Abstract
AbstractIn 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)
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