Reliability of Parallel Systems under Imposed Uniform Strain
Publication: Journal of Engineering Mechanics
Volume 109, Issue 3
Abstract
An imposed strain approach is used for the reliability analysis of brittle parallel systems with arbitrary stress‐strain behavior of its components. It leads to a formal description of the failure event as a parallel system. The failure probability of the strongest component overestimates the system failure probability, so that the consideration of the other components can be recommended for which first‐order reliability techniques supply an efficient tool. Numerical comparisons with certain special exact results show that the correlation structure is taken fairly well into account by this first‐order method. Essential improvements result from better estimates of the component reliability. This induces the definition of so called equivalent components, which might also be useful for the evaluation of more general systems. The accuracy of the method appears sufficient for many engineering applications.
Get full access to this article
View all available purchase options and get full access to this article.
References
1.
Barbour, A. D., “Brownian Motion and a Sharply Curved Boundary,” Advances in Applied Probability, Vol. 13, No. 4, 1981, pp. 736–750.
2.
Barlow, R. E., and Proschan, F., Statistical Theory of Reliability and Life Testing, Holt, Reinhart, and Winston, New York, N.Y., 1975.
3.
Breitung, K., “An Asymptotic Formula for the Failure Probability,” Proceedings of the Euromech 155, DIALOG No. 82/6, Danish Engineering Academy, Lyngby, Denmark, 1982, pp. 183–201.
4.
Cornell, A. C., “Bounds on the Reliability of Structural Systems,” Journal of the Structural Division, ASCE, Vol. 93, No. ST1, Jan., 1967, pp. 171–200.
5.
Daniels, H. E., “The Maximum Size of a Closed Epidemic,” Advances in Applied Probability, Vol. 6, 1974, pp. 607–1621.
6.
Daniels, H. E., “The Statistical Theory of the Strength of Bundles of Threads, Part I,” Proceedings of the Royal Society, A 183, London, England, 1945, pp. 405–435.
7.
Ditlevsen, O., “Generalized Second Moment Reliability Index,” Journal of Structural Mechanics, Vol. 7, No. 4, 1979, pp. 435–451.
8.
Ditlevsen, O., “Narrow Reliability Bounds for Structural Systems,” Journal of Structural Mechanics, Vol. 7, No. 4, 1979, pp. 453–472.
9.
Fieβler, B., Neu'mann, H., and Rackwitz, R., “Quadratic Limit States in Structural Reliability,” Journal of the Engineering Mechanics Division, ASCE, Vol. 105, No. EM4, Aug., 1979, pp. 159–164.
10.
Harlow, D. G., and Phoenix, S. L., “Probability Distributions for the Strength of Composite Materials I: Two‐Level Bounds,” International Journal of Fracture, Vol. 17, No. 4, 1981, pp. 347–371.
11.
Hohenbichler, M., “Approximate Evaluation of the Multinormal Distribution Function,” Berichte zur Zuverlässigkeitstheorie der Bauwerke, SFB 96 der Technischen Universität Munchen, Heft 58, 1981.
12.
Hohenbichler, M., and Rackwitz, R., “Non‐Normal Dependent Vectors in Structural Safety,” Journal of the Engineering Mechanics Division, ASCE, Vol. 107, No. EM6, Dec., 1981, pp. 1227–1238.
13.
Hohenbichler, M., and Rackwitz, R., “On Structural Reliability of Brittle Parallel Systems,” Reliability Engineering, No. 2, 1981, pp. 1–6.
14.
Hohenbichler, M., Gollwitzer, S., and Rackwitz, R., “Parallel Structural Systems with Non‐Linear Stress‐Strain Behaviour,” Berichte zur Zuverlässigkeitstheorie der Bauwerke, SFB 96 der Technischen Universität München, Heft 58, 1981, pp. 23–54.
15.
Kersken‐Bradley, M., “Beanspruchbarkeit von Bauteilquerschnitten bei streuenden Kenngröβen des Kraft‐Verformungs‐Verhaltens innerhalb des Querschnitts,” Berichte zur Zuverlässigkeitstheorie der Bauwerke, SFB 96 der Technischen Universität München, Heft 56, 1981.
16.
McCartney, L. N., and Smith, R. L., “Statistical Theory of the Strength of Fibre Bundles,” Department of Mathematics, Imperial College of Science and Technology, London, Nov., 1981.
17.
Phoenix, S. L., “The Asymptotic Distribution for the Time to Failure of a Fibre Bundle,” Adv. Appl. Prob., Vol. 11, 1979, pp. 153–187.
18.
Phoenix, S. L., and Taylor, H. M., “The Asymptotic Strength Distribution of a General Fibre Bundle,” Advances in Applied Probability, Vol. 5, 1973, pp. 200–216.
19.
Rackwitz, R., “Close Bounds for the Reliability of Structural Systems,” Berichte zur Zuverlässigkeitstheorie der Bauwerke, SFB 96, der Technischen Universität München, Heft 29, 1978.
20.
Rackwitz, R., and Hohenbichler, M., “An Order‐Statistics Approach to Brittle Parallel Systems,” Berichte zur Zuverlässigkeitstheorie der Bauwerke, SFB 96, der Technischen Universität München, Heft 58, 1981.
21.
Rackwitz, R., and Krzykacz, B., “Structural Reliability of Reactor Systems,” Probabilistic Analysis of Nuclear Reactor Safety, Vol. 3, Topical Meeting, May, 1978, Los Angeles, Calif., pp. X8–X11.
22.
Rackwitz, R., and Pientinger, B., “General Structural Reliability,” Proceedings of CEB‐Commission II‐Meeting Pavia, Oct., 1981, CEB‐Bulletin, No. 153, Paris, 1982.
23.
Sen, P. K., and Bhattacharyya, B. B., “Asymptotic Normality of the Extre‐mum of Certain Sample Functions,” Zeitschrift f. Wahrscheinlichkeitstheorie verw., Gebiete, Vol. 34, 1976, pp. 113–118.
Information & Authors
Information
Published In
Copyright
Copyright © 1983 ASCE.
History
Published online: Aug 1, 1983
Published in print: Aug 1983
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.