfiguration supported by a software tool. Comput. Ind. Eng. 121, 62–72 (2018). CrossRefGoogle Scholar
  7. 7.
    Dutra, T.A., de Almeida, S.F.M.: Composite plate stiffness multicriteria optimization using lamination parameters. Compos. Struct. 133, 166–177 (2015). CrossRefGoogle Scholar
  8. 8.
    Fischer, X., Nadeau, J.-P., Sébastian, P., Joyot, P.: Decision support in integrated mechanical design through qualitative constraints. In: Integrated Design and Manufacturing in Mechanical Engineering, pp. 35–42 (2002)CrossRefGoogle Scholar
  9. 9.
    Fontecha Dulcey, G., Fischer, X., Joyot, P., Fadel, G.: Support for decision making in Design of Composite Laminated Structures; part 1: parametric knowledge model., applied composite materials, springer. Nature. (2018)Google Scholar
  10. 10.
    Gascons, M., Blanco, N., Mayugo, J.A., Matthys, K.: A strategy to support design processes for fibre reinforced thermoset composite materials. Appl. Compos. Mater. 19, 297–314 (2012). CrossRefGoogle Scholar
  11. 11.
    Hambali, A., Sapuan, S.M., Ismail, N., Nukman, Y.: Material selection of polymeric composite automotive bumper beam using analytical hierarchy process. J. Cent. S. Univ. Technol. 17, 244–256 (2010). CrossRefGoogle Scholar
  12. 12.
    Irisarri, F.-X., Bassir, D.H., Carrere, N., Maire, J.-F.: Multiobjective stacking sequence optimization for laminated composite structures. Compos. Sci. Technol. 69, 983–990 (2009). CrossRefGoogle Scholar
  13. 13.
    Kamiński, M.M.: Computational Mechanics of Composite Materials: Sensitivity, Randomness, and Multiscale Behaviour. Springer, London (2005)Google Scholar
  14. 14.
    Kwon, Y.W., Allen, D.H., Talreja, R.: Multiscale modeling and simulation of composite materials and structures. Springer, New York (2008)CrossRefGoogle Scholar
  15. 15.
    Macquart, T., Maes, V., Bordogna, M.T., Pirrera, A., Weaver, P.M.: Optimisation of composite structures – enforcing the feasibility of lamination parameter constraints with computationally-efficient maps. Compos. Struct. 192, 605–615 (2018). CrossRefGoogle Scholar
  16. 16.
    Mejia Gutierrez, R., Fischer, X., Bennis, F.: A tutor agent for supporting distributed knowledge modelling in interactive product design. Int. J. Intell. Syst. Technol. Appl. 4, 399 (2008). Google Scholar
  17. 17.
    Michalewicz Z.: Genetic algorithms + data structures = evolution programs. Springer-Verlag, Berlin; New York (1994)Google Scholar
  18. 18.
    Nikbakt, S., Kamarian, S., Shakeri, M.: A review on optimization of composite structures part I: laminated composites. Compos. Struct. 195, 158–185 (2018). CrossRefGoogle Scholar
  19. 19.
    Pahl, G., Wallace, K., Blessing, L., Pahl, G. (eds.): Engineering design: a systematic approach. Springer, London (2007)Google Scholar
  20. 20.
    Reddy, J.N.: An evaluation of equivalent-single-layer and layerwise theories of composite laminates. Compos. Struct. 25, 21–35 (1993). CrossRefGoogle Scholar
  21. 21.
    Sanz-Corretge, J.: A procedure to design optimum composite plates using implicit decision trees. Struct. Multidiscip. Optim. 56, 1169–1183 (2017). CrossRefGoogle Scholar
  22. 22.
    Srinivasan, R., Karandikar, H.M., Mistree, F.: Understanding design-manufacture interaction using compromise decision support problems—III. Design for manufacture of composite pressure vessels. Comput. Struct. 40, 705–717 (1991). CrossRefGoogle Scholar

Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Université de BordeauxI2M CNRS UMR 5295, ENSAM, Esplanade des Arts et MétiersTalenceFrance
  2. 2.Université de BordeauxÉcole Supérieure des Technologies Industrielles Avancées, ESTIA, technopole izarbel, TechnBidartFrance
  3. 3.Universidad Pontificia BolivarianaBucaramangaColombia
  4. 4.Clemson UniversityMechanical engineeringClemsonUSA

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