Abstract
Today, in modern structural design the ultimate goal is generally to find the best possible solution without compromising structural reliability. Toward this aim several reliability-based design codes have been proposed and are currently used in the United States, Canada, Asia, Australia, and Europe for buildings, bridges, and offshore platforms. These codes are calibrated using advanced structural reliability techniques to provide uniform and consistent safety levels over all structural elements (e.g., beams, columns, connections) that are designed by the same code provisions. However, uniform reliability of structural elements does not assure uniform reliability of structural systems. Depending on the type of structural topology, material, configuration, joint behavior, and correlations, the reliability of a structural system can be vastly different (Ang, 1989). Therefore, considerable research has been focused on structural system reliability assessment both in code work and in specific structural investigations for design criteria selection, concept evaluation, as well as on inspection and maintenance strategies. It is assumed in this chapter that we know how to evaluate both element (also referred to as component) and system reliabilities with respect to various limit states.1
The financial support of the National Science Foundation under Grants MSM-8618108, MSM-8800882, and MSM-9013017 for RBSO research at the University of Colorado at Boulder is gratefully acknowledged. Also gratefully acknowledged is the collaboration and support of the writer’s associates: A. Al-Harthy, G. Fu, S. Hendawi, M. Iizuka, S. Katsuki, M. Klisinski, Y.-H. Lee, R. Nakib, and K. Yoshida, all of whom made contributions to the development of RBSO theory, software, and/or applications.
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References
Aashto (American Association for State Highway and Transportation Officials) (1983). Standard Specifications for Highway Bridges, 13th edition. Washington, D.C.: American Association for State Highway and Transportation Officials.
Ang, A. H.-S. (1989). Foreword. In: New Directions in Structural System Reliability. D. M. Frangopol, Ed. Boulder, Colorado: University of Colorado, p. xi.
Ang, A. H.-S., and C. A. Cornell (1974). Reliability bases of structural safety and design. Journal of the Structural Division, ASCE 100(9): 1755–1769.
Ano, A. H.-S., and W. H. Tang (1984). Probability Concepts in Engineering Planning and Design, Vol. II. New York: John Wiley & Sons.
Arora, J. S. (1989a). Introduction to Optimum Design. New York: McGraw-Hill.
Arora, J. S. (1989b). Computational design optimization: A review and future directions. In: New Directions in Structural System Reliability. D. M. Frangopol, Ed. Boulder, Colorado: University of Colorado, pp. 29–44.
Arora, J. S., D. F. Haskell, and A. K. Govill (1980). Optimal design of large structures for damage tolerance. AIAA Journal 118(5):563–570.
Ashley, H. (1982). On making things the best-aeronautical uses of optimization. Journal of Aircraft 19:5–28.
Atrek, E., R. H. Gallagher, K. M. Ragsdell, and O. C. Zienkiewicz, Eds. (1984). New Directions in Optimum Structural Design. New York: John Wiley & Sons.
August, G., A. Baratta, and F. Cascjatri (1984). Probabilistic Methods in Structural Engineering. London: Chapman and Hall.
Bjerager, P. (1989). On computation methods for structural reliability analysis. In: New Directions in Structural System Reliability. D. M. Frangopol, Ed. Boulder, Colorado: University of Colorado, pp. 52–67.
Bjerager, P., and S. Krenk (1989). Parametric sensitivity in first order reliability theory. Journal of Engineering Mechanics, ASCE 115(7):1577–1582.
Borkowski, A., and S. Jendo (1990). Structural Optimization--Mathematical Programming, Vol. 2. M. Save and W. Prager, Eds. New York: Plenum.
Bourgund, U. (1987). Reliability-based optimization of structural systems. In: Stochastic Structural Mechanics, Lecture Notes in Engineering, Vol. 31. Y. K. Lin and G. I. Schuëller, Eds. Berlin: Springer-Verlag, pp. 52–65.
Carmichael, D. G. (1981). Probabilistic optimal design of framed structures. Computer Aided Design 13:261–264.
Casciatti, F., and L. Faravelli (1985). Structural reliability and structural design optimization. In: Proceedings of the 4th International Conference on Structural Safety and Reliability, (Kobe, Japan), Vol. 3. I. Konishi, A. H.-S. Mg, and M. Shinozuka, Eds. Kyoto, Japan: Shinko Printing Company, pp. 261–264.
