Engineering Transactions, 33, 3, pp. 311-322, 1985

On Reliability Analysis and Optimisation of Plastic Plane Frames

K.A. Sikorski
Institute of Fundamental Technological Research, Warszawa

A. Borkowski
Institute of Fundamental Technological Research, Warszawa

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.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).


A. M. FREUDENTHAL, J. M. GARRELTS, M. SHINOZUKA, The analysis of structural safety, J. Struc. Div. ASCE, ST1, 92, 267-325, 1966.

C. A CORNELL, Bounds on the reliability of structural systems, J. Struc. Div. ASCE, ST1, 93, 111-200, 1967.

J. STEVENSIN, F. MOSES, Reliability of frame stiucture, J. Struc. Div. ASCE, 96, 2409-2427, 1970.

J. W. DAVIDSON, L. P. FELTON, G. C. HART, Optimum design of structures with random parameters, Computers and Structures, 7, 3, 481-486, t-977.

S. MAU, R. G. SEXMITH, Minimum expected cost optimization, J. Struc. Div. ASCE, 10, 4, 551-553. 1972.

F. MOSES, Structural system reliability and optimization, Computer and Structures, 7, 2, 283-290, 1977.

D. FRANGOPOL, J. RONDAL, Optimum probability-based design of plastic structures, Eng. Opt., 3, I, 17-25, 1977.

O. DITLEVSEN, Narrow reliability of structural systems, 1. Struc. Mech., 7, 4, 453-472, 1979.

E. H. VANMARKE, Matrix formulation of reliability analysis and reliability-based design, Computer and Structures, 3, 4, 757-770, 1971.

O. KLINGMULLER, Andwendung der Traglastberechnung fur die Beurteilung der Sicherheit von Kostruktionen, Forchungs-berichte aus dem Fachbereich Bauwesen, Gesamthochschule, Essen. 9. 1979.

M. J. GRIMMELT, G. I. SCHUKLER, Benchmark study on methods to determine collapse failure probabilities of redundant structures, Structural Safety, 1, 2, 93-106, 1983.

A. CHARNES, W. W. COOPER, Chance constrained programming, Management Science, 6, 73-79, 1959.

B. B. KOJlliliH, CmoxacmU

P. KALL, Stochastic linear programming, Springer-Verlag, Berlin, Heidelberg 1976.

S. S. RAO. Optimization theory and applications. Wiley Eastern Limited, New Debli 1978.

R. WETS, Stochastic programming, in: Solution techniques and approximation schemes. Mathematical programming the state of the art, A.: Bachen, M. Grotschel, B. Korte, Springer-Verlag, Bonn 1982.

PN-8V/B-U32UU Konstrukcje stalowe. Obliczenia statyczne i projektowanie, PKNMiJ, War­szawa 1980.

C. GAVARINI, Fundamental plastic analysis theorems and duality in linear programming, Ingeneria Civile, 18, 1966.

А. А. ЧиРлс, Методы линейного программирования при расчете упруго-пластических систем, Стройиздат, Ленинград 1969.

O. DITLEVSEN, P. BJERAGER, Reliability of highly redundant plastic structures, DCAMM, 263, 1983.