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A Shortcoming in the Geometrically Non‐Linear Shakedown Theorem
Author(s) -
Schieck B.
Publication year - 2003
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.200310092
Subject(s) - counterexample , mathematics , shakedown , fundamental theorem , brouwer fixed point theorem , discrete mathematics , pure mathematics , fixed point theorem , physics , finite element method , thermodynamics
The original static shakedown theorem of Melan [1], valid for geometrically linear theory, was extended for geometrically non‐linear theory e.g. by Polizzotto and Borino [2], 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.