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Modeling and design optimization of textile-like materials via homogenization and one-dimensional models of elasticity

  • The work consists of two parts. In the first part an optimization problem of structures of linear elastic material with contact modeled by Robin-type boundary conditions is considered. The structures model textile-like materials and possess certain quasiperiodicity properties. The homogenization method is used to represent the structures by homogeneous elastic bodies and is essential for formulations of the effective stress and Poisson's ratio optimization problems. At the micro-level, the classical one-dimensional Euler-Bernoulli beam model extended with jump conditions at contact interfaces is used. The stress optimization problem is of a PDE-constrained optimization type, and the adjoint approach is exploited. Several numerical results are provided. In the second part a non-linear model for simulation of textiles is proposed. The yarns are modeled by hyperelastic law and have no bending stiffness. The friction is modeled by the Capstan equation. The model is formulated as a problem with the rate-independent dissipation, and the basic continuity and convexity properties are investigated. The part ends with numerical experiments and a comparison of the results to a real measurement.

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Metadaten
Author:Vladimir Shiryaev
URN (permanent link):urn:nbn:de:hbz:386-kluedo-40194
Advisor:Grigory Panasenko, Axel Klar
Document Type:Doctoral Thesis
Language of publication:English
Publication Date:2015/03/09
Year of Publication:2015
Publishing Institute:Technische Universität Kaiserslautern
Granting Institute:Technische Universität Kaiserslautern
Acceptance Date of the Thesis:2015/02/27
Date of the Publication (Server):2015/03/09
Tag:Beam models; Elasticity; Homogenization; Optimization; Partial Differential Equations
Number of page:VIII, 110
Faculties / Organisational entities:Fachbereich Mathematik
DDC-Cassification:5 Naturwissenschaften und Mathematik / 510 Mathematik
MSC-Classification (mathematics):35-XX PARTIAL DIFFERENTIAL EQUATIONS
49-XX CALCULUS OF VARIATIONS AND OPTIMAL CONTROL; OPTIMIZATION [See also 34H05, 34K35, 65Kxx, 90Cxx, 93-XX]
74-XX MECHANICS OF DEFORMABLE SOLIDS
Licence (German):Standard gemäß KLUEDO-Leitlinien vom 13.02.2015