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Civil-Comp Proceedings
ISSN 1759-3433
CCP: 83
PROCEEDINGS OF THE EIGHTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY
Edited by: B.H.V. Topping, G. Montero and R. Montenegro
Paper 27

Stacking Sequence Optimization for Laminated Cylindrical Panels Using the Globalized Nelder-Mead Method

M.M. Aghdam1, M. Shakeri1, A. Alibeiglu2 and E. Ameri1

1Department Of Mechanical Engineering, Amirkabir University of Technology, Tehran, Iran
2Department of Mechanical Engineering, Bu Ali Sina University, Iran

Full Bibliographic Reference for this paper
M.M. Aghdam, M. Shakeri, A. Alibeiglu, E. Ameri, "Stacking Sequence Optimization for Laminated Cylindrical Panels Using the Globalized Nelder-Mead Method", in B.H.V. Topping, G. Montero, R. Montenegro, (Editors), "Proceedings of the Eighth International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 27, 2006. doi:10.4203/ccp.83.27
Keywords: laminated composite, cylindrical panel, fundamental frequency, optimization, GBNM.

Summary
The use of fibrous composite materials has advanced extensively not only in the aerospace industry but also in automobile, civil and other fields of engineering as a result of their high stiffness and strength to density ratio. The long fibre composites are typically used in the form of laminated plates and shells, which are known to allow designers to control or optimize the mechanical properties. Since vibration of the structural components is usually the main cause of the fatigue failure, maximum frequency problems are of practical importance in the design of composite laminates subject to external excitation.

Narita and Zhao [1] determined the stacking condition that maximizes the lowest frequency of a laminated composite shallow shell with rectangular platform. Hu and Tsai [2] maximized the fundamental frequency of fibre-reinforced laminated cylindrical shells with respect to fibre orientations using the golden section method. Hu and Ou [3] maximized the fundamental frequency of laminated truncated conical shells with respect to fibre orientation by using sequential linear programming method with a simple move-limit strategy. Narita [4] proposed a new concept of a layerwise optimization approach to optimize vibration behaviour for the maximum natural frequency of laminated composite plate considering fibre orientation angles as design variables. Luersen and Riche [5] proposed the globalized and bounded Nelder-Mead method (GBNM). This algorithm is based on repeated direct Nelder-Mead searches, which work on continuous variables [6]. The method is made global by restarting local searches based on a probability density which biases new local searches towards unexplored regions of the design space. They applied the method for buckling load and longitudinal stiffness maximization of a rectangular plate with respect to fibres orientation. Riche et.al. [7] optimized injection time, maximum mold pressure, stiffness and buckling of a rectangular laminate made by resin transfer moulding processes, using the GBNM method.

Since the application of GBNM method for maximum frequency problems have not been found in the literature, this paper is concerned with application of the GBNM method to an unconstrained and single objective optimization of anisotropic laminated cylindrical panels for maximum fundamental frequency. The results have been compared with the genetic algorithm (GA) [8], which shows that the GBNM compares favourably to the GA in terms of accuracy of results. Also results for different thickness, length and angular span of an eight layer symmetric panel have been given. The panel have simply supported boundary condition on all edges. Design variables are fibre orientation of the constituent lamina which consider as continuous variables bounded by -90 and +90. To solve free vibration equations finite element method has been used. First order shear deformation theory and nine nodes Lagrange shell element have been used to formulate finite element equations.

References
1
Y. Narita, X. Zhao, "An optimal design for the maximum fundamental frequency of laminated shallow shells", Int. J. Solids & Structures, 35(20), 2571-2583, 1998. doi:10.1016/S0020-7683(97)00179-0
2
H.T. Hu, J.Y. Tsai, "Maximization of the fundamental frequencies of laminated cylindrical shells with respect to fiber orientations", J. of Sound and Vibration, 225(4), 723-740, 1999. doi:10.1006/jsvi.1999.2261
3
H.T. Hu, S.C. Ou, "Maximization of the fundamental frequency of laminated truncated conical shell with respect to fiber orientations", Comp. Struct., 52(3-4), 265-275, 2001. doi:10.1016/S0263-8223(01)00019-8
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Y. Narita., "Layerwise optimization for the maximum fundamental frequency of laminated composite plates", J. of Sound and Vibration, 263(5), 1005-1016, 2003. doi:10.1016/S0022-460X(03)00270-0
5
M.A. Luersen, R. Le Riche, "Globalized Nelder-Mead method for engineering optimization" Proc. of the Third International Conference on Engineering Computational Technology, Paper 65, Civil-Comp Press, Prague, Czech Republic 4-6, September, 2002. doi:10.4203/ccp.76.65
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J.A. Nelder, R. Mead, "A simplex for function minimization", Comput. J., 7, 308-313, 1965.
7
R. Le Riche, A. Saouab, J. Breard, "Coupled compression RTM and composite layup optimization", Composites Science and Technology, 63, 2277-2287, 2003. doi:10.1016/S0266-3538(03)00195-7
8
M. Shakeri, A. Alibeigloo, A. Morowat, "Multi-objective optimization of laminated cylindrical panels using a genetic algorithm", Proc. of the Tenth International Conference on Civil, Structural and Environmental Engineering Computing, Paper 124, Civil-Comp Press, Stirling, Scotland, 2005. doi:10.4203/ccp.81.124

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