Abstract
Probabilistic modeling of the failure process of a structural multi-element system with brittle behavior of the elements is much more difficult as compared with rigid-ideal-plastic structures. The basic reason for this is the redistribution of action effects and possible influence of the load-path history on the sequence of failures of individual elements, which strengths are considered as random variables. In the paper, a certain concept of systems with no-unloading is applied in a self-consistent way for probabilistic study of such systems. It is proved for the system with no-unloading that, within the well-defined assumptions on the action effects rule, the probability of system failure under a given action can be calculated via a fit-for-purpose analytical formula. For systems allowing unloading, a set of the so-called majorant action effects is introduced, which makes it possible to find an effective upper bound for the failure probability of the system with unloading.
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