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Serrin integrals and second order problems of plasticity

Published online by Cambridge University Press:  14 November 2011

L. Cesari  and
Wei H. Yang
L. Cesari
Affiliation:
The University of Michigan, Ann Arbor, Michigan 48109, U.S.A.
Wei H. Yang
Affiliation:
The University of Michigan, Ann Arbor, Michigan 48109, U.S.A.
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Synopsis

We use the modern tools of the duality principles and the calculus of variations to formulate, analyse and solve a class of plasticity problems involving second order partial derivatives. The Serrin-type integrals can most appropriately facilitate the existence statements for the extrema from either side of the duality relation in a larger class of BV functions, and interpret the solutions with possible discontinuities on sets of measure zero. The exact solutions of a beam and numerical solutions of a circular plate are presented to demonstrate the theoretical conclusions.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 117 , Issue 3-4 , 1991 , pp. 193 - 207
Copyright
Copyright © Royal Society of Edinburgh 1991

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