Engineering Transactions, 32, 1, pp. 57-74, 1984

Probabilistic Approach to Reliability-Based Optimum Structural Design

A. Brandt
Institute of Fundamental Technological Research, Warszawa
Poland

S. Jendo
Institute of Fundamental Technological Research, Warszawa
Poland

W. Marks
Institute of Fundamental Technological Research, Warszawa
Poland

In the paper foundations are given for the design of structures and structural optimization, based on the theory of probability. In this approach, loads, dimensions and material properties are considered as random values. The safety of the structure should be assured and the constraints should be satisfied with acceptable probabilities. A programming method is proposed with random constraints to reduce the probabilistic optimization problem to a deterministic one. The theoretical considerations are applied to an example in which optima! dimensions of a frame box beam are determined.
Full Text: PDF
Copyright © Polish Academy of Sciences & Institute of Fundamental Technological Research (IPPT PAN).

References

A. M. BRANDT, W. DZIENISZEWSKI, S. JENDO, W. MARKS, S. OWCZAREK and Z. WASIUTYŃSKI, Criteria and methods of optimization in structural design, PWN, Warszawa 1977 [in Polish], or English edition, PWN+M: NIJHOFF, 1984.

K. V. BURY, Reliability-constrained optimum static design for random load sequences, Engng. Opt., 3, 215-220, 1978.

D. G. CARMICHAEL, Probabilistic design of structures in state equation form, Engng. Opt., 3, 83-92, 1978.

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

J. W. DAVIDSON, L. P. PELTON and G. C. HART, Optimum design of structures with random parameters, Computers and Structures, 7, 3, 481-486, 1977.

J. W. DAVIDSON, L. P. PELTON and G. C. HART, Reliability-based optimization for dynamic loads, J. Struct. Div. ASCE Proc., 103 ST 10, 2021-2035, 1977.

C. EIMER, Foundations of the theory of safety of structures, Rozpr. Inżyn., 11, 1, 53-135, 1963 [in Polish].

D. FRANGOPOL, J. RONDAL, Optimum probability-based design of plastic structures, Engng. Opl., 3, 17-25, 1977.

A. M. FREUDENTHAL, The safety of structures, Proc. ASCE, Struct. Div., 71, 1945.

A. M. FREUDENTHAL, Safety and the probability of structural failure, Proc. ASCB, J. Struct. Div., 80, 1954.

A. M. FREUDENTHAL, Critical appraisal of safety criteria and their basis concepts, IABSE, New York, 13-25, 1968.

E. B. HAUGBN, Probabilistic approaches to design, Wiley, London 1968.

H. H. HILTON, M. FEIGEN, Minimum weight analysis based on structural reliability, J. Aerospaces, 27, 9, 641-652, 1960.

S. JENDO, W. MARKS, Stochastic programming in optimum structural design, Proc. of the PAS Conf. on Criteria and Methods of Optimization in Structural Design, Ossolineum, 1980 [in Polish].

S. JENDO, W. MARKS, Nonlinear stochastic programming in optimum structural design, Proc. of the Euromech Colloquium 164, 6, Siegen 1982.

A. J. JOHNSON, Strength, safety and economical-dimensions of structures, Bull. Div. Struct. Eng., Royal Inst. Techn., Stockholm 12, 1953.

R. KALABA, Design of minimal-weight structures for given reliability and cost, J. Aerospace Sciences, 29, 3, 355-356, 1962.

N. A. KHACHATURIAN, Basic concepts in structural optimization, in: Introduction to Structural Optimization, ed. by M. Z. COHN, Study No. 1, Solid Mechanics Division, University of Waterloo Press, 1-18, 1969.

N. A. KHACHATURIAN, G. S. HAIDER, Probabilistic design of determinate structures, Proc. Spec. Conf. ASCE, 623-641, New York 1966.

N. C. LIND, The relation of data to calculated failure probabilities, 8th Congress IABSE, New York 1968.

N. C. LIND, Deterministic formats for the probabilistic design of structures, Study No. 1 Solid Mechanics Division, University Waterloo; Canada 1969.

S. MAU, R. G. SEXMITH, Minimum expected cost optimization, Proc. of ASCE, ST 9, 2043-2057, 1972.

F. MOSES, Approaches to structural reliability and optimization, in: An Introduction to Structural Optimization, ed. by M. Z. COHN, Study No. 1, Solid Mechanics Division, University of Waterloo Press, 81-120, 1969.

F. MOSES, Design for reliability - concepts and applications, in: Optimum Structural Design,ed. by GALLAGHER and ZIENKIEWICZ, Wiley, New York 1973.

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

F. MOSES, D. E. KINSER, Optimum structural design with failure probability constraints, AIAA Journal, 6, 6, 1152-1158, 1967.

J. MURZEWSKI, Safety of building structures, Arkady, Warszawa 1970 [in Polish].

S. NARAYANAN, K. C. NIGAM, Optimum structural, design in random vibration environments, Engng. Opt., 3, 97-108, 1978.

N. C. NIGAM, Structural optimization in random vibration environment, AIAA Journal, 10, 4, 551-553, 1972.

S. R.PARIMI, M. Z. COHN, Optimal criteria in probabilistic structural design, Proc. of IUTAM Symposium on Optimization in Structural Design, ed. by Z. MRÓZ and A. SAWCZUK, Springer­Verlag, Berlin 1975.

M. PROT, La securite, Ann. des Pont et Chaussees, 1, 1941.

M. PROT, La determination rationnelle et le controle des coefficients de securite, Travaux, 222, 1953.

S. S. RAO, Optimization, theory and applications, Wiley Bastern Ltd, New Delhi 1978.

E. ROSENBLUETH, B. MENDOZA, Reliability optimization in isostatic structures, Proc. of ASCE, EM 6, 1625-1642, 1971.

A. R. RZHANICYN, On the problem of the verification of the structural safety, SCIPS, Gosstroizdat, Moscow 1952 [in Russian].

A. R. RZHANICYN, Determination of the safety characteristics and of the safety coefficients from the economical reasons, CNIISK Reports, 4, Gosstroizdat, Moscow 1961 [in Russian].

N. SHIRAISHI, H. FURUTA, Safety analysis and minimum- weight design of rigid frames based on reliability concept, Mem. of Poe. of Engng. Kyoto Univ., 41, part 4, 474-497, 1979.

J. D. STEVENSON, Reliability analysis and optimum design of structural systems with applications to rigid frames, Solid Mechanics, Struct. and Mech. Design Div. Rep. No 14, Case Western Univ., Nov. 1967.

N. S. STReLECKI, On the problem of the general safety coefficient, Projekt i Standart, 10, 1935 [in Russian].

H. SWITZKY, Minimum weight design with structural reliability, AIAA 5th Annual Struct. and Mat. Conf. 316-322, 1964.

C. J. TURKSTRA, A formulation of structural design decisions, Dissertation, Waterloo University 1962.

W. WIERZBICKI, Structural safety as a probability problem, Przegl. Techn. 690, 1936 [in Polish].

W. WIERZBICKI, Working stress as that corresponding to the optimum Conditions of safety and economy, Bull. Acad. Pol. Sci., serie Sci. techn., 5, 5, 1957.

Comite Europeen du Beton et Federation Internationale de la Precontrainte - Recommandations Internationales pour Ie calcul et l'execution des ouvrages en beton, VI-eme Congres de la FIP, Juin 1970, Prague.

Common unified rules for different types of construction and material, CBB Bulletin d'Information, No 124/125, Paris 1978.