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Part of the book series: NATO ASI Series ((NATO ASI F,volume 27))

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

  1. 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.

    Google Scholar 

  2. Schmidt, L.A.: Structural Design by Systematic Synthesis. Proceedings of the Second Conference on Electronic Computation, ASCE, 1960, pp. 105–132.

    Google Scholar 

  3. 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.

    Article  Google Scholar 

  4. 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.

    Google Scholar 

  5. Melosh, R.J.: Convergence in Fully-Stressed Designinq. Symposium on Structural Optimization, AGARD CP-36, 1969, pp. 7–1 to 7–15.

    Google Scholar 

  6. Prager, W.; and Taylor, J.E.: Problems of Optimal Structural Design, J. Appl. Mech., vol. 90, no. 1, Mar. 1968, pp. 102–106.

    Article  Google Scholar 

  7. Venkayya, V.B.; Khot, N.S.; and Reddy, V.S.: Energy Distribution in an Optimum Structural Design. AFFDL-TR-68- 156, Sept. 1968.

    Google Scholar 

  8. Taylor, J.E.: The Strongest Column: An Energy Approach. J. Appl. Mech., vol. 89, no. 2, June 1967, pp. 486–487.

    Article  Google Scholar 

  9. Sheu, C.Y.; and Prager, W.: Recent Developments in Optimal Structural Design. Appl. Mech. Rev., vol. 21, no. 10, Oct. 1968, pp. 985–992.

    Google Scholar 

  10. Prager, W.; and Shield, R.T.: Optimal Design of Multipurpose Structures, Int. J. Solids Struct., vol. 4, no. 4, 1968, pp. 469–475.

    Article  Google Scholar 

  11. 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.

    Google Scholar 

  12. Prager, W.: Optimization of Structural Desiqn. Journal of Optimization Theory and Applications, vol. 6, no. 1, July 1970, pp. 1–21.

    Article  MathSciNet  MATH  Google Scholar 

  13. Shield, R.T.; and Prager, W.: Optimal Structural Desiqn for Given Deflection, A. Anqew. Math. Phys., vol. 21, no. 4, 1970, pp. 513–523.

    MATH  Google Scholar 

  14. Berke, L: An Efficient Approach to the Minimum Weight Design of Deflection Limited Structures. AFFDL-TM-70-4, 1970.

    Google Scholar 

  15. Gellatly, R.A.; and Berke, L.: Optimum Structural Design. AFFDL-TR-70-165, Apr. 1971.

    Google Scholar 

  16. Prager, W.; and Marcal, P.V.: Optimality Criteria in Structural Design, AFFDL-TR-70-166, May 1971.

    Google Scholar 

  17. 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.

    Google Scholar 

  18. Berke, L.: Convergence Behavior of Iterative Resizing Procedures Based on Optimality Criteria. AFFDL-TM-72-1- FBR, 1972.

    Google Scholar 

  19. 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.

    Google Scholar 

  20. Kiusalaas, J.: Minimum Weight Design of Structures Via Optimality Criteria. NASA TN D-7115, 1972.

    Google Scholar 

  21. 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.

    Google Scholar 

  22. Khot, N.S., et al.: Application of Optimality Criterion to Fiber Reinforced Composites. AFFDL-TR-73-6, May 1973.

    Google Scholar 

  23. 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.

    Google Scholar 

  24. Khot, N.S., et al.: Optimization of Fiber Reinforced Composite Structures. Int. J. Solids Struct, vol. 9, no. 10, 1973, pp. 1225–1236.

    Article  Google Scholar 

  25. Khot, N.S.; Venkayya, V.B.; and Berke, L.: Optimization and Structures for Strenqth and Stability Requirements. AFFDL-TR-73-98, Dec. 1973.

    Google Scholar 

  26. 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.

    Article  Google Scholar 

  27. Kiusalaas, J.: Optimal Design of Structures with Buckling Constraints. Int. J. Solids Struct., vol. 9, no. 7, 1973, pp. 863–878.

    Article  MathSciNet  Google Scholar 

  28. 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.

    Google Scholar 

  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.

    Google Scholar 

  30. 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.

    Google Scholar 

  31. 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.

    Article  MATH  Google Scholar 

  32. 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.

    Article  MATH  Google Scholar 

  33. 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.

    Article  MathSciNet  Google Scholar 

  34. Rizzi, P.: Optimization of Multi-Constrained Structures Based on Optimality Criteria. 17th Structures, Structural Dynamics, and Materials Conference, AIAA, 1976, pp. 448–462.

    Google Scholar 

  35. 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.

    Google Scholar 

  36. 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.

    Article  Google Scholar 

  37. 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.

    Google Scholar 

  38. Khot, N.S., et al.: Optimum Design of Composite Wing Structures With Twist Constraint for Aeroelastic Tailoring. AFFDL-TR-76-117, Dec. 1976.

    Google Scholar 

  39. 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.

    Google Scholar 

  40. 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.

    Article  Google Scholar 

  41. Sanders, G.; and Fleury, C.: A Mixed Method in Structural Optimization. Int. J. Numer. Methods Enq., vol. 13, no. 2, 1978, pp. 385–404.

    Article  Google Scholar 

  42. 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.

    Google Scholar 

  43. 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.

    Google Scholar 

  44. 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.

    Article  Google Scholar 

  45. 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.

    Google Scholar 

  46. Haug, E.J.; and Arora, J.S.: Applied Optimal Desiqn, Wilev-Interscience, 1979, p. 215.

    Google Scholar 

  47. 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.

    Google Scholar 

  48. Fleury, C.; and Schmit, L.A. Jr.: Dual Methods and Approximation Concepts in Structural Synthesis. NASA CR-3226, 1980.

    Google Scholar 

  49. 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.

    Google Scholar 

  50. 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.

    Google Scholar 

  51. 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.

    Google Scholar 

  52. 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.

    Google Scholar 

  53. 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.

    Google Scholar 

  54. Bertsekas, D.P.: Constrained Optimization and Lagrange Multiplier Methods. Academic Press, 1982, p. 104.

    MATH  Google Scholar 

  55. 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.

    Google Scholar 

  56. Gellatly, R.A.; and Thorn, R.D.: Force Method Optimization, AFWAL-TR-80-3006, Feb. 1980.

    Google Scholar 

  57. 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.

    Google Scholar 

  58. 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.

    Google Scholar 

  59. Walsh, J.: Application of Mathematical Optimization Procedures to a Structural Model of a Large Finite- Element Wing, NASA TM-87597, 1986.

    Google Scholar 

  60. Prager, W. s Unexpected Results in Structural Optimization, J. Struct. Mech., vol. 9, no. 1, 1981, pp. 71–90.

    Google Scholar 

  61. Khot, N.S.: Optimization of Structures with Multiple Frequency Constraints. Comput Struct., vol. 20, no. 5, 1985, pp. 869–876.

    Article  MATH  Google Scholar 

  62. 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.

    Article  MATH  Google Scholar 

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© 1987 Springer-Verlag Berlin Heidelberg

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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

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-83053-2

  • Online ISBN: 978-3-642-83051-8

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