Non homogeneous Dirichlet conditions for an elastic beam: an asymptotic analysis

Abstract

The asymptotic approximation of the displacement of a linear elastic beam with prescribed non-homogeneous Dirichlet conditions at an end is constructed. The non-homogeneous Dirichlet conditions considered in this work have the form of rigid displacements. The six values needed to state an auxiliary one-dimensional system are obtained and the error of the approximation is estimated. A numerical example illustrates the high precision of the approximation.

Keywords:

• Linear elasticity
• Dirichlet boundary condition
• asymptotic expansion
• dimension reduction
• classical one-dimensional rod- and beam models

AMS Subject Classifications:

• 35C20
• 78M35
• 74B05
• 74K10

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

The collaboration was financially supported by the project “Homogenization based optimization for elasticity on the network of beams”, funded by the French-German program PROCOPE EGIDE [grant number 28481WB]. The first two authors were supported by the project OR 190/4-1 “Mehrskalenmodellierung und -simulation der Mechanik gewebter Strukturen” funded by the German Research Foundation (DFG); and the third author was supported by the Russian Scientific Foundation [grant number 14-11-00306] and by PICS CNRS [grant BIOMAT].