The problem of an elastic line inclusion embedded inside an elastic matrix of
finite extent has several practical applications. Transmission of tension from a
stiffener bar to a plate has been addressed by Goodier and Hsu (1954), Koiter (1955),
Muki and Sternberg (1967) and many others. This problem has a special relevance in
the design of aircraft and space structures and has its origin in the works of
Melan (1932). In these works, the sheet has been treated as a two-dimensional
continuum using the conventional theory of generalized plane stress, with the stiffener
being modeled as one-dimensional elastic bar of zero flexural rigidity. Rigorous
mathematical formulations have been presented for problems such as semi-infinite plate with
an infinite edge stiffener.
A similar problem arises in the analysis of fiber-reinforced composites
wherein more often the elastic fibers are replaced by rigid line inclusions (Kerr et al., 1997; and England, 1971). Closed-form solutions for rigid line inclusions have been
derived for problems with simpler geometry (Brussat and Westmann, 1975). Similar to
the case of cracks, singular stress fields appear at the tip of a rigid line inclusion
(Wang et al., 1985; Chen, 1989; and Chi-Peng, 1991).
Numerical methods may be more suitable for analyzing problems of
practical significance having complex geometry of boundary and line inclusions. Analysis
of reinforced concrete structural elements is another important application for which
a large number of finite element analysis results have been reported (Ngo
and Scordelis, 1967; and Elwi and Hrudey, 1989). An integral equation approach
to model the interaction between cracks and rigid line inclusions has been
presented by Dong et al. (2003). They have numerically evaluated the stress intensity
factors for cracks and rigid line inclusions in elastic continua of infinite extent. |
