Mechanics of Composite Materials

, Volume 52, Issue 2, pp 211–224 | Cite as

Choice of Design Variables in the Stacking Sequence Optimization for Laminated Structures


A special type of new, continuous design variables is introduced in order to find optimum solutions for discrete fiber orientations. In the buckling analysis, as two or three different fiber orientations are considered, optimum solutions can be found in an analytical way. For a greater number of discrete fiber orientations, a special optimization algorithm based on the evolution strategy is used to solve the combinatorial optimization problems dealing with the optimum design of the laminate stacking sequence. The analysis is conducted with the example of simply supported rectangular multilayered composite plates subjected to buckling and the first-ply-failure constraints. The results demonstrate the effectiveness, simplicity, and advantages of the use of continuous design variables in the discrete optimization problem.


laminates stacking sequence design variables optimization problem 



The support of the NCN under the grant UMO-2013/09/B/ST8/00178 is gratefully acknowledged.


  1. 1.
    A. Muc, “Optimization of composite topology for doubly-curved laminated shells under buckling constraints,” Proc. IUTAM Sym. “Optimal design with advanced materials” (Ed. by P. Pedersen), Elsevier, Amsterdam, pp.474-489 (1993).Google Scholar
  2. 2.
    G. Verchery, “Design rules for the laminate stiffness,” Mechanics of Composite Materials, 47, 47-58 (2011),CrossRefGoogle Scholar
  3. 3.
    A. Muc, “Optimal fiber orientations for simply-supported plates under compression,” Compos. Struct., 9, No. 2, 161-172 (1988).CrossRefGoogle Scholar
  4. 4.
    R. Le Riche and R. T. Haftka, “Optimization of laminate stacking sequence for buckling load maximization by genetic algorithm,” AIAA J., 31, No. 5, 951-956 (1993).CrossRefGoogle Scholar
  5. 5.
    S. Karakaya, and O. Soykasap, “Buckling optimization of laminated composite plates using genetic algorithm and generalized pattern search algorithm,” Structural and Multidisciplinary Optimization, 39, No. 5, 477-486 (2009).CrossRefGoogle Scholar
  6. 6.
    Z. Gurdal and R. Olmedo, “In-plane response of laminates with spatially varying fiber orientations: variable stiffness concept,” AIAA J., 31, No. 4, 751–758 (1993).CrossRefGoogle Scholar
  7. 7.
    A. Muc and A. Ulatowska, “Design of plates with curved fiber format,” Compos. Struct., 92, No. 7, 1728-1733 (2010).CrossRefGoogle Scholar
  8. 8.
    M. Miki, Optimum Design of Fibrous Laminated Plates Subjected to Axial Compression, in: Eds. K. Kawata, S. Umekawa, and A. Kobayashi, Composites ‘86: recent advances in Japan and the United States: Proc. of the third Japan-U.S. Conf. on Composite Materials, Tokyo, Japan, 673-681 (1986).Google Scholar
  9. 9.
    H.Fukunaga and G. N. Vanderplaats, “Stiffness optimization of orthotropic laminated composites using lamination parameters,” AIAA J., 29, No. 4,641-648 (1991).Google Scholar
  10. 10.
    C. G. Diaconu, M. Sato, and H. Sekine, “Buckling characteristics and layup optimization of long laminated composite cylindrical shells subjected to combined loads using lamination parameters,” Compos. Struct., 58, No. 4, 423–433 (2002).CrossRefGoogle Scholar
  11. 11.
    M. W. Bloomfield, C. G. Diaconu, and P. M. Weaver, “On feasible regions of lamination parameters for lay-up optimization of laminated composites,” Proc. Royal Soc. A: Mathematical, Physical and Engineering Sci., 465, 1123-1143 (2009).CrossRefGoogle Scholar
  12. 12.
    A. Muc and W. Gurba, “Genetic algorithms and finite element analysis in optimization of composite structures.” Compos. Struct., 54. Nos. 2-3, 275-281 (2001).Google Scholar
  13. 13.
    A. Muc and M. Muc-Wierzgoń, “An evolution strategy in structural optimization problems for plates and shells,” Compos. Struct., 94, No. 4, 1461-1470 (2012).CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  1. 1.Institute of Machine DesignCracow University of TechnologyKrakówPoland

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