Cohn, M. Z. (1972). Analysis and Design of Inelastic Structures: Problems, Vol. 2. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.
Cornell, C A (1967). Bounds on the reliability of structural systems. Journal of the Structural Division, ASCE 93(1): 171–200.
Cornell, C. A. (1969a). A probability-based structural code. Journal of the American Concrete Institute 66(12): 974–985.
Cornell, C A (1969b). Structural safety specifications based on second moment reliability analysis. In: Final Report of the Symposium on Concepts of Safety and Methods of Design. London, England: International Association for Bridge and Structural Engineering, pp. 235–245.
Der Kiureghian, A., and P. Thoft-Christensen, Eds. (1991). Reliability and Optimization of Structural Systems ’80. (Proceedings of the 3rd IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems). Lecture Notes in Engineering, Vol. 61. Berlin: Springer-Verlag.
Dhillon, B. S., and C.-H. Kuo (1991). Optimum design of composite hybrid plate girders. Journal of Structural Engineering, ASCE 117(7):2088–2098.
Ditlevsen, O. (1973). Structural Reliability Analysis and the Invariance Problem. Copenhagen, Denmark: Department of Civil Engineering, Danish Engineering Academy.
Ditlevsen, O. (1979). Narrow reliability bounds for structural systems. Journal of Structural Mechanics 7(4):453–472.
Ditlevsen, O. (1981). Uncertainty Modeling with Applications to Civil Engineering Systems. New York: McGraw-Hill.
Ditlevsen, O., and Bjerager, P. (1986). Methods of structural systems reliability. Structural Safety 3:195–229.
Duckstein, L. (1984). Multiobjective optimization in structural design: The model choice problem. In: New Directions in Optimum Structural Design. E. Atrek, et al., Eds. Chichester, England: John Wiley & Sons, pp. 459–481.
Enevoldsen, I. (1991). Reliability-Based Structural Optimization. Ph.D. Thesis. Aalborg, Denmark: Department of Building Technology and Structural Engineering, Aalborg University.
Enevoldsen, I., and J. D. Sorensen (1990). Reliability-Based Optimization of Series Systems of Parallel Systems. Structural Reliability Theory Paper No. 82. Aalborg, Denmark: Aalborg University.
Enevoldsen, I., J. D. Sorensen, and P. Thoft-Christensen (1989). Shape optimization of mono-tower offshore platform. In: Proceedings of the International Conference on Computer Aided Design of Structures: Applications. C. A. Brebbia and S. Hernandez, Eds. Southampton, England: Computational Mechanics Publications, pp. 297–308.
Enevoldsen, I., J. D. Sorensen, and G. Sigurdsson (1990). Reliability-Based Shape Optimization Using Stochastic Finite Element Methods. Structural Reliability Theory Paper No. 73. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.
Eschenauer, H. A., J. kosxt, and A. Osyczka, Eds. (1990). Multicriteria Design Optimization: Procedures and Applications. Berlin: Springer-Verlag.
Farkas, J. (1984). Optimum Design of Metal Structures. Chichester, England: Ellis Horwood.
Feng, Y. S., and F. Moses (1986a). A method of structural optimization based on structural system reliability. Journal of Structural Mechanics 14(4):437–453.
Feng, Y. S., and F. Moses (1986b). Optimum design, redundancy and reliability of structural systems. Computers and Structures 24(2):239–251.
Ferry-Borges, J. (1954). O Dimensionamento de Estruturas. Lisbon, Portugal: Ministry of Public Works, National Laboratory of Civil Engineering.
Forssell, C. (1924). Ekonomi och byggnadsvasen (economy and construction). Sunt Fornoft 4:74–77 (in Swedish) (Translated to English in excerpts in Lind, N. C. [1970]. Structural Reliability and Codified Design. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.)
Frangopol, D. M. (1984a). A reliability-based optimization technique for automatic plastic design. Computer Methods in Applied Mechanics and Engineering 44:105–117.
Frangopol, D. M. (1984b). Interactive reliability-based structural optimization. Computers and Structures 19(4): 559–563.
Frangopol, D. M. (1985a). Sensitivity of reliability-based optimum design. Journal of Structural Engineering, ASCE 111(8):1703–1721.
