Engineering Transactions, 46, 1, pp. 115–129, 1998

Optimization of Variable Thickness Plates by Genetic Algorithms

M. Pyrz
University of Science and Technology of Lille

The implementation of genetic algorithms to the optimal design of variable thickness plates is presented. Thin, elastic, piecewise constant thickness plates subjected to bending are investigated. The material distribution that minimizes the structural strain energy under constant volume constraint is searched. In numerical examples, square plates loaded by uniform normal pressure are optimized for different boundary conditions. The best designs are compared with the worst solutions, corresponding to the maximization of the strain energy. Significant changes in strain energy can be achieved by modifying thickness distribution for the same material volume. The performances of the approach are discussed.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


J.H. HOLLAND, Adaptation in natural and artificial systems, University of Michigan Press (and MIT Press, Cambridge, MA 1992), 1975.

M.Z. COHN, Theory and practice of structural optimization, Struct. Optim., 7, pp. 20–31, 1994.

P. HAJELA, Genetic search – an approach to the nonconvex optimization problem, AIAA J., 26, pp. 1205–1210, 1990.

W.M. JENKINS, Towards structural optimization via genetic algorithm, Comput. Struct., 40, 5, pp. 1321–1327, 1991.

S. RAJEEV and C.S. KRISHNAMOORTHY, Discrete optimization of structures using genetic algorithms, J. Struct. Engng., 118, 5, pp. 1233–1250, 1992.

R.T. HAFTKA and B. PRASAD, Optimum structural design with plate bending elements – a survey, AIAA J., 19, 4, pp. 517–522, 1981.

N.V. BANICHUK, Problems and methods of optimal structural design, Mathematical Concepts and Methods in Science and Engineering, 26, Plenum Press, New York, pp. 109–134, 1981.

E.J. HAUG, A numerical method for optimization of distributed parameter structures with displacement constraints, Opt. Control Appl. & Meth., 3, pp. 269–282, 1982.

E. HINTON, S.M. AFONSO and N.V.R. RAO, Some studies on the optimization of variable thickness plates and shells, Engng. Computations, 10, pp. 291–306, 1993.

E. HINTON and N.V.R. RAO, Analysis and shape optimisation of variable thickness prismatic folded plates and curved shells. Part 2. Shape optimisation, Thin–Walled Structures, 17, pp. 161–183, 1993.

M. ZHOU, Y.X. GU and G.I.N. ROZVANY, Application of DCOC method to plates and shells, [in:] Procs. of the First World Congress of Structural and Multidisciplinary Optimization, 28 May–2 June 1995, Goslar, Germany, N. OLHOFF and G.I.N. ROZVANY [Eds.], Pergamon, pp. 25–32, 1995.

E. SALAJEGHEH, Discrete variable optimization of plate structures using dual methods, Comput. & Struct., 58, 6, pp. 1131–1138, 1996.

D.E. GOLDBERG, Genetic algorithms in search, optimization, and machine learning, Addison-Wesley Publishing Company Inc., Reading, MA, 1989.

L. DAVIS, Handbook of genetic algorithms, Van Nostrand Reinhold, New York 1991.

Z. MICHALEWICZ, Genetic algorithms + data structures = evolution programs, Springer Verlag, Berlin, Heidelberg 1992.

O.C. ZIENKIEWICZ and R.L. TAYLOR, The finite element method, Vol. 2, McGraw-Hill, pp. 15–22, 1989.

M. PYRZ, Genetic algorithms in optimal design of discontinuous thickness plates, [in:] Proc. of the Second World Congress of Structural and Multidisciplinary Optimization, May 26–30, 1997, Zakopane, Poland, vol.2, W. GUTKOWSKI and Z. MRÓZ [Eds.], Wydawnictwo Ekoinżynieria, pp. 859–864, 1997.

T. BÄCK, Evolutionary algorithms in theory and practice, Oxford University Press, New York 1995.

DOI: 10.24423/engtrans.661.1998