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.
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References
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Acknowledgement
The collaboration was financially supported by the French–German grant PROCOPE EGIDE 28481WB “Homogenization based optimization for elasticity on the network of beams”.
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Bare, Z., Orlik, J., Panasenko, G. (2015). Asymptotic Approximations of a Thin Elastic Beam with Auxiliary Coupled 1D System due to Robin Boundary Condition. In: Mityushev, V., Ruzhansky, M. (eds) Current Trends in Analysis and Its Applications. Trends in Mathematics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-319-12577-0_69
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DOI: https://doi.org/10.1007/978-3-319-12577-0_69
Publisher Name: Birkhäuser, Cham
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