RELIABILITY ANALYSIS OF SERIES STRUCTURAL SYSTEMS (PROBABILITY, DESIGN, FATIGUE).

Abstract

Reliability analysis of series structural systems with emphasis on problems typical for metal fatigue is addressed. Specific goals include the following: (1) Given the distribution of strength of the components and the distribution of external loads on the system what is the probability of failure of the system? (2) Given the target safety index for the system, what would be the target safety index for the components? Exact solutions in the analysis of series structural systems only exists for some special problems. Some of these special problems are investigated. In particular some special cases of the problem of unequal element reliabilities are considered and some interesting observations are made. Numerical integration is in general required even when an exact solution exists. A correction or adjustment factor is developed for an important class of problems. This factor makes it possible to relate element and system probabilities of failure without numerical integration. However in most cases no exact solution to the structural series system problem exists. Approximations by for instance bounds on the probability of failure or Monte Carlo simulation has been the only way of approximating solutions. These two methods are generally not good approximation schemes since they are either too crude or too expensive. In this dissertation an approximation scheme for analysis of series systems where no exact solution exists is developed. The method only requires a simple numerical integration if the component safety index and the correlation coefficient between failure modes is known. Numerous examples are used to verify the method against known exact results and excellent estimates are obtained. Applications by practical examples is also given. In the appendix the problem of convergence of fatigue life distribution is also summarized.