Keywords: blending, lamination parameters, optimization, stacking sequence, laminated composite.

As the use of modern high-performance laminated composite material becomes widespread within the aerospace industry, some advanced requirements such as structural efficiency and blending (ply continuity) [1,2,3,4,5] are also being proposed to build composite structures with high-quality and manufacturability. In this paper, the smeared stiffness-based method is examined for finding the best stacking sequence of laminated composite wing structures in a bi-level optimization process with blending and manufacturing constraints. At the global level optimization, the numbers of plies of the pre-defined angles (0, 90, 45 and -45 degrees) are design variables, buckling, strain and ply angle percentages are constraints and the weight is the objective function. Since the permutation genetic algorithm (permGA) operator changes the stacking sequence without changing the composition of the laminate in the composite laminate optimization problem, a permGA is an ideal tool to shuffle the plies to minimize the difference between the values of computed lamination parameters for a current stack and the ones coming from the top level, for which the out-of-plane lamination parameters are all zero due to the homogeneity throughout the thickness of the laminate assumed in the top level optimization. This is embedded into an easy and efficient blending procedure applied at this level to achieve the global ply continuity. This multi-stage local optimization by permGAs is demonstrated by the optimization of the root part of a generic aircraft wing structure.

The software implementation of this method can be considered as an add-on to an OptiStruct [6] run where the smeared stiffness-based approach is used for the top level optimization. Given the results from the top level optimization, the stack shuffling to satisfy global blending and manufacturing constraints is performed at the local level to match the prescribed values of lamination parameters related to the bending stiffness matrix. This local level optimization can be treated as a postprocessing phase for determining the detailed ply-book of the laminate while guaranteeing satisfaction of the strain and buckling constraints.

1

B.P. Kristinsdottir, Z.B. Zabinsky, M.E. Tuttle, S. Neogi, "Optimal Design of Large Composite Panels with Varying Loads", Composite Structures, 51, 93-102, 2001. doi:10.1016/S0263-8223(00)00128-8

2

B. Liu, R.T. Haftka, "Composite Wing Structural Design Optimization with Continuity Constraint", Proceedings of 42th AIAA SDM Conference, AIAA-2001-1205, Seattle, WA, 2001.

3

O. Seresta, Z. Gürdal, D.B. Adams, L.T. Watson, "Optimal Design of Composite Wing Structures with Blended Laminates", Composites Part B: Engineering, 38, 469-480, 2007. doi:10.1016/j.compositesb.2006.08.005

4

W. Liu, R. Butler, "Optimum Buckling Design of Composite Wing Cover Panels with Manufacturing Constraints", 48th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics & Materials conference, AIAA 2007-2215, Honolulu, Hawaii, 2007.

5

W. Liu, L. Krog, "A Method for Composite Ply Layout Design and Stacking Sequence Optimisation", Proceedings of 7th ASMO UK/ISSMO Conference, Bath, UK, 2008.

6

Altair OptiStruct Version 9.0, Altair Engineering Inc., 2008.

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