In the earlier developed method of direct cutting-out, we take into account the anisotropy of material. This method is based on the procedure of modeling of finite or bounded bodies with thin structural defects of any type and boundary conditions on its contour by an infinite space with the same inhomogeneities as in the original problem and additional thin inhomogeneities (cracks or absolutely rigid inclusions), which form the boundary of the investigated body. Thus, loaded cracks are used to model boundary conditions of the first kind, whereas absolutely rigid inclusions embedded in the matrix with certain tension model boundary conditions of the second kind. The developed approach is verified for several problems of longitudinal shear of an anisotropic half space, a layer, and a wedge in the presence of an internal crack under given boundary conditions of the first kind.
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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 3, pp. 89–100, July–September, 2018.
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Vasil’ev, К.V., Sulym, H.Т. Method of Direct Cutting-Out in the Problems of Elastic Equilibrium of Anisotropic Bodies with Cracks Under Longitudinal Shear. J Math Sci 254, 103–116 (2021). https://doi.org/10.1007/s10958-021-05291-9
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DOI: https://doi.org/10.1007/s10958-021-05291-9