Frangopol, D. M. (1985b). Multicriteria reliability-based optimum design. Structural Safety 3(1):23–28.
Frangopol, D. M. (1985c). Structural optimization using reliability concepts. Journal of Structural Engineering, ASCE 111(11):2288–2301.
Frangopol, D. M. (1985d). Towards reliability-based computer aided optimization of reinforced concrete structures. Engineering Optimization 8(4):301–313.
Frangopol, D. M. (1986a). Computer-automated design of structural systems under reliability-based performance constraints. Engineering Computations 3(2):109–115.
Frangopol, D. M. (1986b). Structural optimization under conditions of uncertainty, with reference to serviceability and ultimate limit states. In: Recent Developments in Structural Optimization. F. Y. Cheng, Ed. New York: American Society of Civil Engineers, pp. 54–71.
Frangopol, D. M. (1986c). Computer-automated sensitivity analysis in reliability-based plastic design. Computers and Structures 22(1):63–75.
Frangopol, D. M. (1987). Unified approach to reliability-based structural optimization. In: Dynamics of Structures. J. M. Roesset, Ed. New York: American Society of Civil Engineers, pp. 156–167.
Frangopol, D. M., Ed. (1989). New Directions in Structural System Reliability. Boulder, Colorado: University of Colorado.
Frangopol, D. M. (1991). Reliability-based optimization research at the University of Colorado: A brief retrospective. In: Progress in Structural Engineering. D. E. Grierson, A. Franchi, and P. Riva, Eds. Dordrecht, The Netherlands: Kluwer Academic, pp. 481–491.
Frangopol, D. M. (1993). How to include reliability constraints in structural optimization. In: Structural Engineering in Natural Hazards Mitigation, Vol. 2. A. H.-S. Ang and R. Vilaverde, Eds. New York: American Society of Civil Engineers, pp. 1632–1637.
Frangopol, D. M., and R. B. Corotis, Eds. (1990). System Reliability in Structural Analysis, Design and Optimization [Special Issue of Structural Safety (Journal). 7(2–4)].
Frangopol, D. M., and G. Fu (1989). Optimization of structural systems under reserve and residual reliability requirements. In: Reliability and Optimization of Structural Systems ’88 (Lecture Notes in Engineering, Vol. 48). P. Thoft-Christensen, Ed. Berlin, Germany: Springer-Verlag, pp. 135–145.
Frangopol, D. M., and G. fu (1990). Limit states reliability interaction in optimum design of structural systems. In: Structural Safety and Reliability, Vol. III. A. H.-S. Mg, M. Shinozuka, and G. I. Schuëller, Eds. New York: American Society of Civil Engineers, pp. 1879–1886.
Frangopol, D. M., and M. Iizuka (1991a). Multiobjective decision support spaces for optimum design of non-deterministic structural systems. In: Probabilistic Safety Assessment and Management, Vol. 2. G. Apostolakis, Ed. New York: Elsevier, pp. 977–982.
Frangopol, D. M., and M. Itzuxa (1991b). Pareto optimum solutions for nondeterministic systems. In: Proceedings of the 6th International Conference on Applications of Statistics and Probability in Civil Engineering (ICASP6), Vol. 1. L. Esteva and S. E. Ruis, Eds. pp. 216–223, Mexico City, Mexico.
Frangopol, D. M., and M. Iizutca (1992a). Structural system design under uncertainty via Pareto optimization. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 551–554.
Frangopol, D. M., and M. Iizuica (1992b). Probability-based structural system design using multicriteria optimization. In: Proceedings of the 4th AIAA/USAF/NASA/OAI Symposium on Multidisciplinary Analysis and Optimization. AIAA-92–4788-CP Paper, Part 2, pp. 794–798, Cleveland, Ohio.
Frangopol, D. M., and M. Klisinsxi (1992). Design for safety, serviceability and damage tolerability. In: Designing Concrete Structures for Serviceability and Safety. SP 133–12. E. G. Nawy and A. Scanlon, Eds. Detroit, Michigan: American Concrete Institute, pp. 225–254.
Frangopol, D. M., and F. Moses (1994). Reliability-based structural optimization In: Advances in Design Optimization. H. Adeli, Ed. London: Chapman and Hall (in press), pp. 492–570.
