This article demonstrates error estimates for beam displacements under simple loading in a Lipschitz domain, suggesting improved accuracy for 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 ).
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Griso et al. (2026) studied this question.
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