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Multicriterion reliability-oriented optimization of structural systems by stochastic programming. (English) Zbl 0896.90105
Summary: The paper deals with multicriterion reliability-oriented optimization of truss structures by stochastic programming. Deterministic approach to structural optimization appears to be insufficient when loads acting upon a structure and material properties of the structure elements have a random nature. The aim of this paper is to show importance of random modelling of the structure and influence of random parameters on an optimal solution. Usually, quality of engineering structure design is considered in terms of displacements, total cost and reliability. Therefore, optimization problem has been formulated and then solved in order to show interaction between displacement and a total cost objective function. The examples of 4-bar and 25-bar truss structures illustrate our considerations. The results of optimization are presented in the form of diagrams.
##### MSC:
 90B25 Reliability, availability, maintenance, inspection in operations research 74P99 Optimization problems in solid mechanics 90C90 Applications of mathematical programming 90C15 Stochastic programming 90C29 Multi-objective and goal programming
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##### References:
 [1] Augusti G, Baratta A, Casciati F (1984) Probabilistic methods in structural engineering. Chapman and Hall · Zbl 0562.73078 [2] Bjerager P (1990) On computational methods for structural reliability analysis. Structural Safety 9:79-96 · doi:10.1016/0167-4730(90)90001-6 [3] Charnes A, Cooper WW (1959) Chance constrained programing. Management Science 6:73-79 · Zbl 0995.90600 · doi:10.1287/mnsc.6.1.73 [4] Eschenauer H, Koski J, Osyczka A (eds) (1990) Multicriteria design optimization: Procedures and applications. Springer, Berlin · Zbl 0743.90116 [5] Jendo S (1990) Multiobjective optimization. In: Save M, Prager W (eds) Structural optimization, Vol. 2, Mathematical programming, Plenum Press, New York, Chap. 18, pp. 311-342 [6] Jendo S, Marks W (1984) Stochastic programming. In: Brandt AM (ed) Criteria and methods of structural optimization, Chapter 9, Kluwer-PWN, Warsaw, pp. 299-313 [7] Jendo S, Putresza J (1989) Multicriteria optimization of bar structures with random parameters. Proc. of Inter. Conf. on Multiple Criteria Decision Making: Applications in Industry and Service, Bangkok, Thailand, pp. 1085-1097 [8] Madsen HO, Krenk S, Lind NC (1986) Methods of structural safety. Prentice-Hall, New York [9] Rao SS (1978) Optimization, theory and applications. Wiley Eastern Lts., New Delhi [10] Tichy M (1993) Applied methods of structural reliability. Kluwer Academic Publishers, Dordrecht · Zbl 0788.73006 [11] Venkayya VB (1971) Design of optimum structures. Comp. & Struct., Vol. 1, No 1/2
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