Summary
Some broad classes of discrete structural models and piecewise linear yield loci and hardening rules are considered. The dynamic elastoplastic response to a given history of rapidly variable loads and imposed strains and displacements (“dislocations”) is studied on the basis of a suitable matrix description. Inadaptation means that the plastic work and, hence, some plastic deformations increase unlimitedly in time, i.e. the structure does not shakedown. Sufficient and necessary conditions for this occurrence are established and formulated in a theorem, which represents the extension to the dynamic range and to work-hardening structures of the second (Koiter's) shakedown theorem of classical plasticity.
Übersicht
Es werden einige Klassen diskreter Strukturmodelle und stückweise linearer Fließ- und Verfestigungsregeln betrachtet. Dabei wird die elasto-plastische Reaktion eines Bauteiles auf eine vorgegebene Belastung durch schnell veränderliche Lasten sowie aufgeprägte Verzerrungen oder Verschiebungen mit Hilfe einer geeigneten Matrizen-Darstellung untersucht. „Inadaptation” bedeutet, daß die plastische Verformungsarbeit und folglich auch einige plastische Deformationen mit der Zeit unbegrenzt anwachsen, so daß kein Abfangen bei endlichen Verformungen („adaptation”) stattfindet. Es werden notwendige und hinreichende Bedingungen für ein derartiges Verhalten aufgestellt und in einem Satz formuliert, der als eine Verallgemeinerung des zweiten (des Koiterschen) Satzes der klassischen Plastizitätstheorie aufgefaßt werden kann.
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Friendly dedicated to L. Finzi, on the occasion of his fiftieth birthday.
The results contained in this paper were obtained in a research project sponsored by the National Italian Research Committee (CNR) and were presented at the 1972 Annual Meeting of the CNR Group for Advanced Problems in Structural Engineering, Milan, 6–7 June 1972.
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Corradi, L., Maier, G. Inadaptation theorems in the dynamics of elastic-work hardening structures. Ing. arch 43, 44–57 (1973). https://doi.org/10.1007/BF00536578
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DOI: https://doi.org/10.1007/BF00536578