Singularities and stress intensities at the corner point of a polygonal hole and rigid polygonal inclusion under antiplane shear

Abstract

A new method is developed to calculate the orders of stress singularity and the stress intensities for the corner of a polygonal hole and a rigid polygonal inclusion under antiplane shear by conformal mapping. The order of stress singularity and the stress intensities are derived explicitly for the corner of a polygonal hole and a rigid polygonal inclusion. Types of polygon used are the regular polygon, lozenge and rectangle. We confirmed that the order of stress singularity and the singular stress fields near the corner coincide with the exact solutions by the method of eigenfunction expansion. Moreover, the order of stress singularity and the stress intensities coincide with the exact solution of a crack and a rigid line inclusion problems when an interior angle of the corner of a lozenge becomes zero.