Journal of Mathematical Sciences

, Volume 238, Issue 1, pp 46–62 | Cite as

Method of Direct Cutting-Out in the Problems of Piecewise Homogeneous Bodies with Interface Cracks Under Longitudinal Shear

  • К. V. Vasil’evEmail author
  • H. T. Sulym

The earlier developed method of direct cutting-out is extended to the class of problems of elastic equilibrium of piecewise homogeneous bodies with internal and interface crack-like defects under antiplane deformation. This method is based on modeling of the initial problem for a body with thin inclusions (in particular, cracks) by a simpler problem of elastic equilibrium of piecewise homogeneous space with elevated number of thin defects, which, in fact, form new boundaries of the analyzed body. The reliability of the proposed approach is checked on examples of problems of longitudinal shear for a piecewise homogeneous wedge, a piecewise homogeneous half space, and a two-layer strip with interface crack subjected to the action of homogeneous loads and concentrated forces.


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Authors and Affiliations

  1. 1.Pidstryhach Institute for Applied Problems in Mechanics and MathematicsUkrainian National Academy of SciencesLvivUkraine
  2. 2.I. Franko Lviv National UniversityLvivUkraine

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