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Some modes of convergence and their application to homogenization and optimal composites design
Mittuniversitetet, Fakulteten för naturvetenskap, teknik och medier, Institutionen för teknik, fysik och matematik.ORCID-id: 0000-0001-6742-5781
Ansvarlig organisasjon
1996 (engelsk)Doktoravhandling, monografi (Annet vitenskapelig)
Abstract [en]

In this thesis, we develop, extend, apply, and discuss a number of methods for the study of limits of sequences of functions and operators. The connection between the notion of two-scale convergence and more general concepts of convergence is investigated and some alternative classes of admissible test functions are characterized. These techniques are extended into compactness results suitable to prove homogenization and corrector results for linear parabolic equations. A further refinement of these methods, together with a characterization of the limits of certain sequences of parameter-dependent functions which has been subject to extension from a quite general class of periodic domains, is introduced. This provides an efficient tool for the homogenization of e.g. nonlinear evolution heat conduction in heterogeneous materials which vibrate with high frequencies or are perforated by periodically arranged nonconducting holes. Moreover, we prove compactness and homogenization for sequences of solutions of linear elliptic and monotone parabolic equations defined in some classes of nonperiodic domains and derive a Darcy's law for a type of nonperiodic porous media. In the linear elliptic case the convergence is strengthened by means of correctors. Finally, we present some numerical results for homogenized stiffness of fibre composites and demonstrate how homogenization techniques for elasticity in composite materials and for liquid flow in porous media can be combined with recent optimization techniques to obtain optimal layout of composite materials.

sted, utgiver, år, opplag, sider
Luleå: Luleå tekniska högskola , 1996. , s. 133
Serie
Doctoral thesis / Tekniska högskolan i Luleå, ISSN 0348-8373 ; 208D
Emneord [en]
Homogenization, two-scale convergence
HSV kategori
Identifikatorer
URN: urn:nbn:se:miun:diva-5605Lokal ID: 1271OAI: oai:DiVA.org:miun-5605DiVA, id: diva2:30638
Tilgjengelig fra: 2008-09-30 Laget: 2008-09-30 Sist oppdatert: 2016-12-12bibliografisk kontrollert

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