Asymptotics for a thin elastic fiber in contact with a rigid body

  • In this work a 3-dimensional contact elasticity problem for a thin fiber and a rigid foundation is studied. We describe the contact condition by a linear Robin-condition (by meaning of the penalized and linearized non-penetration and friction conditions). The dimension of the problem is reduced by an asymptotic approach. Scaling the Robin parameters appropriately we obtain a recurrent chain of Neumann type boundary value problems which are considered only in the microscopic scale. The problem for the leading term is a homogeneous Neumann problem, hence the leading term depends only on the slow variable. This motivates the choice of a multiplicative ansatz in the asymptotic expansion. The theoretical results are illustrated with numerical examples performed with a commercial finite-element software-tool.

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Metadaten
Author:Daniel Zoufiné Baré Contreras
URN (permanent link):urn:nbn:de:hbz:386-kluedo-28280
Publisher:2010
Advisor:Julia Orlik
Document Type:Master's Thesis
Language of publication:English
Publication Date:2011/12/16
Year of Publication:2010
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:518 Numerische Analysis

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