Inserted: 4 apr 2008
Last Updated: 28 jan 2009
Journal: SIAM Journal on Mathematical Analysis
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