Abstract
First, the historical background leading to the optimality criteria approach is discussed pointing out the role of the traditional design methods on one hand, and Prager’s work based on variational principles on the other hand as the two motivating influences. This is followed by the formal development of the method utilizing the separability properties of discretized structures or models. The importance of the single constraint case is pointed out and the associated particularly simple yet powerful optimality criteria is presented followed by extension to multiple constraints. Examples are used to illustrate the approach for displacement, stress and eigenvalue related constraints.
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References
Klein, B.: Direct Use of Extremal Principles in Solving Certain Optimizing Problems Involving Inequalities. J. Oper. Res. Soc. Am., vol. 3, 1955, pp. 1. 68–175, 548.
Schmidt, L.A.: Structural Design by Systematic Synthesis. Proceedings of the Second Conference on Electronic Computation, ASCE, 1960, pp. 105–132.
Razani, R.: Behavior of Fully-Stressed Design of Structures and its Relationship to Minimum Weight Design. AIAA J. vol. 3, no. 12, Dec. 1965, pp. 2262–2268.
Richer, T.P.: Optimum Design-Minimum Weight Versus Fully- Stressed. J. Struct. Div. Am. Soc. Civ. Eng., vol. 92, no. ST6, Dec. 1966, pp. 265–279.
Melosh, R.J.: Convergence in Fully-Stressed Designinq. Symposium on Structural Optimization, AGARD CP-36, 1969, pp. 7–1 to 7–15.
Prager, W.; and Taylor, J.E.: Problems of Optimal Structural Design, J. Appl. Mech., vol. 90, no. 1, Mar. 1968, pp. 102–106.
Venkayya, V.B.; Khot, N.S.; and Reddy, V.S.: Energy Distribution in an Optimum Structural Design. AFFDL-TR-68- 156, Sept. 1968.
Taylor, J.E.: The Strongest Column: An Energy Approach. J. Appl. Mech., vol. 89, no. 2, June 1967, pp. 486–487.
Sheu, C.Y.; and Prager, W.: Recent Developments in Optimal Structural Design. Appl. Mech. Rev., vol. 21, no. 10, Oct. 1968, pp. 985–992.
Prager, W.; and Shield, R.T.: Optimal Design of Multipurpose Structures, Int. J. Solids Struct., vol. 4, no. 4, 1968, pp. 469–475.
Sheu, C.Y.; and Prager, W.: Minimum-Weight Desiqn with Piecewise Constant Specific Stiffness, Journal of Optimization Theory and Application, vol. 2, no. 3, Mav 1968, pp. 179–186.
Prager, W.: Optimization of Structural Desiqn. Journal of Optimization Theory and Applications, vol. 6, no. 1, July 1970, pp. 1–21.
Shield, R.T.; and Prager, W.: Optimal Structural Desiqn for Given Deflection, A. Anqew. Math. Phys., vol. 21, no. 4, 1970, pp. 513–523.
Berke, L: An Efficient Approach to the Minimum Weight Design of Deflection Limited Structures. AFFDL-TM-70-4, 1970.
Gellatly, R.A.; and Berke, L.: Optimum Structural Design. AFFDL-TR-70-165, Apr. 1971.
Prager, W.; and Marcal, P.V.: Optimality Criteria in Structural Design, AFFDL-TR-70-166, May 1971.
Venkayya, V.B., etal.: Design of Optimum Structures for Dynamic Loads. Proceedings of the Third Conference on Matrix Methods in Structural Mechanics, R.M. Bader, et al., eds.. Air Force Flight Dynamics Lab, Oct. 1971.
Berke, L.: Convergence Behavior of Iterative Resizing Procedures Based on Optimality Criteria. AFFDL-TM-72-1- FBR, 1972.
Gellatly, R.A.; and Berke, L.: Optimality-Criter ion Based Algorithm. Optimum Structural Design, R.H. Gallagher, and O.C. Zienkiewicz, eds., John Wiley & Sons, 1972, np. 33–49.
Kiusalaas, J.: Minimum Weight Design of Structures Via Optimality Criteria. NASA TN D-7115, 1972.
Nagtegaal, J.C.: A New Approach to Optimal Design of Elastic Structures. Comput. Methods Appl. Mech. Enq., vol. 2, no. 3, July-Aug. 1973, pp. 255–264.
