Reliability Analysis of Elasto-Plastic Structures

This paper only deals with framed and trussed structures which can be modelled as systems with ductile elements. The elements are all assumed to be linear-elastic perfectly plastic. The loading is assumed to be concentrated and time-independent. The strength of the elements and the loads are modelled by normally distributed stochastic variables. This last assumption is not essential, since non-normally distributed variables can be approximated by equivalent normally distributed variables by well-known methods. All geometrical dimensions and stiffness quantities are assumed to be deterministic. Failure of this type of system is defined either as formation of a mechanism or by failure of a prescribed number of elements. In the first case failure is independent of the order in which the elements fail, but this is not so by the second definition. The reliability analysis consists of two parts. In the first part significant failure modes are determined. Nonsignificant failure modes are those that only contribute negligibly to the failure probability of the structure. Significant failure modes are determined by the (l-unzipping method by Thoft-Christensen [1]. Two different formulations of this method are described and the two definitions of failure can be used by the first formulation, but only the failure definition based on formation of a mechanism by the second formulation. The second part of the reliability analysis is an estimate of the failure probability for the structure on the basis of the significant failure modes. The significant failure modes are as usual modelled as elements in a series system (see e.g. Thoft-Christensen & Baker [2)). Several methods to perform this estimate are presented including upper- and lower-bound estimates. Upper bounds for the failure probability estimate are obtained if the failure mechanisms are used. Lower bounds can be calculated on the basis of series systems where the elements are the non-failed elements in a non-failed structure (see Augusti & Baratta [3]).