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The Laplace and the linear elasticity problems near polyhedral corners and associated eigenvalue problems

The solutions to certain elliptic boundary value problems have singularities with a typical structure near polyhedral corners. This structure can be exploited to devise an eigenvalue problem whose solution can be used to quantify the singularities of the given boundary value problem. It is necessary to parametrize a ball centered at the corner. There are different possibilities for a suitable parametrization; from the numerical point of view, spherical coordinates are not necessarily the best choice. This is why we do not specify a parametrization in this paper but present all results in a rather general form. We derive the eigenvalue problems that are associated with the Laplace and the linear elasticity problems and show interesting spectral properties. Finally, we discuss the necessity of widely accepted symmetry properties of the elasticity tensor. We show in an example that some of these properties are not only dispensable, but even invalid, although claimed in many standard books on linear elasticity.

Identiferoai:union.ndltd.org:DRESDEN/oai:qucosa.de:swb:ch1-200601506
Date01 September 2006
CreatorsMeyer, Arnd, Pester, Cornelia
ContributorsTU Chemnitz, SFB 393
PublisherUniversitätsbibliothek Chemnitz
Source SetsHochschulschriftenserver (HSSS) der SLUB Dresden
LanguageEnglish
Detected LanguageEnglish
Typedoc-type:preprint
Formattext/html, text/plain, image/png, image/gif, text/plain, image/gif, application/pdf, application/x-gzip, text/plain, application/zip
SourcePreprintreihe des Chemnitzer SFB 393, 04-12

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