Applied Composite Materials

, Volume 19, Issue 5, pp 785–798 | Cite as

Multi-objective Genetic Topological Optimization for Design of Blast Resistant Composites

  • M. P. Sheyka
  • A. B. Altunc
  • M. M. Reda TahaEmail author


Composites make it possible to produce materials with properties that are unattainable with single phase materials. This paper examines the use of multi-objective genetic topological optimization to design blast resistant composites. The fundamental problem of the design of a two-layer composite plate that is subjected to blast is considered using the finite element method. Two materials are used to form the microstructure of each layer. The microstructure and thickness of each layer is optimized for the two-layer plate to minimize the weight and stress-to-strength ratio. A set of optimal blast resistant composite microstructures that meet design requirements is demonstrated.


Finite element method Composites Topology Optimization 



This research is mainly funded by the Army Research Office (ARO) Grant # W911NF-08-1-0421. The authors greatly appreciate this support. Special Thanks to G. Cruz from University of Texas, San Antonio for his help in blast simulation.


  1. 1.
    Langdona, G.S., Nuricka, G.N., Lemanskia, S.L., et al.: Failure characterization of blast-loaded fibre-metal laminate panels based on aluminum and glass-fibre reinforced polypropylene. Compos Sci Technol 67(7), 1385–1405 (2007)CrossRefGoogle Scholar
  2. 2.
    Tsai, L., Prakash, V.: Structure of weak shock waves in 2-D layered material systems. Int. J. Solids Struct. 42(2), 727–750 (2005)CrossRefGoogle Scholar
  3. 3.
    Bendsoe, M.P., Kikuchi, N.: Generating optimal topologies in structural design using a homogenization method. Comput. Methods Appl. Mech. Eng. 71, 197–224 (1988)CrossRefGoogle Scholar
  4. 4.
    Pederson, P.: On the minimum mass layout if trusses. In: AGARD conf. proc. No. 36, Symposium on Structural Optimization, AGARD-CP-36-70Google Scholar
  5. 5.
    Zhou, M., Rozvany, G.I.N.: DCOC: an optimality criteria method for large systems, Part I. Theory Struct. Optim. 5(1–2), 12–25 (1992)CrossRefGoogle Scholar
  6. 6.
    Cheng, G., Olhoff, N.: An investigation concerning optimal design of solid elastic plates. Int. J. Solid Struct. 17(3), 305–323 (1981)CrossRefGoogle Scholar
  7. 7.
    Sigmund, O.: Materials with prescribed constitutive parameters: an inverse homogenization problem. Int. J. Solid Struct. 31(17), 2313–2329 (1994)CrossRefGoogle Scholar
  8. 8.
    Rodrigues, H.C., Fernandes, P.: A material based model for topology optimization of thermoelastic structures. Int. J. Numer. Methods Eng. 38(12), 1951–1965 (1995)CrossRefGoogle Scholar
  9. 9.
    Haslinger, J.: Finite element approximation for optimal shape design: theory and applications. Wiley, New York (1988)Google Scholar
  10. 10.
    Fonseca JSO. PhD thesis: Design of microstructures of periodic composite materials. Ann Arbor: U of Michigan (1997)Google Scholar
  11. 11.
    Sanchez-Palencia, E.: Equations aux derivees partielles dans un type de milieux heterogenes. Computes Rendus de l’Academie des Sciences de Paris 272(A-B), A1410–A1413 (1971)Google Scholar
  12. 12.
    Keller, J.B.: Effective behavior of heterogeneous media. In: Landman, U. (ed.) Statistical mechanics and statistical methods in theory and application: a tribute to Elliot W. Montroll, pp. 429–443. Plenum Press, Plenum (1977)Google Scholar
