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Erschienen in:
2015 | OriginalPaper | Buchkapitel
Asymptotic Approximations of a Thin Elastic Beam with Auxiliary Coupled 1D System due to Robin Boundary Condition
verfasst von : Z. Bare, J. Orlik, G. Panasenko
Erschienen in: Current Trends in Analysis and Its Applications
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Abstract
In Bare et al. (Appl. Anal., 2013, doi:10.1080/00036811.2013.823481), the dimension of a 3D linear elasticity boundary value problem with Robin boundary condition is asymptotically reduced. Assumption 1.4 in Bare et al. (Appl. Anal., 2013, doi:10.1080/00036811.2013.823481), leads to a 1D system in which the bending and tensile components are decoupled. With a generalization in this contribution, we obtain a coupled 1D system. We prove that the asymptotic error estimate in Bare et al. (Appl. Anal., 2013, doi:10.1080/00036811.2013.823481) remains true and illustrate the influence of the tension and torsion on the bending by a numerical example.