Error Estimates for Beam Linear Elasticity Problems

In this article, we first present a decomposition of the displacements of a straight beam P δ . The beam has length L and cross-section ω δ = δ ω where ω is a bounded Lipschitz domain in R 2 and δ a small parameter. The beam is clamped at atleast one end and subjected to simple loading. Using the tools of the dimension reduction method, we obtain the limit problems and error estimates (global error, of order δ 1 / 2 , L 2 global error and H 1 interior error with respect to δ ).