Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 30743
Optimum Shape and Design of Cooling Towers

Authors: A. M. El Ansary, A. A. El Damatty, A. O. Nassef


The aim of the current study is to develop a numerical tool that is capable of achieving an optimum shape and design of hyperbolic cooling towers based on coupling a non-linear finite element model developed in-house and a genetic algorithm optimization technique. The objective function is set to be the minimum weight of the tower. The geometric modeling of the tower is represented by means of B-spline curves. The finite element method is applied to model the elastic buckling behaviour of a tower subjected to wind pressure and dead load. The study is divided into two main parts. The first part investigates the optimum shape of the tower corresponding to minimum weight assuming constant thickness. The study is extended in the second part by introducing the shell thickness as one of the design variables in order to achieve an optimum shape and design. Design, functionality and practicality constraints are applied.

Keywords: Optimization, Cooling Towers, finite element, Genetic Algorithm, B-splines

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2824


[1] O.C. Zienkiewicz, J.C. Campbell, "Shape optimization and sequential linear programming", in: R.A. Gallagher, O.E. Zienkiewicz (Eds.), Optimum Structural Design, Wiley, New York, pp. 109-126, 1973.
[2] C.V. Ramakrishnan, A. Francavilla, "Structural shape optimization using penalty functions", J. Struct. Mech. 3 (4), 403-422, 1975.
[3] R.J. Yang, D.L. Dewhirst, J.E. Allison, A. Lee, "Shape optimization of connecting rod pin end using a generic model", Finite element Analysis. 257-264, 1992.
[4] K.H. Chang, K.K. Choi, "A geometry-based parameterization method for shape design of elastic solids", Mech. Struct. And Mach. 215-252, 1992.
[5] P.L. Gould, and S.L. Lee, "Bending of hyperbolic cooling towers", J. Struct. Div. ASCE 93 (ST5) 125-146, 1967.
[6] J. Pieczara, "Optimization of cooling tower shells using a simple genetic algorithm", Struct Multidisc Optim 19, 311-316, 2000.
[7] W. B. Kratzig, W. Zerna, "Resistance of hyperbolic cooling towers to wind and earthquake loading", In: Pister KS, editor. Structural engineering and structural mechanics. Englewood Cliffs, NJ: Prentice- Hall; P. 419-45, 1980.
[8] ACI-ASCE Committee 334, "Recommended Practice for the Design and Construction of Reinforced Concrete Cooling Towers", ACI J., 74(1), 22-31, 1977.
[9] H. J. Niemann, "Wind effects on cooling-tower shells", Journal of Structural Engineering, ASCE; 106(3):643-61, 1980.
[10] ASCE, "Minimum design loads for Buildings and other structures", ASCE 7-98, Reston, Va, 1999.
[11] B. J. Vickery, J. Galsworthy, and A. A. El Damatty, BLWT-SS46-2007. "Wind loads and Interference effects for the cooling tower at the Cardinal #3 Plant", November, 2007.
[12] A. M. El Ansary, "Optimum Design of Shell Structures" Ph.D. dissertation. The University of Western Ontario, London, Ontario, Canada. 2010.
[13] L. Piegl, W. Tiller, "The NURBS book", Berlin, Heidel-berg, New York:Springer, 1995.
[14] B. Koziey, F. A. Mirza, "Consistent thick shell element", Computers and Structures, 65(12):531-41, 1997.
[15] A. A. El Damatty, F. A. Mirza, R. M. Korol, "Large displacements extension of consistent shell element for static and dynamic analysis", Computers and Structures; 62(6):943-60, 1997.
[16] D. E. Goldberg, "Genetic Algorithms in search", Optimization and Machine Learning. Addison-Wesley Publishing Company, Inc., New York, 1989.
[17] L. Davis, Handbook of Genetic Algorithms, Van Nostrand Reinhold, New York, 1991.
[18] P. L. Gould, W. B. Kratzig "Cooling tower structures", In: Chen W, editor. Handbook of structural engineering. Boca Raton, FL: CRC Press Inc. P. 473-504, 1998.
[19] D. Busch, R. Harte, W. B. Kratzig, U. Montag, "New natural draft cooling tower of 200 m of height", Eng.Struct. 12;24(12):1509-21, 2002.
[20] Z. Michalewicz, D. B. Fogel, "How to solve it: modern heuristics", 2nd Ed. New York, 2004.