Maximization of Fundamental Frequency of Laminated Composite Cylindrical Shells by Ant Colony Algorithm

Koide, Rubem Matimoto; Luersen, Marco Antonio

doi:10.5028/jatm.v5i1.233

ABSTRACT:

The success in developing modern aerospace systems addresses competitive subjects as optimization, reduced costs, sustainability, environment, weight, and safety. There is an increased demand for lighter materials such as laminated composites. In order to match the demand of aeronautical companies, the shell structures are very important. The dynamic behavior of composite structures is also essential to improve the potential applications of these materials. The knowledge of the dynamic response of the cylindrical shell structures is an important issue in their design, in which the ply thicknesses are often preestablished and the ply orientations are usually restricted to a small set of angles due to manufacturing constraints. Obtaining the best stacking sequence of laminated shell may lead to a problem of combinatorial optimization. As this problem is hard to be solved, several techniques have been developed. Ant colony optimization is a class of heuristic optimization algorithms inspired by the behavior of real ants, related to their ability to find the shortest path between the nest and the food source. Thus, this paper deals with optimal stacking sequence of laminated cylindrical composite shells with the aim of maximizing their fundamental frequency using this approach. The ant colony algorithm was implemented in Matlab platform and was linked to Abaqus academic version to compute the structural response. Cylindrical shells with and without a cutout geometry were studied. Fundamental frequencies were maximized for both cases, and results were presented and discussed.

KEYWORDS:
Frequency maximization; Laminated cylindrical shells; Ant colony optimization; Heuristic optimization

Full text is available only in PDF.

REFERENCES

Amabili, M., 2011, "Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories", Composite Structures, Vol. 94, pp. 207-220.
Barbero, E. J., Reddy, J N. and Teply, J.L., 1990, "General two-dimensional theory of laminated cylindrical shells", AIAA Journal, Vol. 28, No. 3, pp. 544-553.
Chern, Y. and Chao, C.C., 2000, "Comparison of natural frequencies of laminates by 3-D theory, Part II: curved panels", Journal of Sound and Vibrations, Vol. 230, pp. 1009-1030.
Dorigo, M. and Stützle, T., 2004, "Ant colony optimization", MIT, Cambridge, USA.
Ganapathi, M. and Haboussi, M., 2003, "Free vibrations of thick laminated anisotropic non-circular cylindrical shells", Composite Structures, Vol. 60, pp. 125-133.
Ganapathi, M., Patel, B.P. and Patel, H.G., 2004, "Free flexural vibration behavior of laminated angle-ply elliptical cylindrical shells", Computers and Structures, Vol. 82, pp. 509-518.
Gharib, A. and Shakeri, M., 2010, "Stacking sequence optimization of laminated cylindrical shells for buckling and free vibration using genetic algorithm and neural networks", Second International Conference on Engineering Optimization, Lisbon.
Goupee, A. and Vel, S.S., 2006, "Optimization of natural frequencies of bidirectional functionally graded beams", Structural Multidisciplinary Optimization, Vol. 32, pp. 473-484.
Heyliger, P.R. and Jilani, A., 1993, "Free vibrations of laminated anisotropic cylindrical shells", Journal of Engineering Mechanics, Vol. 119, pp. 1062-1077.
Hu, H. and Tsai, J., 1999, "Maximization of the fundamental frequencies of laminated cylindrical shells with respect to fiber orientations", Journal of Sound and Vibration, Vol. 225, No. 4, pp. 723-740.
Hu, H. and Wang, S., 1992, "Optimization for buckling resistance of fiber-composite laminate shells with and without cutouts", Composite Structures, Vol. 22, pp. 03-13.
Irisarri, F.X., Laurin, F., Leroy, F.H. and Maire, J.F., 2011, "Computational strategy for multiobjective optimization of composite stiffened panels", Composite Structures, Vol. 93, pp. 1158-1167.
Lam, K.Y. and Qian, W., 2000, "Free vibration of symmetric angle-ply thick laminated composite cylindrical shells", Composites Part B, Vol. 31, pp. 345-354.
Le Riche, R. and Haftka, R., 1993, "Optimization of Laminate Stacking Sequence for Buckling Load Maximization by Genetic Algorithm", AIAA Journal, Vol. 31, pp. 951-956.
Mota Soares, C.M., Franco Correia, V., Mateus, H. and Herskovits, J., 1995, "A discrete model for the optimal design of thin composite plate-shell type structures using a two-level approach", Composite Structures, Vol. 30, pp. 147-157.
Narita, Y. and Robinson, P., 2006, "Maximizing the fundamental frequency of laminated cylindrical panels using layerwise optimizations", International Journal of Mechanical Sciences, Vol. 48, pp. 1516-1524.
Poore, A.L., Barut, A.E. and Madenci, E., 2008, "Free vibration of laminated cylindrical shells with a circular cutout", Journal of Sound and Vibration, Vol. 312, pp. 55-73.
Rao, A. and Arvind, N., 2007, "Optimal stacking sequence design of laminate composite structures using tabu embedded simulated annealing", Structural Engineering and Mechanics, Vol. 25, pp. 239-268.
Rao, A.R.M. and Lakshmi, K., 2009, "Multi-objective optimal design of hybrid laminate composite structure using scatter search", Journal of Composite Materials, Vol. 43, pp. 2157-2182.
Shafei, E. and Kabir, M.Z., 2011, "Dynamic stability optimization of laminated composite plates under combined boundary loading", Applied Composite Material, Vol. 18, pp. 539-557.
Sharma, A.K. and Mittal, N.D., 2010, "Review on stress and vibration analysis of composite plates", Journal of Applied Sciences, Vol. 10, No. 23, pp. 3156-3166.
Soldatos, K.P., 1994, "Review of three dimensional dynamic analyses of circular cylinders and cylindrical shells", American Society of Mechanical Engineers, Vol. 47, No. 10, pp. 501-516.
Todoroki, A., Shinoda, T., Mizutani, Y. and Matsuzaki, R., 2001, "New surrogate model to predict fracture of laminated CFRP for structural optimization", Journal of Computational Science and Technology, Vol. 5, No. 1, pp. 26-37.

