Effect of the Type of Load at Infinity over Circular Discontinuity in Elastic Regime: A Theoretical Review

A comprehensive review on the methodology to obtain two dimensional stress field around a
discontinuity in the form of a circular hole in the plate subjected to various types of, uniform,
axisymmetric and non-axisymmetric monotonic loads at infinity viz. uni-axial tensile, equal bi-axial
(tensile-tensile and tensile-compressive) and pure shear is presented with the help of the basic
principles of elasticity. The material of the plate is considered to be homogenous, isotropic and linear
elastic. Effect of the difference in the type of far field load over the nature and the magnitude of stress
fields is examined. Fundamental bi-harmonic equation involving Airy’s stress function is used. The
stress function, determined by assuming it in the form of trigonometric series and by employing
suitable mathematical substitutions, is made to satisfy the bi-harmonic equation. Constants of the
stress function are found from the boundary conditions. Stress concentrations at the surface of the
hole and at locations away from the hole are obtained for all the investigated load cases. Stress
solutions in cases of bi-axial loads of un-identical magnitudes are also presented.