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Non‐classical interface problems for piecewise homogeneous anisotropic elastic bodies
Author(s) -
Jentsch Lothar,
Natroshvili David
Publication year - 1995
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670180103
Subject(s) - mathematics , piecewise , homogeneous , anisotropy , interface (matter) , mathematical analysis , geometry , calculus (dental) , mechanics , combinatorics , physics , quantum mechanics , medicine , dentistry , bubble , maximum bubble pressure method
Two non‐classical model interface problems for piecewise homogeneous anisotropic bodies are studied. In both problems on the contact surface jumps of the normal components of displacement and stress vectors are given. In addition, in the first problem (Problem H) the tangent components of the displacement vectors are given from both sides of the contact surface, while in the second one (Problem G) the tangent components of the stress vectors are prescribed on the same surface. The existence and uniqueness theorems are proved by means of the boundary integral equation method, and representations of solutions by single layer potentials are established. In the investigation the general approach of regularization of the first kind of integral equations is worked out for the case of two‐dimensional closed smooth manifolds. An equivalent global regularizer operator is constructed explicitly in the form of a singular integro‐differential operator.