Sensitivity of Reliability‐Based Optimum Design
Publication: Journal of Structural Engineering
Volume 111, Issue 8
Abstract
A reliability‐based optimization sensitivity analysis technique based on the feasible directions concept is presented for plastic design of redundant structures. This technique is specialized to a formulation of the problem of plastic optimization for minimum weight based on a rational reliability constraint for sizing members. The technique is demonstrated with a structural design example where emphasis is placed on the sensitivity of the reliability‐based optimum solution to both the correlation among strengths and the method for evaluating the overall probability of plastic collapse.
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References
1.
Ang, A. H.‐S., and Ma, H.‐F., “On the Reliability of Structural Systems,” Proceedings, 3rd International Conference on Structural Safety and Reliability, Trondheim, Norway, 1981, pp. 295–314.
2.
Arora, J. S., and Haug, J. E., “Methods of Design Sensitivity Analysis in Structural Optimization,” AIAA Journal, Vol. 17, No. 9, Sept., 1979, pp. 970–973.
3.
Barthelemy, J. F., and Sobieszczanski‐Sobieski, J., “Optimum Sensitivity Derivatives of Objectives Functions in Nonlinear Programming,” AIAA Journal, Vol. 21, No. 6, June, 1983, pp. 913–915.
4.
Belsare, S. V., and Arora, J. S., “An Algorithm for Engineering Design Optimization,” International Journal for Numerical Methods in Engineering, Vol. 19, 1983, pp. 841–858.
5.
Chou, K. C., McIntosh, C., and Corotis, R. B., “Observations on Structural System Reliability and the Role of Model Correlations,” Structural Safety, Vol. 1, 1983, pp. 189–198.
6.
Cornell, C. A., “Bounds on the Reliability of Structural Systems,” Journal of the Structural Division, ASCE, Vol. 93, No. ST1, Feb., 1967, pp. 171–200.
7.
Ditlevsen, O., “Narrow Reliability Bounds for Structural Systems,” Journal of the Structural Mechanics, Vol. 7, No. 4, 1979, pp. 453–472.
8.
Frangopol, D. M., and Rondal, J., “Considerations on Optimum Combination of Safety and Economy,” Proceedings, 10th Congress of the International Association for Bridge and Structural Engineering, Final Report, Tokyo, Japan, Sept., 1976, pp. 45–48.
9.
Frangopol, D. M., “Interactive Reliability‐Based Structural Optimization,” Computers and Structures, Vol. 19, No. 4, 1984, pp. 559–563.
10.
Frangopol, D. M., “Sensitivity Studies in Optimum Reliability‐Based Design of Plastic Structures, Proceedings, 25th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Palm Springs, Calif., AIAA Paper No. 84‐0854‐CP, Vol. 1, May, 1984, pp. 21–33.
11.
Frangopol, D. M., “Alternative Solutions in Reliability‐Based Optimum Design,” Proceedings, Fifth Engineering Mechanics Division Specialty Conference, ASCE, Laramie, Wyo., Aug., 1984, pp. 1232–1236.
12.
Frangopol, D. M., “A Reliability‐Based Optimization Technique for Automatic Plastic Design,” Computer Methods in Applied Mechanics and Engineering, Vol. 44, 1984, pp. 105–117.
13.
Frangopol, D. M., “Computer‐Automated Sensitivity Analysis in Reliability‐Based Plastic Design,” Journal of Computers and Structures, in press, 1985.
14.
Frangopol, D. M., “Towards Reliability‐Based Computer Aided Optimization of Reinforced Concrete Structures,” Engineering Optimization, in press, 1985.
15.
Grierson, D. E., “The Intelligent Use of Structural Analysis,” Perspectives in Computing, Vol. 3, No. 4, pp. 32–39.
16.
Grimmelt, M. J., and Schuëller, G. I., “Benchmarck Study on Methods to Determine Collapse Failure Probabilities of Redundant Structures,” Structural Safety, Vol. 1, 1982/1983, pp. 93–106.
17.
Han, S. P., “A Gobally Convergent Method for Nonlinear Programming,” Journal of Optimization Theory and Applications, Vol. 22, 1977, pp. 297–309.
18.
Haug, E. J., and Arora, J. S., “Design Sensitivity Analysis of Elastic Mechanical Systems,” Computer Methods in Applied Mechanics and Engineering, Vol. 15, 1979, pp. 36–61.
19.
Hilton, H. H., and Feigen, M., “Minimum Weight Analysis Based on Structural Reliability,” Journal Aerospace Science, Vol. 27, No. 9, 1960, pp. 641–652.
20.
Kelley, H. J., “The Cutting Plane Method for Solving Complex Programs,” SIAM Journal, Vol. 8, 1960, pp. 703–712.
21.
Kirsch, U., Optimum Structural Design, McGraw‐Hill Book Co., New York, N.Y., 1981.
22.
