Mechanics of Solids (about journal) Mechanics of Solids
A Journal of Russian Academy of Sciences
in January 1966
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IssuesArchive of Issues2010-5pp.733-742

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A.M. Khludnev, "Problem of a Crack on the Boundary of a Rigid Inclusion in an Elastic Plate," Mech. Solids. 45 (5), 733-742 (2010)
Year 2010 Volume 45 Number 5 Pages 733-742
DOI 10.3103/S0025654410050092
Title Problem of a Crack on the Boundary of a Rigid Inclusion in an Elastic Plate
Author(s) A.M. Khludnev (Lavrentyev Institute of Hydrodynamics, Siberian Branch of Russian Academy of Sciences, pr-t Akad. Lavrentyeva 15, Novosibirsk, 630090 Russia,
Abstract The problem of equilibrium of a thin elastic plate containing a rigid inclusion is considered. On part of the interface between the elastic plate and the rigid inclusion, there is a vertical crack. It is assumed that, on both crack edges, the boundary conditions are given as inequalities describing the mutual impenetrability of the edges. The solvability of the problem is proven and the character of satisfaction of the boundary conditions is described. It is also shown that the problem is the limit problem for a family of other problems posed for a wider region and describing equilibrium of elastic plates with a vertical crack as the rigidity parameter tends to infinity.
Keywords elastic plate, rigid inclusion, crack, mutual impenetrability condition
1.  A. M. Khludnev, "Crack Theory with Possible Contact of the Faces," Uspekhi Mekh. 3 (4), 41-82 (2005).
2.  A. M. Khludnev and V. A. Kovtunenko, Analysis of Cracks in Solids (WIT-Press, Southampton, Boston, 2000).
3.  K.-H. Hoffmann and A. M. Khludnev, "Fictitious Domain Method for the Signorini Problem in a Linear Elasticity," Adv. Math. Sci. Appl. 14 (2), 465-481 (2004).
4.  I. Ekeland and R. Temam, Convex Analysis and Variational Problems (North-Holland, Amsterdam, 1976; Mir, Moscow, 1979).
5.  A. Morassi and E. Rosset, "Detecting Rigid Inclusions, or Cavities, in an Elastic Body," J. Elasticity 73, 101-126 (2003).
Received 23 October 2007
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