Frangopol, D. M., and R. Naxib (1990). Examples of system optimization and reliability in bridge design. In: Structural Safety and Reliability, Vol. II. A. H.-S. Mg, M. Shinozuka, and G. I. Schuëller, Eds. New York: American Society of Civil Engineers, pp. 871–878.
Frangopol, D. M., and J. Rondal (1976). Considerations on optimum combination of safety and economy. In: Final Report of the 10th Congress of the International Association for Bridge and Structural Engineering, Zurich, Switzerland: International Association for Bridge and Structural Engineering, pp. 45–48.
Frangopol, D. M., M. Klisinski, and M. Iizuica (1991). Computational experience with damage-tolerant optimization of structural systems. In: Proceedings of the 1st International Conference on Computational Stochastic Mechanics. P. D. Spanos and C. A. Brebbia, Eds. Southampton, England: Computational Mechanics Publications/London: Elsevier Applied Science, pp. 199–210.
Freudenthal, A. M. (1956). Safety and the probability of structural failure. Transactions. ASCE, 121:1337–1375.
Freudenthal, A. M., J. M. Garrelts, and M. Shinozuxa. (1966). The analysis of structural safety. Journal of the Structural Division, ASCE 92(1):267–325.
Fu, G., and D. M. Frangopol (1988). Reliability-Based Multiobjective Structural Optimization. Phase 2: Applications to Frame Systems. Structural Research Series, No. 88–01. Boulder, Colorado: Department of Civil Engineering, University of Colorado.
Fu, G., and D. M. Frangopol (1990a). Balancing weight, system reliability and redundancy in a multiobjective optimization framework. Structural Safety 7(2–4):165–175.
Fu, G., and D. M. Frangopol (1990b). Reliability-based vector optimization of structural systems. Journal of Structural Engineering, ASCE 116(8):2141–2161.
Furuta, H. (1980). Fundamental Study on Geometrical Configuration and Reliability of Framed Structures Used for Bridges. Ph.D. Thesis. Kyoto, Japan: Department of Civil Engineering, Kyoto University.
Gellalty, R. A., and R. H. Gallagher (1966). A procedure for automated minimum weight structural design. Part I-Theoretical bases, Part II-Applications. Aeronautics Quarterly 17(3):216–230 and 17(4):332–342.
Gill, P. E., W. Murray, and M. H. Wright (1981). Practical Optimization. New York: Academic Press.
Grierson, D. E. (1983). The intelligent use of structural analysis. Perspectives in Computing 3(4):32–39.
Grierson, D. E., and C. E. Cameron (1984). Computer Automated Synthesis of Building Frameworks. Paper No. 189. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.
Grimmelt, M., and G. I. Schuller (1982). Benchmark study on methods to determine collapse failure probabilities of redundant structures. Structural Safety 1(2):93–106.
Haftka, R. T., and M. P. Kamat (1985). Elements of Structural Optimization. Amsterdam: Martinius Nijhoff.
Hasofer, A. M., and N. C. Lind (1974). Exact and invariant second moment code format. Journal of the Engineering Mechanics Division, ASCE 100(1):111–121.
Haug, E. J., and J. S. Arora (1979). Applied Optimal Design: Mechanical and Structural Systems. New York: Wiley-Interscience.
Hendawi, S., and D. M. Frangopol (1993). Reliability-based optimization of composite-hybrid plate girders. In: Proceedings of the 6th International Conference on Structural Safety and Reliability. ICOSSAR ’83, Innsbruck, Austria. G. I. Schuëller, M. Shinozuka, J. T. P. Yao, and A. A. Balkema, Eds. (in press).
Hilton, H. H., and M. Feigen (1960). Minimum weight analysis based on structural reliability. Journal of the Aerospace Sciences 27:641–653.
Iizuka, M. (1991). Time Invariant and Time Variant Reliability Analysis and Optimization of Structural Systems. Ph.D. Thesis. Boulder, Colorado: Department of Civil Engineering, University of Colorado.
Ishikawa, N., and M. Itzuka (1987). Optimum reliability-based design of large framed structures. Engineering Optimization 10(4):245–261.
Johnson, A. I. (1953). Strength, Safety and Economical Dimensions of Structures. Stockholm, Sweden: Division of Building Statistics and Structural Engineering, Royal Institute of Technology.