Lind, N. C., and Basler, E., “Safety Level Decisions,” Proceedings, International Conference on Planning and Design of Tall Buildings, Vol. Ib, 1972, pp. 961–972.
23.
Massonnet, C. E., and Save, M. A., Plastic Analysis and Design, Blaisdell Publishing Co., New York, N.Y., Vol. 1, 1965.
24.
Morris, A. J., ed., Foundations of Structural Optimization: A Unified Approach, John Wiley and Sons, Inc., Chicester, 1982.
25.
Moses, F., and Kinser, D. E., “Optimum Structural Design with Failure Probability Constraints,” AIAA Journal, Vol. 5, No. 6, 1967, pp. 1152–1158.
26.
Moses, F., “Approaches to Structural Reliability and Optimization,” Study No. 1, Solid Mechanics Division, University of Waterloo, Ontario, Canada, 1969, pp. 81–120.
27.
Moses, F., “Sensitivity Studies in Structural Reliability,” Study No. 3, Solid Mechanics Division, University of Waterlooo, Waterloo, Ontario, Canada, 1979, pp. 1–17.
28.
Moses, F., and Stevenson, J. D., “Reliability‐Based Structural Design,” Journal of the Structural Division, ASCE, Vol. 96, No. ST2, Feb., 1970, pp. 221–244.
29.
Moses, F., “Design for Reliability—Concepts and Applications,” 13, Optimum Structural Design, R. H. Gallaher and O. C. Zienkiewicz, eds., John Wiley and Sons, Inc., New York, N.Y., 1973.
30.
Nakib, R., and Frangopol, D. M., “Reliability‐Based Analysis and Optimization of Ductile Structural Systems,” Report No. 8501, Department of Civil, Environmental and Architectural Engineering, University of Colorado, Boulder, Colo., Feb., 1985.
31.
Parimi, S. R., and Cohn, M. Z., “Optimal Solutions in Probabilistic Structural Design,” Journal Mécanique Appliauée, Vol. 2, No. 1, 1978, pp. 47–92.
32.
Powell, M. J. D., “The Convergence of Variable Metric Methods for Nonlinearly Constrained Optimization,” Nonlinear programming, O. L. Mangasarian, R. R. Meyer, and S. M. Robinson, eds., Vol. 3, Academic Press, New York, N.Y., 1978.
33.
Ridha, A. R., and Wright, R. N., “Minimum Cost Design of Frames,” Journal of the Structural Division, ASCE, Vol. 93, No. ST4, Apr., 1967, pp. 165–183.
34.
Rosenblueth, E., “Code Specification of Safety and Serviceability,” Proceedings, International Conference on Planning and Design of Tall Buildings, Vol. Ib, 1972, pp. 931–959.
35.
Schmit, L. A., “Problem Formulation, Methods and Solutions in the Optimum Design of Structures,” Study No. 1, Solid Mechanics Division, University of Waterloo, Ontario, Canada, 1969, pp. 19–46.
36.
Schmit, L. A., and Cheng, K. J., “Optimum Design Sensitivity Based on Approximations Concepts and Dual Methods,” Proceedings, 23rd AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, New Orleans, La., AIAA Paper No. 82‐0713‐CP, 1982.
37.
Sobieszczanski‐Sobieski, J., Barthelemy, J. F., and Riley, K. M., “Sensitivity of Optimum Solutions to Problem Parameters,” AIAA Journal, Vol. 20, No. 9, 1982, pp. 1291–1299.
38.
Surahman, A., and Rojiani, K. B., “Reliability‐Based Optimum Design of Concrete Frames,” Journal of Structural Engineering, ASCE, Vol. 109, No. 3, Mar., 1983, pp. 741–757.
39.
Turkstra, C. J., Theory of Structural Design Decisions, Study No. 2, Solid Mechanics Division, University of Waterloo, Waterloo, Ontario, Canada, 1969.
40.
Vanderplaats, G. N., and Moses, F., “Structural Optimization by Methods of Feasible Directions,” Journal of Computers and Structures, Vol. 3, 1973, pp. 739–755.
41.
Vanderplaats, G. N., “A Robust Feasible Directions Algorithm for Design Synthesis,” Proceedings, 24th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Lake Tahoe, Nev., AIAA Paper No. 83‐0938‐CP, Vol. 1, 1983, pp. 392–399.
42.
Vanderplaats, G. N., “Efficient Calculation of Optimum Design Sensitivity,” Proceedings, 25th AIAA/ASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Palm Springs, Calif., AIAA Paper No. 84‐0855‐CP, Vol. 1, 1984, pp. 34–40.
43.
Vanmarcke, E. H., “Matrix Formulation of Reliability Analysis and Reliability‐Based Design,” Journal of Computers and Structures, Vol. 3, 1971, pp. 757–770.
44.
Zoutendijk, G., Methods of Feasible Directions, Elsevier, Amsterdam, The Netherlands, 1960.
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Copyright © 1985 ASCE.
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Published online: Aug 1, 1985
Published in print: Aug 1985
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