Error estimation in the Bernoulli–Navier model for elastic rods

Article type: Research Article

Authors: Irago, H.^; | Viaño, J.M.

Affiliations: Departamento de Matemática Aplicada, Universidad de Santiago de Compostela, 15706 Santiago de Compostela, Spain E‐mail: {irago,viano}@usc.zmat.es

Note: [] Corresponding author.

Abstract: Let u(\varepsilon) be the rescaled three‐dimensional displacement field solution of the linear elastic model for a clamped prismatic straight rod {\varOmega}^\varepsilon having cross section with diameter of order \varepsilon, and let u^0 be the corresponding Bernoulli–Navier displacement. In this article we establish that the error \|u(\varepsilon)-u^0\|_{1,{\varOmega}} in the reference space [H^1({\varOmega})]^3 is of order \varepsilon^{1/2}. We mainly use an auxiliar corrector function and we prove that this estimation cannot be improved using other corrector functions of the same family.

Keywords: Asymptotic analysis, elastic rods, error estimations, Bernoulli–Navier model

Journal: Asymptotic Analysis, vol. 21, no. 1, pp. 71-87, 1999