Kalaba, R. E. (1962). Design of minimum weight structures given reliability and cost. Journal of the Aerospace Sciences 29:355–356.
Kim, S. H., and Y. K. Wen (1987). Reliability-Based Structural Optimization under Stochastic Time Varying Loads. Civil Engineering Studies, Structural Research Series No. 533. Urbana, Illinois: University of Illinois.
Kim, S. H., and Y. K. Wen (1990). Optimization of structures under stochastic loads. Structural Safety 7(2–4): 177–190.
Kirsch, U. (1981). Optimum Structural Design. New York: McGraw-Hill.
Koski, J. (1984). Multicriterion optimization in structural design. In: New Directions in Optimum Structural Design. E. Atrek, R. H. Gallagher, K. M. Ragsdell, and O. C. Zienkiewicz, Eds. Chichester, England: John Wiley & Sons, pp. 483–503.
Lee, Y.-H., S. Hendawi, and D. M. Frangopol (1993). RELTRAN: A Structural Reliability Analysis Program: Version 2.0. Report No. CU/SR-93/6. Boulder, Colorado: Department of Civil Engineering, University of Colorado.
Lev, O. E., Ed. (1981). Structural Optimization: Recent Developments and Applications. New York: American Society of Civil Engineers.
Levy, R., and O. Lev (1987). Recent developments in structural optimization. Journal of Structural Engineering, ASCE 113(9): 1939–1962.
Lind, N. C. (1971). Consistent partial safety factors. Journal of the Structural Division,ASCE 97(6):1651–1670.
Liu, Y, and F. Moses (1991). Bridge design with reserve and residual reliability constraints. Structural Safety 11(1):29–42.
Madsen, H. O., S. Krenk, and N. C. Lind (1986). Methods of Structural Safety. Englewood Cliffs, New Jersey: Prentice-Hall.
Mahadevan, S., and A. Haldar (1991). Reliability-based optimization using SFEM. In: Reliability and Optimization of Structural Systems ‘90 (Lecture Notes in Engineering, Vol. 61), A. Der Kiureghian and P. Thoft-Christensen, Eds. Berlin: Springer-Verlag, pp. 241–250.
Mau, S. T., and R. G. Sexsmith (1972). Minimum expected cost optimization. Journal of the Structural Division, ASCE 98(9):2043–2058.
Melchers, R. E. (1987). Structural Reliability Analysis and Prediction. Chichester, England. Ellis Horwood.
Moses, E (1969). Approaches to structural reliability and optimization. In: An Introduction to Structural Optimi-zation. M. Z. Cohn, Ed. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo, pp. 81–120.
Moses, F. (1973). Design for reliability-concepts and applications. In: Optimum Structural Design. R. H. Gallagher and O. C. Zienkiewicz, Eds. London: John Wiley & Sons, pp. 241–265.
Moses, F. (1974). Reliability of structural systems. Journal of the Structural Division, ASCE 100(9):1813–1820.
Moses, F. (1977). Structural system reliability and optimization Computers and Structures 7:283–290.
Moses, F. (1979). Sensitivity studies in structural reliability. In: Structural Reliability and Codified Design. Wa-terloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo, pp. 1–17.
Moses, F. (1982). System reliability developments in structural engineering. Structural Safety 1(1):3–13.
Moses, F., and D. E. Kinser (1967). Optimum structural design with failure probability constraints. AMA Journal 5(6):1152–1158.
Moses, F., and J. D. Stevenson (1970). Reliability-based structural design. Journal of the Structural Division, ASCE 96(2):221–244.
Mota Soares, C. A., Ed. (1987). Computer-aided optimal design: Structural and mechanical systems. In: Pro-ceedings of the NATO Advanced Study Institute. Series F, Vol. 27. New York: Springer-Verlag.
Murotsu, Y., and S. Shag (1990). Optimum shape design of truss structures based on reliability. Structural Optimization 2(2):65–76.
Murotsu, Y., M. Mita, and S. Shag (1992). Optimal configuration for fiber reinforced composites under uncer-tainties of material properties and loadings. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 547–550.
Nakib, R., and D. M. Frangopol (1990a). RSBA and RSBA-OPT: Two computer programs for structural system reliability analysis and optimization. Computers and Structures 36(1):13–27.
