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Asymptotics for a thin elastic fiber in contact with a rigid foundation
Author(s) -
Bare Zoufine,
Orlik Julia
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110242
Subject(s) - boundary value problem , elasticity (physics) , ode , linear elasticity , robin boundary condition , mathematics , mathematical analysis , materials science , physics , mixed boundary condition , finite element method , thermodynamics , composite material
In this work a 3‐D contact elasticity problem for a thin fiber and a rigid foundation is studied. We describe the contact condition by a linear Robin‐boundary‐condition (by meaning of the penalized and linearized non‐penetration and friction conditions). The Robin parameters are scaled differently in the longitudinal and cross‐sectional directions. The dimension of the problem is reduced by a standard ([3], [4]) asymptotic approach with an additional expansion suggested to fulfil the contact conditions. The 3‐D contact conditions result into 1‐D Robin‐boundary‐conditions for corresponding ODEs. The Robin‐coefficients of the 1‐D problem depend on the ones from the 3‐D statement and on the cross‐section of the fiber. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)