Abstract:
The elastic equilibrium of an isotropic plane with one linear defect under conditions of longitudinal shear is considered. The strain field is constructed by the solution of a twodimensional boundary-value Riemann problem with variable coefficients. A special method that reduce the general two-dimensional problem to two one-dimensional problems is proposed. The strain field is described by three types of asymptotic relations: for the tups of the defect, for the tips of the reinforcing edge, and also at a distance from the closely spaced tips of the defect and the rib. The general form of asymptotic relations for strains with finite energy is deduced from analysis of the variational symmetries of the equations of longitudinal shear. A paradox of the primal mixed boundary-value problem for cracks is formulated and a method of solving the problem is proposed.
Citation:
V. A. Khandogin, “Mixed problem of crack theory for antiplane deformation”, Prikl. Mekh. Tekh. Fiz., 39:3 (1998), 163–172; J. Appl. Mech. Tech. Phys., 39:3 (1998), 467–475
\Bibitem{Kha98}
\by V.~A.~Khandogin
\paper Mixed problem of crack theory for antiplane deformation
\jour Prikl. Mekh. Tekh. Fiz.
\yr 1998
\vol 39
\issue 3
\pages 163--172
\mathnet{http://mi.mathnet.ru/pmtf3281}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 1998
\vol 39
\issue 3
\pages 467--475
\crossref{https://doi.org/10.1007/BF02468132}
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https://www.mathnet.ru/eng/pmtf3281
https://www.mathnet.ru/eng/pmtf/v39/i3/p163
This publication is cited in the following 1 articles:
Iuliia Vasileva, Klaus Gürlebeck, Vasily Silvestrov, “Mixed antiplane boundary‐value problem for a piecewise‐homogeneous elastic body with a semi‐infinite interfacial crack”, Math Methods in App Sciences, 39:15 (2016), 4419
Citation in format AMSBIB
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