O. Chkadua
abstract:
Spatial boundary value problems of statics of couple-stress elasticity for
anisotropic homogeneous media (with contact on a part of the boundary) with an
open crack are studied supposing that one medium has a smooth boundary and the
other one has an open crack.
Using the method of the potential theory and the theory of pseudodifferential
equations on manifolds with boundary, the existence and uniqueness theorems are
proved in Besov and Bessel-potential spaces. The smoothness and a complete
asymptotics of solutions near the contact boundaries and near crack edge are
studied.
Properties of exponents of the first terms of the asymptotic expansion of
solutions are established. Classes of isotropic, transversally-isotropic and
anisotropic bodies are found, where oscillation vanishes.