  13. 13.
    Bakhvalov, N., Panasenko, G.: Homogenization: averaging process in periodic media. Kluwer, Dordrecht (1989)CrossRefGoogle Scholar
  14. 14.
    De Kruijf, N., Zho, S., Li, Q., et al.: Topological design of structures and composite materials with multiobjectives. Int. J. Solids Struct. 44, 7092–7109 (2007)CrossRefGoogle Scholar
  15. 15.
    Guedes, JM. PhD thesis: Nonlinear comutational models for composite materials using homogenization. N. Kikuchi, advisor. Ann Arbor: U of Michigan (1990)Google Scholar
  16. 16.
    Smith, P.D., Hetherington, J.G.: Blast and ballistic loading of structures. Laxtons, Oxford (1994)Google Scholar
  17. 17.
    Newmark, N.M., Hansen, R.J.: Design of blast resistant structures. In: Harris, C. (ed.) Shock and vibration handbook, vol. 3. McGraw-Hill, New York (1961)Google Scholar
  18. 18.
    Lohner, R.: Applied CFD, techniques: an introduction based on finite element methods. John Wiley and Sons, Chichester (2001)Google Scholar
  19. 19.
    Sigmund O. PhD thesis: Design of material structures using topology optimization. Lyngby: Technical University of Denmark (1994)Google Scholar
  20. 20.
    Currie, I.G.: Fundamental mechanics of fluids, 3rd edn. CRC Press, Boca Raton (2003)Google Scholar
  21. 21.
    Logan, D.L.: A first course in the finite element method, 3rd edn. Wadsworth Group, Pacific Grove (2002)Google Scholar
  22. 22.
    Pareto, V.: Manual of political economy. Macmillan, New York (1971)Google Scholar
  23. 23.
    Miettinen, K.: Nonlinear multiobjective optimization. Kluwer, Boston (1999)Google Scholar
  24. 24.
    Osyczka, A.: Multicriterion optimization in engineering. Ellis Horwood, Chichester (1984)Google Scholar
  25. 25.
    Rosenberg RS. PhD thesis: Simulation of genetic populations with biochemical properties. Ann Arbor: U of Michigan (1967)Google Scholar
  26. 26.
    Deb, K.: Multi-objective optimization using evolutionary algorithms. John Wiley, Chichester (2001)Google Scholar
  27. 27.
    Srinivas, N., Deb, K.: Multiobjective optimization using nondominated sorting in genetic algorithms. Evol Comput 2(3), 221–248 (1995)CrossRefGoogle Scholar
  28. 28.
    Rammohan, R., Farfan, B., Su, M.F., et al.: Hybrid genetic optimization for design of photonic crystal emitters. Eng Optim 42(9), 791–809 (2010)CrossRefGoogle Scholar
  29. 29.
    Konak, A., Coit, D.W., Smith, A.: Multi-objective optimization using genetic algorithms: a tutorial. Reliab Eng Syst Saf 91, 992–1007 (2006)CrossRefGoogle Scholar
  30. 30.
    Taboada, H.A., Espiritu, J.F., David, W., et al.: MOMS-GA: a multi-objective multi-state genetic algorithm for system reliability optimization design problems. IEEE Trans Reliab 57(1), 182–191 (2008)CrossRefGoogle Scholar
  31. 31.
    Liao, X., Li, Q., Yang, X., et al.: A two-stage multi-objective optimisation of vehicle crashworthiness under frontal impact. Int. J. Crashworthiness 13(3), 279–288 (2008)CrossRefGoogle Scholar
  32. 32.
    ANSYS-AUTODYN. Interactive non-linear dynamic analysis software, version 11.0 User’s Manual. Century Dynamics Inc. (2007)Google Scholar

Copyright information

© Springer Science+Business Media B.V. 2012

Authors and Affiliations

  • M. P. Sheyka
    • 1
  • A. B. Altunc
    • 1
  • M. M. Reda Taha
    • 1
    Email author
  1. 1.Department of Civil EngineeringUniversity of New MexicoAlbuquerqueUSA

Personalised recommendations