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theories of rods

ESAIM: Mathematical Modelling and Numerical Analysis (1)

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Incompressibility in Rod and Shell Theories
Stuart S. Antman, Friedemann Schuricht
Journal:

ESAIM: Mathematical Modelling and Numerical Analysis / Volume 33 / Issue 2 / March 1999

Published online by Cambridge University Press:

15 August 2002, pp. 289-304

Print publication:

March 1999
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We treat the problem of constructing exact theories of rods and shells for thin incompressible bodies. We employ a systematic method that consists inimposing constraints to reduce the number of degrees of freedom of each crosssection to a finite number. We show that it is very difficult to produce theories that exactly preserve the incompressibility and we show that it is impossible to do so for naive theories. In particular, many exact theories have nonlocal effects.