Mixed problem of crack theory for antiplane deformation
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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.
KeywordsAsymptotic Expression Rigid Inclusion Asymptotic Relation Longitudinal Shear Linear Defect
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- 1.M. P. Savruk,Failure Mechanics and Strength of Materials, Handbook, Part 2:Stress-Intensity Coefficients for Bodies with Cracks [in Russian], Naukova Dumaka, Kiev (1988).Google Scholar
- 2.Y. Murakami (ed.),Stress Intensity Factors Handbook, Pergamon, Oxford-New York (1987).Google Scholar
- 3.M. P. Sheremet'ev,Plates with a Reinforced Rib [in Russian], Izd. L'vov. Univ., L'vov (1960).Google Scholar
- 4.G. N. Savin and V. I. Tul'chii,Plates Reinforced by Compound Rings and Elastic Overlays [in Russian], Naukova Dumka, Kiev (1971).Google Scholar
- 5.A. A. Khrapkov, “Some cases of the elastic equilibrium of an infinite wedge with an asymmetric cut at the tip under the action of concentrated forces,”Prikl. Mat. Mekh., No. 4, 677–689 (1971).Google Scholar
- 7.L. T. Berezhnitskii, V. V. Panasyuk, and N. G. Stashchuk,Interaction of Rigid Inclusions and Cracks in a Deformable Body [in Russian], Naukova Dumka, Kiev (1983).Google Scholar
- 8.P. Olver,Applications of Lie Groups to Differential Equations, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo (1986).Google Scholar
- 10.G. P. Cherepanov,Failure Mechanics of Composite Materials [in Russian], Nauka, Moscow (1983).Google Scholar