Engineering Transactions, 25, 2, pp. 239-246, 1977

One Some Basic Problems of the Theory of Shakedown

J. Karczewski
Institute of Fundamental Technological Reseach, Warsaw

J.A. Konig
Institute of Fundamental Technological Reseach, Warsaw

The paper presents the observation that discrete structures of the global condition of shakedown does not need necessarily require that the shakedown condition of each element should be satisfied. A simple example illustrates the thesis. The practical importance of further research work on shake-down analysis of structures with unstable elements is emphasised.

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


M. GRÜNING, Die Tragfähigkeit statisch unbestimmien Tragwerke aus Stahl bei belibig haüfig wiederholter Belastung, Springer, Berlin 1926.

H. BLKICH, Über die Bemessung statisch unbestimmter Stahlwerke unter Berücksichtigung des elastischplastischen Berhaltens des Baustoffes, Bauingenieur, 13, 261-267, 1932. A. R. RZANICYN, Rascet sooruienii S uéetom plasticeskich svojstv materialov, Gostroizdat, Moskva 1954.

B. G. NEAL, The plastic method of structural analysis, Chapman and Hall, Oxford 1956.

P. G. HODGE, Plastic analysis of structures, McGraw-Hill, New York 1959.

W. T. KOITER, General theorems for elastic-plastic solids, Progress in Solid Mechanics, North Holland, Amsterdam, 165-221, 1960.

J. A. KÖNIG, Theory of shakedown of elastic-plastic structures, Arch. Mech. Stos., 18, 227-238, 1966.

G. MAIER, A shakedown matrix theory allowing for workhardening and second-order geometric

effects, Int. Symp. Poundations of Plasticity, Warsaw 1972, Preprints, 417-433.

J. A. KÖNIG, Elastic-plastic structural design for variable repeated loads [in Polish], IPPT Reports, 24, 1974.

A. CYRAS, Optimization theory in limit analysis of a solid deformable body [in Russian], Mintis Publ. House, Vilna 1971. W. OLSZAK, P. PERZYNA, A. SAWCZUK et all., Teoria plastyczności, PWN, Warszawa 1965.

Soprotivienie deformirovaniju i razrußeniju pri malom cisle cikloy nagruzenija, Gosud. naucno-issledov, inst. masinovedenija, Izd. Nauka, Moskva 1967.

G. MAIER, Shakedown of plastic structures with unstable parts, J. Eng. Mech. Div., 98, 1322-1327, 1972.

K. SZUWALSKI, M. ZYCZKOWSKI, On the phenomenon of decohesion in perfect plasticity, Int. J. Solids Struct., 9, 85-98, 1973.