Analysis of the orders of stress singularity at the corner point of a diamond-shape rigid inclusion or hole in an infinite plate under antiplane bending by conformal mapping

Abstract

The orders of the stress singularity at the corner point of a diamond-shape rigid inclusion or hole in an infinite elastic plate are studied. Combining the complex stress functions in elasticity theory with the conformal mapping, the stress functions are expressed in power series with infinite terms. By virtue of the stress functions and the consideration of singular behavior of stress at the corner point, the orders of the stress singularity at the corner point are determined. It is found there are two kinds of order at the corner point, which correspond to Mode I and Mode II deformations, respectively. The stress intensities corresponding to the orders are defined, and the influence of Poisson's ratio of the plate on the values of the orders is discussed.