Abstract
During the seventies people who worked in the field of structural optimization were divided into two distinct and somewhat belligerent camps. On the one side the mathematical programming camp believed in employing the general methods of linear and nonlinear programming such as the simplex method, penalty function techniques, gradient projection techniques or methods of feasible directions (see Chapter 5). On the other side the optimality criteria camp subscribed to the use of methods described in the present chapter. The mathematical programming camp decried the lack of generality of optimality criteria methods, and the optimality criteria camp sneered at the inefficiency of the general mathematical programming approach.
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References
Mitchell, A.G.M., “The limits of economy of material in framed structures,” Phil. Mag., 6, pp. 589–597, 1904.
Cilly, F.H., “The exact design of statically determinate frameworks, and exposition of its possibility, but futility,” Trans. ASCE, 43, pp. 353–407, 1900.
Schmit, L.A., “Structural design by systematic synthesis,” Proceedings 2nd ASCE Conference on Electronic Computation, New York, pp. 105–132, 1960.
Reinschmidt, K., Cornell, C.A., and Brotchie, J.F., “Iterative design and structural optimization, ” J. Strct. Div. ASCE, 92, pp. 281–318, 1966.
Razani, R., “The behavior of the fully stressed design of structures and its relationship to minimum weight design,” AIAA J., 3, pp. 2262–2268, 1965.
Dayaratram, P. and Patnaik, S., “Feasibility of fully stressed design,” AIAA J., 7, pp. 773–774, 1969.
Lansing, W., Dwyer, W., Emerton, R. and Ranalli, E., “Application of fully-stressed design procedures to wing and empennage structures,” J. Aircraft, 8, pp. 683–688, 1971.
Giles, G.L., Blackburn, C.L. and Dixon, S.C., “Automated procedures for sizing aerospace structures (SAVES),” Presented at the AIAA/ASME/SAE 13th Structures, Structural Dynamics and Materials Conference, 1972.
Berke, L. and Khot, N.S., “Use of optimality criteria for large scale systems,” AGARD Lecture Series No. 170 on Structural Optimization, AGARD-LS-70, 1974.
Adelman, H.M., Haftka, R.T. and Tsach, U., “Application of fully stressed design procedures to redundant and non-isotropic structures,” NASA TM-81842, July 1980.
Adelman, H.M. and Narayanaswami, R., “Resizing procedure for structures under combined mechanical and thermal loading,” AIAA J., 14, pp. 1484–1486, 1976.
Venkayya, V.B., “Design of Optimum Structures,” Comput. Struct., 1, pp. 265309, 1971.
Siegel, S., “A flutter optimization program for aircraft structural design,” Proc. AIAA 4th Aircraft Design, Flight Test and Operations Meeting, Los Angeles, California, 1972.
Stroud, W.J., “Optimization of composite structures,” NASA TM-84544, August 1982.
Falk, J.E., “Lagrange multipliers and nonlinear programming, ” J. Math. Anal. Appl., 19, pp. 141–159, 1967.
Fleury, C., “Structural weight optimization by dual methods of convex programming,” Int. J. Num. Meth. Engrng., 14, pp. 1761–1783, 1979.
Fleury C., and Braibant, V., “Structural Optimization: A New Dual Method Using Mixed Variables,” Int. J. Num. Meth. Eng., 23, pp. 409–428, 1985.
Schmit, L.A., and Fleury, C., “Discrete-continuous variable structural synthesis using dual methods,” AIAA J., 18, pp. 1515–1524, 1980.
Garfinkel, R.S. and Nemhauser, G.L., Integer Programming. John Wiley, New York, 1972.
Prager, W., and Shield, R.T., “Optimal Design of Multipurpose Structures,” International Journal of Solids and Structures, 4, pp. 469–475, 1968.
Venkayya, V.B, Khot, N.S., and Reddy, V.S., “Energy Distribution in an Optimum Structural Design,” AFFDL-TR-68–156, 1968.
Berke, L., “An Efficient Approach to the Minimum Weight Design of Deflection Limited Structures,” AFFDL-Tm-70–4, 1970.
Venkayya, V.B., Khot, N.S., and Berke, L., “Application of Optimality Criteria Approaches to Automated design of Large Practical Structures,” Second Symposium on Structural Optimization, AGARD-CP-123, pp. 3–1 to 3–19, 1973.
Gellatly, R.A, and Berke, L., “Optimality Criteria Based Algorithm,” Optimum Structural Design, R.H. Gallagher and O.C., Zienkiewicz, eds., pp. 33–49, John Wiley, 1972.
Khot, N.S., “Algorithms based on optimality criteria to design minimum weight structures,” Eng. Optim., 5, pp. 73–90, 1981.
Venkayya, V.B., “Optimality Criteria: A Basis for Multidisciplinary Optimization,” Computational Mechanics, 1989 (in press).
Khot, N.S., “Algorithms Based on Optimality Criteria to Design Minimum Weight Structures,” Engineering Optimization, 5, pp. 73–90, 1981.
Wilkinson, K. et al. “An automated procedure for flutter and strength analysis and optimization of aerospace vehicles,” AFFDL-TR-75–137, December 1975.
Khot, N.S., “Optimal design of a structure for system stability for a specified eigenvalue distribution,” Proceedings, International Symposium on Optimum Structural Design, Tucson, Arizona, pp. 1–3, October, 1981.
Venkayya, V.B., “Structural optimization: a review and some recommendations,” Int. J. Num. Meth. Engrng., 13, pp. 203— 228, 1978.
Berke, L., and Khot, N.S., “Structural Optimization Using Optimality Criteria,” Computer Aided Optimal Design: Structural and Mechanical Systems (C.A. Mota Soares, Editor ), Springer-Veralg, 1987.
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Haftka, R.T., Gürdal, Z., Kamat, M.P. (1990). Dual and Optimality Criteria Methods. In: Elements of Structural Optimization. Solid Mechanics and Its Applications, vol 1. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-7862-2_9
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DOI: https://doi.org/10.1007/978-94-015-7862-2_9
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