Efficient Algorithm for Stochastic Structural Optimization
Publication: Journal of Structural Engineering
Volume 115, Issue 7
Abstract
A stochastic structural optimization procedure using element‐level reliabilities as constraints is proposed here. The procedure is robust and efficient and closely resembles the practical approach used in design offices. The procedure is developed in modules which can be linked and unlinked. Element‐level reliabilities are estimated using the stochastic finite element method or Monte Carlo simulation with variance reduction techniques whenever necessary. The method can consider different limit states with different desired levels of reliability as well as the system reliability as constraints, resulting in a balanced distribution of weight. A constrained optimization algorithm is used which is tailored to the information and the requirements of the structural optimization problem considered here. The algorithm contains a simple and efficient search procedure that uses variable, discrete step sizes. Several alternatives for reliability analysis and trial structure selection, and strategies for reduction of the number of constraints are included and explained with the help of numerical examples to show the desirability of the proposed method.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Ayyub, B. M., and Haldar, A. (1984). “Practical structural reliability techniques.” J. Struct. Engrg., ASCE, 110(8), 1707–1724.
2.
Bazaraa, M. S., and Shetty, C. M. (1979). Nonlinear programming: theory and algorithms. John Wiley & Sons, Inc., New York, N.Y.
3.
Bjorhovde, R., Galambos, T. V., and Ravindra, M. K. (1978). “LRFD criteria for steel beam‐columns.” J. Struct. Div., ASCE, 104(9), 1371–1388.
4.
Burnside, O. H. (1985). “Probabilistic structural analysis for space propulsion system components.” Advances in Aerospace Structural Analysis, O. H. Burnside and C. H. Parr, eds., Am. Soc. Mech. Engrs., New York, N.Y., 75–85.
5.
Chen, X., and Lind, N. C. (1983). “Fast probability integration by three parameter normal tail approximation.” Struct. Safety, 1(4), 269–276.
6.
Der Kiureghian, A., and Ke, J.‐B. (1985). “Finite‐element based reliability analysis of frame structures.” Proc. 4th Int. Conf. on Struct. Safety and Reliability, Int. Assoc. Struct. Safety and Reliability, 1, 395–404.
7.
Feng, Y. S., and Moses, F. (1986). “A method of structural optimization based on structural system reliability.” J. Struct. Mech., 14(4), 437–453.
8.
Frangopol, D. M. (1985a). “Sensitivity of reliability‐based optimum design.” J. Struct. Engrg., ASCE, 111(8), 1703–1721.
9.
Frangopol, D. M. (1985b). “Structural optimization using reliability concepts.” J. Struct. Engrg., ASCE, 111(11), 2288–2301.
10.
Frangopol, D. M. (1986). “Computer‐automated sensitivity analysis in reliabilitybased plastic design.” Comput. and Struct., 22(1), 63–75.
11.
Haldar, A., and Mahadevan, S. (1987). “A design‐oriented stochastic finite element method.” Proc. 9th. Int. Conf. on Struct. Mech. in Reactor Tech., Int. Assoc. Struct. in Reactor Technology, 17, 307–312.
12.
Handa, K., and Anderson, K. (1981). “Application of finite element methods in the statistical analysis of structures.” Proc. 3rd Int. Conf. on Struct. Safety and Reliability, Int. Assoc. Struct. Safety and Reliability, 409–417.
13.
Hisada, T., and Nakagiri, S. (1985). “Role of the stochastic finite element method in structural safety and reliability.” Proc. 4th Int. Conf. on Struct. Safety and Reliability, Int. Assoc. Struct. Safety and Reliability, 1, 385–394.
14.
Ishikawa, N., and Iizuka, M. (1987). “Optimum reliability‐based design of large framed structures.” Engrg. Optim., 10(4), 245–261.
15.
Lev, O. E. (1981). Structural optimization: recent developments and applications. ASCE, New York, N.Y.
16.
Levy, R., and Lev, O. E. (1987). “Recent developments in structural optimization.” J. Struct. Engrg., ASCE, 113(9), 1939–1962.
17.
Liu, P.‐L., and Der Kiureghian, A. (1986). “Optimization algorithms for structural reliability analysis.” Report UCB/SESM‐86/09, Dept. of Civ. Engrg., Univ. of California, Berkeley, Calif.
18.
Liu, W.‐K., Belytschko, T., and Mani, A. (1985). “Probabilistic finite elements for transient analysis in non‐linear continua.” Advances in Aerospace Structural Analysis, O. H. Burnside and C. H. Parr, eds., Am. Soc. Mech. Engrs., New York, N.Y., 9–24.
19.
Manual of steel construction: load and resistance factor design. (1986). Chicago, Ill.
20.
Mau, S.‐T., and Sexsmith, R. G. (1972). “Minimum expected cost optimization.” J. Struct. Div., ASCE, 98(9), 2043–2058.
21.
Moses, F. (1977). “Structural system reliability and optimization.” Comp. and Struct., 7(2), 283–290.
22.
Moses, F., and Kinser, D. E. (1967). “Optimum structural design with failure probability constraints.” AIAA J., 5(6), 1152–1158.
23.
Moses, F., and Stevenson, J. D. (1970). “Reliability‐based structural design.” J. Struct. Div., ASCE, 96(2), 221–244.
24.
Rackwitz, R., and Fiessler, B. (1978). “Structural reliability under combined random load sequences.” Comp. and Struct., 9(5), 489–494.
25.
Rojiani, K. B., and Bailey, G. L. (1984). New directions in optimum structural design, E. Atrek, et al., eds., John Wiley & Sons, Inc., New York, N.Y., 443–457.
26.
Rosenbleuth, E., and Mendoza, E. (1971). “Reliability optimization in isostatic structures.” J. Engrg. Mech. Div., ASCE, 97(6), 1625–1642.
27.
Schmit, L. A. (1981). “Structural synthesis—its genesis and development.” AIAA J., 19(10), 1249–1263.
28.
Turkstra, C. J. (1967). “Choice of failure probabilities.” J. Struct. Div., ASCE, 93(6), 189–200.
29.
Wu, Y.‐T. (1984). “Efficient methods for mechanical and structural reliability analysis and design,” thesis presented to University of Arizona, at Tucson, Ariz., in partial fulfillment of the requirements for the degree of Doctor of Philosophy.
Information & Authors
Information
Published In
Journal of Structural Engineering
Volume 115 • Issue 7 • July 1989
Pages: 1579 - 1598
Copyright
Copyright © 1989 ASCE.
History
Published online: Jul 1, 1989
Published in print: Jul 1989
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.