Abstract
The purpose of this work is to present a simple, practical and automatic procedure for the rigid-plastic analysis and design of frame structures under both proportional and repeated loadings. The applicability of linear programming techniques to this kind of problem was pointed out some twenty years ago. The principle of the method is widely exposed in the literature1–17. In this paper we restrict ourselves to some particular aspects of the automatic calculations and practical implementations. These are:
-
1)
the efficient choice between the statical and kinematical formulations leading to a minimum number of variables. This affects considerably the size of the problem:
-
2)
the automatic construction of the characteristic matrices, mainly the independent equilibrium-compatibility matrix;
-
3)
the direct calculations of dual variables which allows the necessary results to be obtained by a simple procedure;
-
4)
the realistic verifications of the stability conditions imposed by European norms for steel structures.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Ch. Massonnet and M. Save, Calcul plastique des constructions. Vol. 1 Structures dépendent dun paramètre. Sème édition, Nélissen B., Liége. (1976).
B. G. Neal, The Plastic Methods of Structural Analysis. Chapman and Hall, London, (1956).
P. G. Hodge, Jr.. Plastic Analysis of Structures. McGraw-Hill, (1959).
D. B. Martin: Plasticity, Fundamentals and General Results. MIT Press, Cambridge, Massachusetts. Londres, 1975.
K. I. Majid, Non-linear Structures. Butterworths, London, (1978).
M. Z. Cohn. S. K. Ghosh. and S. R. Parimi. “A Unified Approach to Theory of Plastic Structures.” Solid Mech. Division, University of Waterloo, Canada, Report nr 26, June (1973).
A. Charles, C. E. Lemke, and O. C. Zienkiewicz, “Virtual work. Linear Programming and Plastic Limit Analysis,” Proc. Royal Soc. A, 251, (1959).
W. S. Dorn, “On the Plastic Collapse of Structures and Linear Programming,” Ph.D. Thesis, Dept. of Mathematics, Carnegie Institute of Techn. Pittsburgh, Pa. May (1955).
W. S. Dorn and H. J. Greenberg, “Linear Programming and Plastic Limit Analysis of Structures.” Quart. J. Appl. Math., 15, (1957).
G. Ceradini and C. Gavarini, “Calcolo a rottura e programmazione lineare,” Giornale del Genio Civile, 3, (1965).
D. E. Grierson and G. M. L. Gladwell, “Collapse Load Analysis Using Linear Programming.” J. Str. Dit. ASCE.. 97. (ST 5), May, (1971).
R. K. Livesley. “The Automatic Design of Structural Frames,” Quart. J. Mec/n. and Appl. Matin.. 8. (3), September (1956).
W. Prager, “Linear Programming and Structural Design,” Rand Research Mennora ch nt KM-2021. ASTIA Document AP 150661. December (1957).
G. Maier, R. Srininavan, and M. Save, “On Limit Design of Frames using Linear Programming.” “Proc. int. Symp. on Computer-Aided Structural Design. University of Warwick, Coventry, (1972).
G. Sacchi, M. Maier, and M. Save, “Limit Design of Frames for Movable Loads by Linear Programming,” IUTAM Symposium on Optimization in Structural Design. Warsaw 1973, (ed. Sawczuk and Mroz ), Springer, (1975).
G. Maier, “Mathematical Programming Methods in Structural Analysis,” Proc. Int. Si’mp. on Variational Methods in Engineering, (ed. C. Brebbia and H. Tottenham ), Southampton University Press, (1973).
Nguyen Dang Hung and G. De Saxce, “Analyse et dimensionnement plastique des structures 6 barres dans des conditions de stabilité,” Construction métallique, (3), 15–28, (1981).
C. E. C. M., European Recommendations for Steel Constructions, ECCS-EG 77–2E, March (1978).
D. E. Grierson, “Elastic-Plastic Deformation Analysis usine Linear Programming,” Solid Mech. Div., University of Waterloo, Report No.. 88, July (1971).
M. Z. Cohn, Analysis and Design of Inelastic Structures. Vol. 2. Problems, University of Waterloo Press, (1972).
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1990 Springer-Verlag Wien
About this chapter
Cite this chapter
Hung, N.D., Morelle, P. (1990). Optimal Plastic Design and the Development of Practical Software. In: Smith, D.L. (eds) Mathematical Programming Methods in Structural Plasticity. International Centre for Mechanical Sciences, vol 299. Springer, Vienna. https://doi.org/10.1007/978-3-7091-2618-9_12
Download citation
DOI: https://doi.org/10.1007/978-3-7091-2618-9_12
Publisher Name: Springer, Vienna
Print ISBN: 978-3-211-82191-6
Online ISBN: 978-3-7091-2618-9
eBook Packages: Springer Book Archive