Analytical Solutions for In-Plane and Out-of-Plane Problems with Elliptic Hole or Elliptic Rigid Inclusion and Their Applications. 5th Report. Basic Theory and Numerical Examples for Isotropic Out-of-Plane Shear Problems.

Abstract

This paper presents a unified analysis of isotropic out-of-plane shear problems containing an elliptic hole or an elliptic rigid inclusion, and shows the closed-form analytical solutions. The applied forces considered in this paper are longitudinal shear stress at infinity, point force, screw dislocation, dipole force, and dipole dislocation at an arbitrary point. The analysis is based on the complex variable method using the conformal mapping technique. By making use of the results, the stress intensity factors (or singularity coefficients) of a crack (or rigid line inclusion) are given. Stress distribution and displacement field are shown by many graphical representations as several numerical examples. The previous results published by several authors can be included as particular cases of our solutions.