Sikorski, K. A.; Borkowski, A. On reliability analysis and optimization of plastic plane frames. (English) Zbl 0573.73099 Rozpr. Inż. 33, 311-322 (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 reduceable to appropriate deterministic linear or nonlinear mathematical programming problems. Several examples of the analysis and optimization of framed structures illustrate the proposed procedure. MSC: 74P99 Optimization problems in solid mechanics 90C90 Applications of mathematical programming Keywords:reliability; plastic plane frames; small displacements; quasi-static proportional loading; normal distribution; static approach; probabilistic analysis; rigid-perfectly-plastic material; chance constrained approach; stochastic programming; ultimate load factor; optimum distribution of plastic moduli; stress state remains statically admissible; lower bound on the reliability index; correlation between stochastic parameters; resistances; loads; discrete model; reduceable to appropriate deterministic linear or nonlinear mathematical programming problems; framed structures PDFBibTeX XMLCite \textit{K. A. Sikorski} and \textit{A. Borkowski}, Rozpr. Inż. 33, 311--322 (1985; Zbl 0573.73099)