Khot, N.S., et al.: Application of Optimality Criterion to Fiber Reinforced Composites. AFFDL-TR-73-6, May 1973.
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, 1973, pp. 3–1 to 3–19.
Khot, N.S., et al.: Optimization of Fiber Reinforced Composite Structures. Int. J. Solids Struct, vol. 9, no. 10, 1973, pp. 1225–1236.
Khot, N.S.; Venkayya, V.B.; and Berke, L.: Optimization and Structures for Strenqth and Stability Requirements. AFFDL-TR-73-98, Dec. 1973.
Prager, W.: Minimum Weight Design of Statically Determinate Truss Subject to Constraints on Compliance, Stress, and Cross-Sectional Area. J. Appl. Mech., vol. 40, no. 1, Mar. 1973, pp. 313–314.
Kiusalaas, J.: Optimal Design of Structures with Buckling Constraints. Int. J. Solids Struct., vol. 9, no. 7, 1973, pp. 863–878.
Berke, L.: and Khot, N.S.: Use of Optimality Criteria Methods for Large Scale Systems. Structural Optimization, AGARD-LS-70, 1974, pp. 1–1 to 1–29.
Berke, L.: and Venkayya, V.B.: Review of Optimality Criteria Approaches to Structural Optimization. Structural Optimization Symposium, L.A. Schmit, ed., ASME, New York, 1974, pp. 23–34.
Wilkinson, K.; Lerner, E.; and Taylor, R.F.: Practical Design of Minimum Weight Aircraft Structures for Strength and Flutter Requirements. AIAA Paper 74–986, Aug. 1974.
Venkayya, V.B.; and Khot, N.S.: Design of Optimum Structures to Impulse Type Loading. AIAA J., vol. 13, no. 8, Aug. 1975, pp. 989–994.
Khot, N.S.; Venkayya, V.B.; and Berke, L.: Optimum Structural Design with Stability Constraints. Int. J. Numer Methods Eng., vol. 10, no. 5, 1976, pp. 1097–1114.
Khot, N.S.; Venkayya, V.B.; and Berke, L.: Optimum Design of Composite Structures with Stress and nisplacement Constraints. AIAA J., vol. 14, no. 2, Feb. 1976, pp. 131–132.
Rizzi, P.: Optimization of Multi-Constrained Structures Based on Optimality Criteria. 17th Structures, Structural Dynamics, and Materials Conference, AIAA, 1976, pp. 448–462.
Segenreich, S.A.; and Mcintosh, S.C., Jr.: Weight Optimization Under Multiple Equality Constraints Using an Optimality Criteria. 17th Structures, Structural Dynamics, and Materials Conference, AIAA, 1976, Additional Paper No. 3.
Dobbs, M.W.; and Nelson, R.B.: Application of Optimality Criteria to Automated Structural Desiqn. AIAA J., vol. 14, no. 10, Oct. 1976, pp. 1436–1443.
Taylor, J.E.; and Rossow, M.P.V; Optimal Structural Desiqn Algorithm Using Optimality Criteria. Advances in Engineering Science, vol. 2, NASA CP-2001-vol-2, 1976, pp. 521–530.
Khot, N.S., et al.: Optimum Design of Composite Wing Structures With Twist Constraint for Aeroelastic Tailoring. AFFDL-TR-76-117, Dec. 1976.
Khot, N.S.; Venkayya, V.B.; and Berke, L.: Experiences with Minimum Weight Design of Structures Using Optimality Criteria Methods. 2nd International Conference on Vehicle Structural Mechanics, SAE-P-71, Society of Automotive Engineers, 1977, pp. 191–201.
Wilkinson, K., et al: FASTOP: A Flutter and Strength Optimization Program for Lifting-Surface Structures, J. Aircr., vol. 4, no. 6, June 1977, pp. 581–587.
Sanders, G.; and Fleury, C.: A Mixed Method in Structural Optimization. Int. J. Numer. Methods Enq., vol. 13, no. 2, 1978, pp. 385–404.
Berke, L.; and Khot, N.S.: A Simple Virtual Strain Energy Method to Fully Stress Design Structures With Dissimilar Stress Allowables and Material Properties. AFFDL-TM-77- 28-FBR, Dec. 1977.
