## L. Freddi - F. Murat - R. Paroni

# Anisotropic inhomogeneous rectangular thin-walled beams

created by freddi on 04 Apr 2008

modified on 28 Jan 2009

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BibTeX]

*Published Paper*

**Inserted:** 4 apr 2008

**Last Updated:** 28 jan 2009

**Journal:** SIAM Journal on Mathematical Analysis

**Volume:** 40

**Number:** 5

**Pages:** 1923-1951

**Year:** 2009

**Abstract:**

The paper is devoted to the asymptotic analysis of the
problem of linear elasticity for an anisotropic and inhomogeneous
body occupying, in its reference configuration, a cylindrical
domain with a rectangular cross section with sides proportional to
$\epsilon$ and $\epsilon^2$ and clamped on one of its bases. The sequence
of solutions $u^\epsilon$ of the equilibrium problem is shown to
converge in an appropriate topology, as $\epsilon$ goes to zero, to
the solution of a problem for a beam in which the extensional,
flexural and torsional effects are all coupled together.

**Keywords:**
dimension reduction, linear elasticity, partial Korn's inequalities

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