Reliability of Highly Redundant Plastic Structures

Abstract

Reliability analysis of highly redundant ideal‐plastic structures is difficult due to the existence of a very large number of possible failure modes. If only some of the failure modes are identified and included in the reliability calculation, the result will be an overestimation of the reliability. However, the lower bound theorem of plasticity theory allows for a calculation that underestimates the reliability. This theorem is applied to construct lower bounds that are optimized in a certain sense. Only a suboptimization is practicable. Therefore the resulting lower bounds are not particularly close to the exact reliability. However, some theorems originating from the lower bound optimization analysis turn out to be useful for defining a strategy of search for the most important collapse mechanisms of certain general types of models of plastic frame and truss structures. The total reliability can only be calculated up to upper and lower bounds, but examples show that the upper bound defined by the identified mechanisms is close to the mathematically exact reliability.