Khan, M.R.; Willmert, K.D.; and Thornton, W.A.: A New Optimality Criterion Method for Large Scale Structures. 19th AIAA/ASME/SAE Structures, Structural Dynamics and Materials Conference, AIAA, 1978, pp. 47–58.
Isakson, G., et al.: ASOP-3: A Program for Optimum Structural Design to Satisfy Strength and Deflection Constraints, J. Aircr., vol. 15, no. 7, July 1978, pp. 422–428.
Markowitz, J.; and Isakson, G.: FASTOP-3: A Strength, Deflection and Flutter Optimization Program for Metallic and Composite Structures, Vol. I Theory and Application, Vol. II - Program User’s Manual, AFFDL-TR-78-50, May 1978.
Haug, E.J.; and Arora, J.S.: Applied Optimal Desiqn, Wilev-Interscience, 1979, p. 215.
Schmidt, L.A., Jr.; and Fleury, C.: An Improved Analysis/ Synthesis Capability Based on Dual Methods - ACCESS 3. 20th Structures, Structural Dynamic and Materials Conference, AIAA, 1979, pp. 23–50.
Fleury, C.; and Schmit, L.A. Jr.: Dual Methods and Approximation Concepts in Structural Synthesis. NASA CR-3226, 1980.
Khot, N.S.; Berke, L.; and Venkayya, V.B.: Minimum Weight Design of Structures by the Optimality Criterion and Projection Method. 20th Structures, Structural Dynamics and Materials Conference, AIAA, 1979, pp. 11–22.
Lerner, E.: The Application of Practical Optimization Techniques in the Preliminary Structural Design of a Forward-Swept Wing. Second International Symposium on Aeroelasticity and Structural Dynamics, Deutsche Gesellschaft fuer Luft- und Raumfahrt, Bonn, Germany, 1985, po. 381–392.
Lerner, E.; and Markowitz, J.: An Efficient Structural Resizing Procedure for Meeting Static Aeroeleastic Design Objectives. J. Aircr., vol. 16, no. 2, Feb. 1979, pp. 65–71.
Cross, H. t The Relation of Analysis to Structural Design, Am. Soc. Civ. Eng. Proc., vol. 61, no. 8, Oct. 1935, pp. 1119–1130; and vol. 61, no. 10, pt. 1, Dec. 1935, pp. 1551–1557.
Khot, N.S.: Berke, L.: and Venkayya, V. B. s Comparison of Optimality Criteria Algorithms for Minimum Weight Design of Structures, AIAA J., Vol. 17, no. 2, Feb. 1979, pp. 182–190.
Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, 1982, p. 104.
Gellatly, R.A.; and Berke, L.: A Preliminary Study of a New Approach to the Optimization of Strength Limited Structures, AFFDL-TM-75-162-FBR, Sept. 1975.
Gellatly, R.A.; and Thorn, R.D.: Force Method Optimization, AFWAL-TR-80-3006, Feb. 1980.
Gellatly, R.A.; and Thorn, R.D.: Optimality Criteria Using a Force Method of Analysis Approach. Foundations of Structural Optimizations A Unified Approach. A.J. Morris, ed., Wiley-Interscience, 1982, pp. 237–272.
Adelman, H.M.; Haftka, R.T.; and Tsach, U.: Application of Fully Stressed Design Procedures to Redundant and Non-Isotropic Structures, NASA TM-81842, 1980.
Walsh, J.: Application of Mathematical Optimization Procedures to a Structural Model of a Large Finite- Element Wing, NASA TM-87597, 1986.
Prager, W. s Unexpected Results in Structural Optimization, J. Struct. Mech., vol. 9, no. 1, 1981, pp. 71–90.
Khot, N.S.: Optimization of Structures with Multiple Frequency Constraints. Comput Struct., vol. 20, no. 5, 1985, pp. 869–876.
Khot, N.S.: and Kamat, M.P.: Minimum Weight Design of Truss Structures with Geometric Nonlinear Behavior. AIAA J., vol. 23, no. 1, Jan. 1985, pp. 139–144.
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Berke, L., Khot, N.S. (1987). Structural Optimization Using Optimality Criteria. In: Mota Soares, C.A. (eds) Computer Aided Optimal Design: Structural and Mechanical Systems. NATO ASI Series, vol 27. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-83051-8_7
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DOI: https://doi.org/10.1007/978-3-642-83051-8_7
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