Abstract
The optimal design of elastic trusses is discussed from a dynamic programming point of view. Emphasis is placed on minimum volume design of statically determinate trusses with displacement and stress constraints in the discrete case, i.e., when the cross-sectional areas of the bars are available from a discrete set of values. This, a design constraint usually very difficult to handle with standard nonlinear programming algorithms, is naturally incorporated in the present formulation. In addition, the functional equation approach is shown to furnish a direct solution to the problem of determining a design, among all possible ones satisfying certain volume and displacement constraints, for which the maximum stress is a minimum. A successive approximation approach is briefly indicated as an extension of the method to solve statically indeterminate trusses. Finally, several numerical examples are presented and the main features of the methods are briefly exposed.
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References
Toakley, A. R.,The Optimum Design of Triangulated Frameworks, International Journal of Mechanical Science, Vol. 10, pp. 115–127, 1968.
Chern, J. M., andPrager, W.,Minimum-Weight Design of Statically Determinate Trusses Subject to Multiple Constraints, International Journal of Solids and Structures, Vol. 7, pp. 931–940, 1971.
Distefano, N.,Nonlinear Processes in Engineering, Academic Press, New York, New York, 1974.
Kalaba, R.,Design of Minimal Weight Structures for Given Reliability and Cost, Journal of the Aerospace Sciences, Vol. 29, pp. 355–356, 1962.
Palmer, A. C., andSheppard, D. J.,Optimizing the Shape of Pin-Jointed Structures, Proceedings of the Institution of Civil Engineers, Vol. 47, pp. 363–376, 1970.
Bellman, R., andDreyfus, S.,Applied Dynamic Programming, Princeton University Press, Princeton, New Jersey, 1962.
Dreyfus, S., andPrather, K. L.,Improved Algorithms for Knapsack Problems, University of California, Berkeley, Operations Research Center, Report No. 70-30, 1970.
Gilmore, P. C., andGomory, R.,The Theory and Computations of Knapsack Functions, Operations Research, Vol. 14, pp. 1045–1074, 1966.
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Dedicated to Professor W. Prager
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Distefano, N., Rath, A. A dynamic programming approach to the optimization of elastic trusses. J Optim Theory Appl 15, 13–26 (1975). https://doi.org/10.1007/BF00933018
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DOI: https://doi.org/10.1007/BF00933018