Publication Dates

Publication in this collection
Jan-Mar 2013

History

Received
19 Aug 2012
Accepted
25 Nov 2012

This is an Open Access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

[1] Amabili, M., 2011, "Nonlinear vibrations of laminated circular cylindrical shells: Comparison of different shell theories", Composite Structures, Vol. 94, pp. 207-220.

[2] Barbero, E. J., Reddy, J N. and Teply, J.L., 1990, "General two-dimensional theory of laminated cylindrical shells", AIAA Journal, Vol. 28, No. 3, pp. 544-553.

[3] Chern, Y. and Chao, C.C., 2000, "Comparison of natural frequencies of laminates by 3-D theory, Part II: curved panels", Journal of Sound and Vibrations, Vol. 230, pp. 1009-1030.

[4] Dorigo, M. and Stützle, T., 2004, "Ant colony optimization", MIT, Cambridge, USA.

[5] Ganapathi, M. and Haboussi, M., 2003, "Free vibrations of thick laminated anisotropic non-circular cylindrical shells", Composite Structures, Vol. 60, pp. 125-133.

[6] Ganapathi, M., Patel, B.P. and Patel, H.G., 2004, "Free flexural vibration behavior of laminated angle-ply elliptical cylindrical shells", Computers and Structures, Vol. 82, pp. 509-518.

[7] Gharib, A. and Shakeri, M., 2010, "Stacking sequence optimization of laminated cylindrical shells for buckling and free vibration using genetic algorithm and neural networks", Second International Conference on Engineering Optimization, Lisbon.

[8] Goupee, A. and Vel, S.S., 2006, "Optimization of natural frequencies of bidirectional functionally graded beams", Structural Multidisciplinary Optimization, Vol. 32, pp. 473-484.

[9] Heyliger, P.R. and Jilani, A., 1993, "Free vibrations of laminated anisotropic cylindrical shells", Journal of Engineering Mechanics, Vol. 119, pp. 1062-1077.

[10] Hu, H. and Tsai, J., 1999, "Maximization of the fundamental frequencies of laminated cylindrical shells with respect to fiber orientations", Journal of Sound and Vibration, Vol. 225, No. 4, pp. 723-740.

[11] Hu, H. and Wang, S., 1992, "Optimization for buckling resistance of fiber-composite laminate shells with and without cutouts", Composite Structures, Vol. 22, pp. 03-13.

[12] Irisarri, F.X., Laurin, F., Leroy, F.H. and Maire, J.F., 2011, "Computational strategy for multiobjective optimization of composite stiffened panels", Composite Structures, Vol. 93, pp. 1158-1167.

[13] Lam, K.Y. and Qian, W., 2000, "Free vibration of symmetric angle-ply thick laminated composite cylindrical shells", Composites Part B, Vol. 31, pp. 345-354.

[14] Le Riche, R. and Haftka, R., 1993, "Optimization of Laminate Stacking Sequence for Buckling Load Maximization by Genetic Algorithm", AIAA Journal, Vol. 31, pp. 951-956.

[15] Mota Soares, C.M., Franco Correia, V., Mateus, H. and Herskovits, J., 1995, "A discrete model for the optimal design of thin composite plate-shell type structures using a two-level approach", Composite Structures, Vol. 30, pp. 147-157.

[16] Narita, Y. and Robinson, P., 2006, "Maximizing the fundamental frequency of laminated cylindrical panels using layerwise optimizations", International Journal of Mechanical Sciences, Vol. 48, pp. 1516-1524.

[17] Poore, A.L., Barut, A.E. and Madenci, E., 2008, "Free vibration of laminated cylindrical shells with a circular cutout", Journal of Sound and Vibration, Vol. 312, pp. 55-73.

[18] Rao, A. and Arvind, N., 2007, "Optimal stacking sequence design of laminate composite structures using tabu embedded simulated annealing", Structural Engineering and Mechanics, Vol. 25, pp. 239-268.

[19] Rao, A.R.M. and Lakshmi, K., 2009, "Multi-objective optimal design of hybrid laminate composite structure using scatter search", Journal of Composite Materials, Vol. 43, pp. 2157-2182.

[20] Shafei, E. and Kabir, M.Z., 2011, "Dynamic stability optimization of laminated composite plates under combined boundary loading", Applied Composite Material, Vol. 18, pp. 539-557.

[21] Sharma, A.K. and Mittal, N.D., 2010, "Review on stress and vibration analysis of composite plates", Journal of Applied Sciences, Vol. 10, No. 23, pp. 3156-3166.

[22] Soldatos, K.P., 1994, "Review of three dimensional dynamic analyses of circular cylinders and cylindrical shells", American Society of Mechanical Engineers, Vol. 47, No. 10, pp. 501-516.

[23] Todoroki, A., Shinoda, T., Mizutani, Y. and Matsuzaki, R., 2001, "New surrogate model to predict fracture of laminated CFRP for structural optimization", Journal of Computational Science and Technology, Vol. 5, No. 1, pp. 26-37.

Brasil