A shortcoming in the geometrically non-linear shakedown theorem. (English) Zbl 1201.74082
Summary: The original static shakedown theorem of Melan, valid for geometrically linear theory, was extended for geometrically non-linear theory e.g. by Polizzotto and Borino, who presented a proof for large rotations with small strains. However, a counterexample to this extended Melan’s theorem has been found. The reason of the failure is investigated and is corrected by an additional condition in the theorem. The outline of the proof is given.
MSC:
| 74C99 | Plastic materials, materials of stress-rate and internal-variable type |
References:
| [1] | : Theorie statisch unbestimmter Systeme aus ideal plastischem Baustoff. Sitzb. Akad. Wiss., Wien, IIa, 145 (1936), 195 pp. · JFM 62.1547.01 |
| [2] | and : Shakedown and steady-state responses of elastic-plastic solids in large displacements. Int. J. Solids Structures 33.23 (1996), 3415-3437. · Zbl 0909.73030 |
| [3] | : The transition from spatial covariant notation to co-rotational formulation in finite elastoplasticity. Lecture notes of the GAMM conference in Regensburg, April 1997. ZAMM 78 (1998), S703-S704. |
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