Compressibility and shear compliance of a pore possessing an (n + 1)-fold axis of symmetry via the use of a conformal mapping function containing an arbitrary number of terms

Abstract

We propose a simple yet effective method to determine the compressibility and the shear compliance of a pore possessing an (n + 1)-fold axis of symmetry with n ≥ 2 embedded in an infinite isotropic elastic body. The conformal mapping function which maps the exterior of the pore onto the exterior of the unit circle in the image plane contains an arbitrary number of terms. When the mapping function has N+1 terms, the compressibility and shear compliance are found by solving, respectively, sets of N and 2N coupled linear algebraic equations. Detailed numerical results for the compressibility and shear compliance of equilateral polygonal holes and a five-pointed star shaped hole are presented to demonstrate the proposed solution method.