Nam, R., and D. M. Frangopol (1990b). Reliability-based structural optimization using interactive graphics. Computers and Structures 37(1):27–34.
Osyczka, A. (1984). Multicriterion Optimization in Engineering. Chichester, England- Ellis Horwood.
Paez, A., and E. Torroja (1959). La Determination del Coefficiente de Seguridad en las Distintas Obras. Madrid, Spain: Instituto Technic de la Construcion y del Cemento.
Parimi, S. R., and M. Z. Conty (1978). Optimum solutions in probabilistic structural design. Journal of Applied Mechanics 2(1):47–92.
Rackwitz, R., and R. Cuntze (1987). Formulations of reliability-oriented optimization Engineering Optimization 11(1,2):69–76.
Rackwitz, R., and P. Thoft-Christensen, Eds. (1992). Reliability and optimization of structural systems ’91. In: Proceedings of the 4th IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems. Lecture Notes in Engineering, Vol. 76. Berlin: Springer-Verlag.
Rao, S. S. (1984). Optimization: Theory and Applications, 2nd ed. New York: John Wiley & Sons.
Reklaitis, G. V., A. Ravindran, and K. M. Ragsdell (1983). Engineering Optimization. New York: WileyInterscience.
Rojiani, K. B., and G. L. Bailey (1984). Reliability-based optimum design of steel structures. In: New Directions in Optimum Structural Design. E. Atrek, et al., Eds. Chichester, England: John Wiley & Sons, pp. 332–57.
Rosenblueth, E. (1986). Optimum reliabilities and optimum design. Structural Safety 3(1):69–83.
Rosenblueth, E., and L. Esteva (1972). Reliability basis for some Mexican codes. In: Probabilistic Design of Reinforced Concrete Buildings. ACI Publication SP-31. Detroit, Michigan: American Concrete Institute, pp. 1–41.
Rosenblueth, E., and E. Mendoza (1971). Reliability optimization in isostatic structures. Journal of the Engineering Mechanics Division, ASCE 97(6):1625–1640.
Save, M., and W. Prager (1985). Structural Optimization-Optimality Criteria, Vol. 1. New York: Plenum.
Schmrr, L. A. (1960). Structural design by systematic synthesis. In: Proceedings of the 2nd ASCE Conference on Electronic Computation. pp. 105–122, Pittsburgh, Pennsylvania.
Schmit, L. A. (1984). Structural optimization-some key ideas and insights. In: New Directions in Optimum Structural Design. E. Atrek, et al., Eds. Chichester, England: John Wiley & Sons, pp. 1–45.
Sci-Imrr, L. A., and K. J. Cheng (1982). Optimum design sensitivity based on approximation concepts and dual methods. In: Proceedings of the 23rd AIAA/ASMEIASCE/AHS Structures, Structural Dynamics and Materials Conference. AIAA Paper No. 82–0713-CP, New Orleans, Louisiana.
Shag, S. (1991). Reliability-Based Shape Optimization of Structural and Material Systems. Ph.D. Thesis. Osaka, Japan: Division of Engineering, University of Osaka Prefecture.
Swnozuka, M. (1983). Basic analysis of structural safety. Journal of Structural Engineering, ASCE 109(3):721–740.
Sobieszczanski-Sobieski, J., J. E. Bartiielemy, and K. M. Riley (1982). Sensitivity of optimum solutions to problem parameters, AIAA Journal 20(9):1291–1299.
Soltani, M., and R. B. Corot’s (1988). Failure cost design of structural systems. Structural Safety 5:238–252.
Sørensen, J. D. (1986). Reliability-Based Optimization of Structural Elements. Structural Reliability Theory Paper No. 18. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.
Sørensen, J. D. (1987). Reliability-Based Optimization of Structural Systems. Structural Reliability Theory Paper No. 32. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.
Sørensen, J. D. (1988). Optimal Design with Reliability Constraints. Structural Reliability Theory Paper No. 45. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.
Sørensen, J. D., and I. Enevoldsen (1989). Sensitivity Analysis in Reliability-Based Shape Optimization. Structural Reliability Theory Paper No. 69. Aalborg, Denmark. Institute of Building Technology and Structural Engineering, Aalborg University.
