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Closed‐form solutions for stress singularities at bi‐material wedges in Reissner‐Mindlin plates
Author(s) -
Felger Julian,
Becker Wilfried
Publication year - 2016
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201610049
Subject(s) - gravitational singularity , singularity , exponent , isotropy , mathematical analysis , eigenvalues and eigenvectors , mathematics , classical mechanics , geometry , physics , philosophy , linguistics , quantum mechanics
In this work, stress singularities in isotropic bi‐material junctions are investigated using Reissner‐Mindlin plate theory by means of a complex potential formalism. The governing system of partial differential equations is solved employing methods of asymptotic analysis. The resulting asymptotic near‐fields including the singularity exponent λ are obtained in a closed‐form analytical manner as solutions of a corresponding eigenvalue problem. The singular solution character is discussed for different geometrical configurations. In particular, the present study investigates the influence of the material constants on the singularity exponent. It is shown, that the Reissner‐Mindlin theory allows for distinguishing between singularities of the bending moments and the transverse shear forces. Further, stronger singularities than the classical crack‐tip singularity are observed. The results allow for further application such as a combination with numerical methods. (© 2016 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)