Abstract:
Under study is the equilibrium problem
of a two-dimensional elastic body with a crack
crossing a thin rigid inclusion at some point.
Nonpenetration conditions in the form of inequalities are put
on the crack faces
and at the intersection point of the crack with the rigid inclusion.
The equilibrium problem of an elastic body with a crack
crossing a thin elastic inclusion
is also considered.
The theorems of unique solvability of these problems are proved,
and some complete systems of boundary conditions are obtained.
The equivalence of the two formulations, variational and differential,
is examined.
We establish that the limit transition with respect to the rigidity parameter
in the problems on the equilibrium of an elastic body with an elastic inclusion
leads to the equilibrium problem of an elastic body with a rigid inclusion.
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