Asymptotic approximations of a thin elastic beam with auxiliary coupled 1D system due to Robin boundary condition

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.