Structural and Multidisciplinary Optimization

, Volume 48, Issue 2, pp 379–393 | Cite as

A laminate parametrization technique for discrete ply-angle problems with manufacturing constraints

  • Graeme J. KennedyEmail author
  • Joaquim R. R. A. Martins
Research Paper


In this paper we present a novel laminate parametrization technique for layered composite structures that can handle problems in which the ply angles are limited to a discrete set. In the proposed technique, the classical laminate stiffnesses are expressed as a linear combination of the discrete options and design-variable weights. An exact \(\ell _{1}\) penalty function is employed to drive the solution toward discrete 0–1 designs. The proposed technique can be used as either an alternative or an enhancement to SIMP-type methods such as discrete material optimization (DMO). Unlike mixed-integer approaches, our laminate parametrization technique is well suited for gradient-based design optimization. The proposed laminate parametrization is demonstrated on the compliance design of laminated plates and the buckling design of a laminated stiffened panel. The results demonstrate that the approach is an effective alternative to DMO methods.


Laminate parametrization Discrete angle problems Manufacturing constraints 



The computations for this paper were performed on the GPC supercomputer at the SciNet HPC Consortium at the University of Toronto. SciNet is funded by the Canada Foundation for Innovation, under the auspices of Compute Canada, the Government of Ontario, and the University of Toronto.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Graeme J. Kennedy
    • 1
    Email author
  • Joaquim R. R. A. Martins
    • 1
  1. 1.Department of Aerospace EngineeringUniversity of MichiganAnn ArborUSA

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