Weight Optimum Design of Pressurized and Axially Loaded Stiffened Conical Shells to Prevent Stress and Buckling Failures

Document Type : Research Paper


Department of Mechanical Engineering, Qom University of Technology, Qom, Iran


An optimal design of internal pressurized stiffened conical shell is investigated using the genetic algorithm (GA) to minimize the structural weight and to prevent various types of stress and buckling failures. Axial compressive load is applied to the shell. Five stress and buckling failures as constraints are taken into account. Using the discrete elements method as well as the energy method, global buckling load and stress field in the stiffened shell are obtained. The stiffeners include rings and stringers. Seven design variables including shell thickness, number of rings and stringers, stiffeners width and height are considered. In addition, the upper and lower practical bounds are applied for the design variables. Finally, a graphical software package named as Optimal Sizer is developed to help the designers.


[1] Patel J.M., Patel T.S., 1980, Minimum weight design of the stiffened cylindrical shell under pure bending, Computers & Structures 11: 559-563.
[2] Simitses G.J., Giri J., 1978, Optimum weight design of stiffened cylinders subjected to torsion combined with axial compression with and without lateral pressure, Computers & Structures 8: 19-30.
[3] Simões L.M.C., Farkas J., Jármai K., 2006, Reliability-based optimum design of a welded stringer-stiffened steel cylindrical shell subject to axial compression and bending, Structural and Multidisciplinary Optimization 31: 147-155.
[4] Bushnell D., Bushnell W.D., 1996, Approximate method for the optimum design of ring and stringer stiffened cylindrical panels and shells with local, inter-ring, and general buckling modal imperfections, Computers & Structures 59(3): 489-527.
[5] Léné F., Duvaut G., Mailhé M.O., Chaabane S.B., Grihon S., 2009, An advanced methodology for optimum design of a composite stiffened cylinder, Composite Structure 91: 392-397.
[6] Simitsess G.J., Sheinman I., 1978, Optimization of geometrically imperfect stiffened cylindrical shells under axial compression, Computers & Structures 59(9): 377-381.
[7] Irisarri F.X., Laurin F., Leroy F.H., Maire J.F., 2011, Computational strategy for multiobjective optimization of composite stiffened panels, Composite Structure 93: 1158-1167.
[8] Rao S.S., Reddy E.S., 1981, Optimum design of stiffened conical shells with natural frequency constraints, Computers & Structures 14(1-2): 103-110.
[9] Colson B., Bruyneel M., Grihon S., Raick C., Remouchamps A., 2010, Optimization methods for advanced design of aircraft panels: a comparison, Optimization and Engineering 11: 583-596.
[10] Ambur D.R., Jaunky N., 2001, Optimal design of grid-stiffened panels and shells with variable curvature, Composite Structure 52: 173-180.
[11] Luspa L., Ruocco E., 2008, Optimum topological design of simply supported composite stiffened panels via genetic algorithms, Computers & Structures 86: 1718-1737.
[12] Bagheri M., Jafari A.A., Sadeghifar M., 2011, Multi-objective optimization of ring stiffened cylindrical shells using a genetic algorithm, Journal of Sound and Vibration 330: 374-384.
[13] El Ansary A.M., El Damatty A.A., Nassef A.O., 2012, A coupled finite element genetic algorithm for optimum design of stiffened liquid-filled steel conical tanks, Thin-walled Structures 49(4): 482-493.
[14] Mehrabani M.M., Jafari A.A., Azadi M., 2012, Multidisciplinary optimization of a stiffened shell by genetic algorithm, Journal of Mechanical Science and Technology 26(2): 517-530.
[15] Marín L., Trias D., Badalló P., Rus G., Mayugo J.A., 2012, Optimization of composite stiffened panels under mechanical and hygrothermal loads using neural networks and genetic algorithms, Composite Structure 94: 3321-3326.
[16] Lam K.Y., Hua L., 1997, Vibration analysis of a rotating truncated circular conical shell, International Journal of Solids and Structures 34(17): 2183-2197.
[17] Talebitooti M., Ghayour M., Ziaei-Rad S., Talebitooti R., 2010, Free vibrations of rotating composite conical shells with stringer and ring stiffeners, Archive of Applied Mechanics 80(3): 201-215.
[18] Baker E.H., Cappelly A.P., Lovalevsky L., Risb F.L., Verette R.M., 1968, Shell Analysis Manual, NASA CR-912, Washington D.C.