Optimization of Composite Stiffened Cylindrical Shell using PSO Algorithm


Faculty of New Science and Technologies, University of Tehran


Composite stiffened cylindrical shells are widely used as primary elements in aerospace structures. In the recent years, there has been a growing research interest in optimum design of composite stiffened cylindrical shell structures for stability under buckling load.  This paper focuses upon the development of an efficient optimization of ring-stringer stiffened cylindrical shell. The optimization problem used in this study involves weight minimization of ring-stringer stiffened composite cylindrical shell with buckling load and stress, which are considered as design constraints. The proposed methodology is based on Particle Swarm Optimization (PSO) algorithm. The material of shell is composite, but the material of stiffeners is considered to be isotropic. The approach adopted in modeling utilizes the Rayleigh-Ritz energy method and the stiffeners are treated as discrete members. In addition, a 3-D Finite Element (FEM) model of the ring-stringer stiffened cylindrical shell is developed that takes into consideration the exact geometric configuration. The results obtained using the Rayleigh-Ritz energy method are compared with those using 3-D FE model. The proposed methodology is implemented on the ring-stringer stiffened cylindrical shell using the PSO algorithm. The obtained results show a 13% reduction in the weight of the ring-stringer stiffened cylindrical shell whilst all the design constraints are satisfied. In addition, the results show that the proposed methodology provides an effective way of solving composite stiffened cylindrical shell design problems.


Article Title [فارسی]

Optimization of Composite Stiffened Cylindrical Shell using PSO Algorithm

[1] Simitses, G. J., “Buckling and Postbuckling of Imperfect Cylindrical Shells: A Review“, Applied
Mechanics Reviews, Vol. 39, No. 10, pp. 1517-1524, 1986.
[2] Akbulut, M. and F. O. Sonmez (2008). "Optimum design of composite laminates for minimum
thickness." Comput. Struct. 86(21-22): 1974-1982.
[3] Lopez, R., et al. (2009). Optimization of laminated composites considering different failure criteria.
[4] Coburn, B. H., et al. (2014). "Buckling analysis of stiffened variable angle tow panels." Composite Structures 111: 259-270.
[5] Ye, F., et al. (2017). "Variable stiffness composite material design by using support vector regression
assisted efficient global optimization method." Structural and Multidisciplinary Optimization 56(1):203-219.
[6] Ganguli, R. (2013). Optimal Design of Composite Structures: A Historical Review.
[7] Bahubalendruni, M. V. A. R. and B. B. Biswal, (2014). Study of optimization of composite structures with respect to industrial applications. 2014 IEEE 8th International Conference on Intelligent Systems and Control (ISCO). 
[8] Henrichsen, S. R. (2015). Optimization of Laminated Composite Structures, Aalborg Universitetsforlag.
[9] Koide, R. M. and M. A. Luersen (2013)."Maximization of Fundamental Frequency of Laminated Composite Cylindrical Shells by Ant Colony Algorithm." Journal of Aerospace Technology and Management 5: 75-82.
[10] Léné, F., et al. (2009). "An advanced methodology for optimum design of a composite stiffened cylinder." Composite Structures 91(4): 392-397.
[11] Muc, A., “Transverse shear effects in discrete optimization of laminated compressed cylindrical
shells“, Composite Structures, Vol. 38, No. 1, pp.489-497, 1997/05/01, 1997.
[12] Paweł Foryś, Optimization of cylindrical shells stiffened by rings under external pressure including
their post-buckling behaviour, Institute of Applied Mechanics, Cracow University of Technology, al. Jana Pawła II 17, 31-864 Kraków, Poland.
[13] Khong, P., “Optimal Design of Laminates for Maximum Buckling Resistance and Minimum Weight“, 1999.
[14] Walker, M., Smith, R. E., “A technique for the multiobjective optimisation of laminated composite
structures using genetic algorithms and finite element analysis“, Composite Structures, Vol. 62,
No. 1, pp. 123-128, 10//, 2003.
[15] Adams, D. B., Watson, L. T., Gürdal, Z., Anderson-Cook, C. M., “Genetic algorithm optimization and
blending of composite laminates by locally reducing laminate thickness“, Advances in Engineering Software, Vol. 35, No. 1, pp. 35-43,1//, 2004.
[16] MH Shojaeifard, R Talebitooti, A Yadollahi, Optimization of sound transmission through laminated composite cylindrical shells by using a genetic algorithm, mechanics of composites
materials, September 2011, 47:481.
[17] Park, J. H., Hwang, J. H., Lee, C. S., Hwang, W.,“Stacking sequence design of composite laminates
for maximum strength using genetic algorithms“,Composite Structures, Vol. 52, No. 2, pp. 217-231,5//, 2001
[18] A. Gharib, Shakeri M, , Stacking sequence optimization of laminated cylindrical shells for
buckling and free vibration using genetic algorithm and neural networks, 2nd International Conference on Engineering Optimization, September 6 - 9,2010, Lisbon, Portugal.
Sadeghifar, M., Bagheri, M., Jafari, A. A.,
“Multi objective optimization of or thogonally stiffened cylindrical shells for minimum weight and maximum axial buckling load“, Thin-Walled
Structures, Vol. 48, No. 12, pp. 979-988, 12//, 2010.
[20] R. Talebitooti, MH Shojaeefard, S
Yarmohammadisatri, Shape design optimization of
cylindrical tank using b-spline curve, Computers and
Fluids, Vol 109, 10 March 2015, Pages 100-112.
[21] Kennedy, J., Eberhart, R., “Particle swarm optimization“, in Proceeding of, 1942-1948 vol.4.
[22] P. Y. Jiang, Z. M. Lin, J. Xu, and J. Q. Sun, “A Particle Swarm Optimization Algorithm for
Minimizing Weight of the Composite Box Structure,” in Advanced Materials Research, 2012, vol. 430, pp. 70–475.
[23] I. C. Trelea, “The particle swarm optimization algorithm: convergence analysis and parameter
selection,” Inf. Process. Lett., vol. 85, no. 6, pp.317–325, 2003.
[24] S. Suresh, P. B. Sujit, and A. K. Rao, “Particle swarm optimization approach for multi-objective composite box-beam design,” Compos. Struct., vol. 81, no. 4, pp. 598–605, 2007.
[25] N. Chang, W. Wang, W. Yang, and J. Wang, “Ply stacking sequence optimization of composite laminate by permutation discrete particle swarm optimization,” Struct. Multidiscip. Optim., vol. 41, no. 2, pp. 179–187, 2010.
[26] Akl, W., Ruzzene, M., Baz, A., “Optimal design of underwater stiffened shells“, Structural and Multidisciplinary Optimization, Vol. 23, No. 4, pp.297-310, 2002.
[27] Tian, J., Wang, C. M., Swaddiwudhipong, S., “Elastic buckling analysis of ring-stiffened cylindrical shells under general pressure loading via the Ritz method“, Thin-Walled Structures, Vol. 35, No. 1, pp. 1-24, 9//, 1999.
[28] Rinehart, S. A., Wang, J. T. S., “Vibration of simply supported cylindrical shells with longitudinal stiffeners“, Journal of Sound and Vibration, Vol. 24, No. 2, pp. 151-163, 1972/09/22,1972.
[29] Lim, C., Ma, Y., “Computational p-element method on the effects of thickness and length on self weight buckling of thin cylindrical shells via various shell theories“, Computational mechanics,Vol. 31, No. 5, pp. 400-408, 2003.