Abstract
Based on a new consistent internal-variable theory of elasto-plasticity, the author’s idea of adaptation (SACZUK [1992]) is generalized to non-linear problems for elastic-plastic structures. The underlying theory of elastic-plastic behaviour of materials in which, among others, no yield rule and intermediate configuration are assumed to exist, where the transition from micro- to macroscales is natural, and where the constitutive relations do not need the so-called loading criteria, is modelled by a metric generalization of the Riemannian geometry. It is used to reformulate the known statical approaches to path-dependent adaptation. The new adaptation theorems proposed, which have no counterparts in the available literature, are generalization of known versions to the finite shakedown theorems.
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References
1984 Atluri, S.N., ”On constitutive relations at finite strains: hypo-elasticity and elastoplasticity with isotropic or kinematic hardening”, Compt, Meth. Appl. Mech. Engng, 43, 137.
1990 Gross-Weege, J., ”A unified formulation of statical shakedown criteria for geometrically nonlinear problems”, Int. J. Plasticity, 6, 433.
1959 Hodge, P. G., Plastic Analysis of Structures, Mc Graw-Hill Book Company, New York, Toronto, London.
1982 König, J.A., ”Shakedown analysis in structural design”, in: Mahrenholtz, O. and Sawczuk, A. (eds), Mechanics of Inelastic Media and Structures, pp. 133–142, PWN — Polish Scientific Publishers, Warszawa.
1987 König, J.A., Shakedown of Elastic-Plastic Structures, PWN — Polish Scientific Publishers, Warszawa.
1960 Koiter, W.T., ”General theorems for elastic-plastic solids”, in: Sneddon, I. N. and Hill, R. (eds), Progress in Solid Mechanics, Vol. 1, pp. 165–221, North-Holland, Amsterdam.
1986 Matsumoto, M., Foundations of Finsler Geometry and Special Finsler Spaces, Kaiseisha Press.
1936 Melan, E., ”Theorie Statisch unbestimmter Systeme aus ideal-plastischem Baustoff”, Sitzungsbericht der Akad. D. Wiss. (Wien), Akt. IIa, 145, 195.
1987 Petryk, H., ”Non-uniqueness and instability of plastic deformation processes”, DSc Thesis, IFTR Report of PASci, Warszawa (in Polish).
1959 Rund, H., The Differential Geometry of Finsler Spaces, Springer, Berlin, Göttingen, Heidelberg.
1990 Saczuk, J. and Stumpf, H., ”On statical shakedown theorems for nonlinear problems”, Mitt. Inst, für Mech., Ruhr-Univ. Bochum, Germany, Vol. 74.
1993a Saczuk, J., ”A contribution to the theory of elastic-plastic materials. I. Ideas of a new theory of elasto-plasticity”, Int. J. Engng Sci., (submitted).
1993b Saczuk, J., ”A contribution to the theory of elastic-plastic materials. II. The balance laws and constitutive equations”, Int. J. Engng Sci., (submitted).
1992 Saczuk, J., ”A version of path-dependent adaptation of elastic-plastic structures”, EUROMECH 298, Warszawa, September 14-18.
1965 Truesdell, C. and Noll, W., ”The non-linear field theories of mechanics”, in: FlÜgge, S. (ed), Encyclopedia of Physics, Vol. III/3, Springer, Berlin, Heidelberg, New York.
1986 Weichert, D., ” On the influence of geometrical nonlinearities on the shakedown of elastic-plastic structures”, Int. J. Plasticity, 2, 135.
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© 1995 Springer Science+Business Media Dordrecht
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Saczuk, J. (1995). On Theorems of Adaptation of Elastic-Plastic Structures. In: Mróz, Z., Weichert, D., Dorosz, S. (eds) Inelastic Behaviour of Structures under Variable Loads. Solid Mechanics and Its Applications, vol 36. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-0271-1_11
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DOI: https://doi.org/10.1007/978-94-011-0271-1_11
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