A physical interpretation of the irredundant part of the first Piola-Kirchhoff-stress tensor of a discrete medium forming a skin

Binz, Ernst

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URL: https://ub-madoc.bib.uni-mannheim.de/1716
URN: urn:nbn:de:bsz:180-madoc-17164
Document Type: Working paper
Year of publication: 1993
The title of a journal, publication series: Mannheimer Manuskripte zu Risikotheorie, Portfolio Management und Versicherungswirtschaft
Volume: 155
Place of publication: Mannheim
Publication language: English
Institution: School of Business Informatics and Mathematics > Sonstige - Fakultät für Wirtschaftsinformatik und Wirtschaftsmathematik
MADOC publication series: Veröffentlichungen der Fakultät für Mathematik und Informatik > Institut für Mathematik > Mannheimer Manuskripte
Subject: 510 Mathematics
Classification: MSC: 74A99 74K99 ,
Subject headings (SWD): Differentialgeometrie , Algebraische Topologie , Riemannscher Raum , Triangulierung
Abstract: Deformable continua in an Euclidean space are characterized by the first Piola-Kirchhoff stress tensor. In doing so it is assumed that the continuum forms a connected, smooth and oriented Riemannian submanifold M of IR n with boundary M. Taking (covariant) divergence of the tensor a (assumed to be smooth) yields the internal force density on M. The internal force density caused on M is (n) with n the oriented unit normal of M in M. (Fortsetzung s. Original-Dokument)
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