Reliability analysis of rigid-plastic structures by the static approach

Abstract

Despite the inherent advantage of providing an upper bound on the system failure probability, P f , methods for the reliability analysis of rigid-plastic structures based on the static theorem of plastic analysis have received very limited attention compared to those using kinematic theorems. The static approach is studied from different viewpoints in this paper, with particular attention given to its relationship to the kinematic approach. A search strategy based on mathematical programming is developed to minimize the upper bound for P f . Many properties of this bound observed from numerical examples are readily explained in the basic variable space and the redundant force space. Guidelines for selecting the best set of redundant forces and the best starting points for searching are proposed. Of special interest are the equivalence of redundant force sets, and the use of multiple redundant sets.