Asymptotics for a thin elastic fiber in contact with a rigid foundation |
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Authors: | Zoufine Bare Julia Orlik |
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Institution: | Fraunhofer Institut für Techno- und Wirtschaftmathematik (ITWM), Fraunhofer-Platz 1, 67663 Kaiserslautern |
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Abstract: | 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) |
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