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The orders of singular stresses at plane bi‐ and trimaterial junctions ‐ Closed‐form analytical solutions
Author(s) -
Sator Christian,
Becker Wilfried
Publication year - 2011
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201110125
Subject(s) - gravitational singularity , singularity , exponent , isotropy , plane (geometry) , vertex (graph theory) , homogeneous , mathematics , mathematical analysis , stress (linguistics) , geometry , physics , combinatorics , optics , graph , philosophy , linguistics
The plane problem of a bi‐ or trimaterial‐junction, consisting of dissimilar, homogeneous, isotropic and linear elastic sectors is considered. The asymptotic behaviour of the stresses of this composite situation is analyzed by the complex variable method, based on an appropriate choice of the Kolosov‐potentials which are applicable in the vicinity of the vertex. In the analyses, the identification of the singularity exponent is emphasized. With the help of a novel approach it is demonstrated how to derive some solutions for the orders of the stress singularities at bi‐ and trimaterial combinations in a closed‐form analytical manner. (© 2011 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)