Engineering Transactions, 31, 3, pp. 317-330, 1983

The Terms and Shapes of the Functions Necessary for Calculation of the Dissipated Power in the Problem of Indentation of a Punch Into a Two-Ply Material

J. Kaczorowski
Institute of the Foundations of Machine Constructions, Kraków

The paper presents a method of calculation of the majorant of the limit load for the example of a punch into a semispace consisting of an isotropic laminar material. Proving the validity of the suggested theorems and lemma for a selected class of strain types, the calculation of the minimum dissipated power has been significantly simplified. The problem of finding the minimum of the func­tional has been reduced to the search for the minimum of a function of a single variable.

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D. BERTHET, C. HAYOT, J. SALENCON, Poinconnement d'un milieu semi-infini en materiau plastique de Tresca non-homogine, Arch. Mech., 24, 127, 1972.

A. DOLLD, B. ECKMANN, Applications of method of functional analysis to problems in mechanics, Lecture Notes in Math., 503, 1976.

A. DOLLD, B. ECKMANN, Nonlinear operators and the calculus of variations, Lecture Notes in Mathematics 543, 1976.

I. EKELAND, R. TEMAN, Conves analysis and variational problems, North-Holland, Amsterdam 1976.

G. FAVRETTI, Impronta di un punzone rigido sa un materiale non omogeneo, Ing. Mecc., 14, 9, 37. 1965.

H. FORD, Advanced mechanics of materials, Langmans, London 1963.

R. GŁOWIŃSKI, J. LIONS, R. TREMOLIERS, Analyse numerique des inequations variationnelles, Dunod, Paris 1976.

A. P. GREEN, The plastic yielding of notched bars due to bending, Quart. J. Appl. Math., 6, 223, 1953.

О. Д. Григорев, Об условии поло:жительности мощпости рассеиваиил u пласшм течении жесп, омластического тела, Zur. Prokl. Mech. Fiz., 1, 164, 1962,

R. HILL, The mathematical theory of plasticity, Oxford Clarendon Press, 1950.

H. G. HOPKINS, Mathematical method in plasticity theory, Problems of Plasticity, 235, 1974.

Ł. M. KACZANOW, Foundations of the theory of plasticity, North Holland, Amsterdam 1971.

L. KRONSJO, P. B. MELLOR, Plane-strain extrusion through concave dies, Int. J. Mech. Sci., 8, 515, 1966,

A. l. KUZNETZOV, The problem of torsion and piane strain of non-homogeneous plastic bodies, Arch. Mech. Stos., 10, 4, 447, 1958.

T. MuURA, S. LEE, R. H. BRYANT, W. H. RIMAWI, Limit analysis by direct method of variation, J. Eng. Mech. Div. Proc. ASCE, EM 5, 93, 67, 1967,

J. ODEN, J. REDDY, Variational methods in theoretical mechanics, Universitext Springer Verlag, 11976.

W. OLSZAK, J. RYCHLEWSKI, Y. URBANOWSKI, Plasticity under homogeneous conditions, Adv, Appl, Mech, 7, 131, 1968.

J. OSTROWSKA, Initial plastic flow of a semi-space with a strong layer nonhomogeneity, Arch. Mech. Stos., 20, 6, 1968.

W. PRAGER, Probleme der Plastizitatstheorie, Birkhauser, Basel und Stuttgart 1955.

L. PRANDTL, Ober die Harte Plastischer Korper, Gotinger Nachrichten Mat.-Phys., 1920.

D. RADENKOWIC, Theorems limites pour un material de Coulcmb a dilatation non standardisee, C. R. Acad. Sci., Paris, 252, 4103, 1961.

J. RYCHLEWSKI, The piane plastic strain problem of a wedge with jump nonhomogeneity, J. de Mecanique, 3, 4, 461, 1964.

J. RYCHLEWSKI, Plastic torsion of bars with jump nonhomogeneity, Acta. Mech., I, 36, 1965.

J. RYCHLEWSKI, Plastic torsion of a rectangular bar with a jump nonhomogeneity, Int. J. Sol. Struct., 1, 243, 1965.

J. RYCHLEWSKI, Piane plastic strain for jump homogeneity, Int. J. Non. Lin. Mech., 1, 57, 1966.

J. SALENCON, Eccoulcment plastique libre et analyse limitee pour les materiaux standards et lion standards, Annales de l'Institut Technique du Batiment et des Travaux Publics, 25, 89, 1972.

J. SALENCON, Theorie des charges limites, Sciences et Techniques de l'Armement, 47, 2, 287, 1973.

IJ. SALENCON, Un example de non validite de la theorie classique des charges limites pour un systeme non standard.

A. SAWCZUK, P. G. HODGE, Limit analysis and the yield line theory, J. Appl. Mech., 35, 357, 1968.

W. SZCZEPIŃSKI, lntroduction to the mechanics of plastic forming of metals, PWN, Warszawa 1979.

W. SZCZEPIŃSKI, Mechanika plastycznego płynięcia, PWN, Warszawa 1978.

J. RYCHLEWSKI, Oli a certain class of incipient plastic flow problems for the semi-space, Arch. Mech. Stos , 19, 1967.

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