Sørensen, J. D., and P. Thoft-Christensen (1987). Integrated Reliability-Based Optimal Design of Structures. Structural Reliability Theory Paper No. 29. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.
Spillers, W. R. (1975). Iterative Structural Design. Amsterdam: North-Holland.
Surahman, A., and K. B. Rojiiani (1983). Reliability-based optimum design of concrete frames. Journal of Structural Engineering, ASCE 109(3):741–757.
Swrrzky, H. (1964) Minimum weight design with structural reliability. In: Proceedings of the 5th AIAA Annual Structures and Materials Conference, Palm Springs, California, pp. 316–322.
Tao, Z., J. H. Ellis, and R. B. Corons (1992). Markov decision processes in structural optimization. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 539–542.
Templeman, A. B. (1983). Optimization methods in structural design practice. Journal of Structural Engineering, ASCE 109(12):2420–2433.
Thoft-Christensen, P., Ed. (1987a). Reliability and optimization of structural systems. In: Proceedings of the 1st IFIP W7.5 Working Conference on Reliability and Optimization of Structural Systems. Lecture Notes in Engineering, Vol. 33. Berlin: Springer-Verlag.
Thoft-Christensen, P. (1987b). Application of Optimization Methods in Structural Systems Reliability Theory. Structural Reliability Theory Paper No. 33. Aalborg, Denmark: Institute of Building Technology and Structural Engineering, Aalborg University.
Thoft-Christensen, P., Ed. (1989). Reliability and optimization of structural systems ‘88. In: Proceedings of the 2nd IFIP WG 7.5 Conference on Reliability and Optimization of Structural Systems. Lecture Notes in Engineering, Vol. 48. Berlin: Springer-Verlag.
Thoft-Christensen, P. (1991). On reliability-based structural optimization. In: Reliability and Optimization of Structural Systems ‘80 (Lecture Notes in Engineering, Vol. 61), A. Der Kiureghian and P. Thoft-Christensen, Eds. Berlin: Springer-Verlag, pp. 387–402.
Thoft-Christensen, P. (1992). Risk-based structural optimization. In: Probabilistic Mechanics and Structural and Geotechnical Reliability. Y. K. Lin, Ed. New York: American Society of Civil Engineers, pp. 535–538.
Thoft-Christensen, P., and M. J. Baker (1982). Structural Reliability Theory and Its Applications. Berlin: Springer-Verlag.
Thoft-Christensen, P., and Y Murotsu (1986). Applications of Structural Systems Reliability Theory. Berlin: Springer-Verlag.
Thoft-Christensen, P., and J. D. Sorensen (1987). Optimal strategy for inspection and repair of structural systems. Civil Engineering Systems 4:94–100.
Turkstra, C. J. (1970). Theory of Structural Design Decisions. SM Study No. 2. N. C. Lind, Ed. Waterloo, Ontario, Canada: Solid Mechanics Division, University of Waterloo.
Vanderplaats, G. N. (1982). Structural optimization: Past, present, and future. AIAA Journal 20:992–1000.
Vanderplaats, G. N. (1984a). Numerical Optimization Techniques for Engineering Design. New York: McGraw-Hill.
Vanderplaats, G. N. (1984b). Efficient calculation of optimum design sensitivity. In: Proceedings of the 25th AIAAIASME/ASCE/AHS Structures, Structural Dynamics and Materials Conference, Palm Springs, California. AIAA Paper No. 84–0855-CP, 1. pp. 34–40.
Vanderplaats, G. N. (1986). ADS-a Fortran Program for Automated Design Synthesis: Version 1:10. Santa Barbara, California: Engineering Design Optimization.
Vanmarcke, E. (1971). Matrix formulation of reliability analysis and reliability-based design. Computers and Structures 3:757–770.
Vanmarcke, E. (1984). Random Fields: Analysis and Synthesis. Cambridge, Massachusetts: MIT Press.
Yao, J. T. P. (1985). Safety and Reliability of Existing Structures. Boston: Pitman.
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Frangopol, D.M. (1995). Reliability-Based Optimum Structural Design. In: Sundararajan, C. (eds) Probabilistic Structural Mechanics Handbook. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1771-9_16
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DOI: https://doi.org/10.1007/978-1-4615-1771-9_16
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