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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The free boundary for elastic-plastic torsion problems


Authors: Avner Friedman and Gianni A. Pozzi
Journal: Trans. Amer. Math. Soc. 257 (1980), 411-425
MSC: Primary 35R35; Secondary 49A29, 73C99, 73K99
DOI: https://doi.org/10.1090/S0002-9947-1980-0552267-9
MathSciNet review: 552267
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Abstract: Consider the variational inequality: Find $u \in K$ such that $\int _Q {\nabla u \cdot \nabla (\upsilon - u) \geqslant \mu \int _Q {(\upsilon - u) (\mu > 0)} }$ for any $\upsilon \in K$, where $K = \{ w \in H_0^1(Q); \left | {\nabla w} \right | \leqslant 1\}$ and Q is a 2-dimensional simply connected domain in ${R^2}$ with piecewise ${C^3}$ boundary. The solution u represents the stress function in a torsion problem of an elastic-plastic bar with cross section Q. The sets $E = \{ x \in Q; \left | {\nabla u(x)} \right | < 1\}$, $P = \{ x \in Q; \left | {\nabla u(x)} \right | = 1\}$ are the elastic and plastic sets respectively. The purpose of this paper is to study the free boundary $\partial E \cap Q$; more specifically, an estimate is derived on the number of points of local maximum of the free boundary.


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Article copyright: © Copyright 1980 American Mathematical Society