Removal of the stress field singularity for the Williams problem (1952) basing on a non-Euclidean continuum model

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Abstract

A singular solution for the elastic stress field in the Williams problem on the equilibrium of plates with corner cutouts is considered. A scheme has been constructed for the minimal expansion of the classical elastic continuum model without taking into account the Saint-Venant compatibility conditions for deformations, which leads to a non-Euclidean continuum model. Within this model framework, the total stress field is shown to contain no singularity for all cutout angles.

About the authors

M. A. Guzev

aInstitute for Applied Mathematics Far Eastern Branch, Russian Academy of Sciences; Perm National Research Polytechnic University

Author for correspondence.
Email: guzev@iam.dvo.ru

Academician of the RAS

Russian Federation, Vladivostok; Perm

References

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