On Reliability Analysis and Optimisation of Plastic Plane Frames - Sikorski, K.A.; Borkowski, A. (Engineering Transactions, 1985)
The paper deals with a static approach to the probabilistic analysis and optimization of structures. A rigid-perfectly-plastic material is assumed and the two types of problems are discussed. The first one corresponds to the so-called chance constrained approach in the theory of stochastic programming. It allows either to evaluate the ultimate load factor or to find the optimum distribution of plastic moduli under the prescribed probability that the stress state remains statically admissible. The second approach gives the lower bound on the reliability index of a structure taking into account possible correlation between stochastic parameters (resistances or loads). In a discrete model of a structure all the cases considered turn out to be reducible to appropriate deterministic linear or nonlinear mathematical programming problems. Several examples of the analysis and optimization of framed structures illustrate the proposed procedure.