Stress Analysis Of Isotropic Plate Having Few Openings

Abstract

In order to facilitate certain operations holes and openings are made in structures and machine components. These discontinuities are weakening agent for the structure or machine. In order to predict failure of the component and to arrive at life assessment of the structure/machine component, the stress field around such hole must be known under different loading conditions. Here an attempt is made to obtain generalized solution for regular and irregular (chemically eroded) hole using Muskhelishvili’s complex variable method. The area outside the given hole is mapped conformaly to the area out side the unit circle in ζ-plane and Cauchy’s integrals are evaluated to obtain generalised stress functions. General solutions thus obtained are coded in MATLAB 6.5. The different loading conditions considered here includes uniaxial tension, hydrostatic tension, shear at infinity and internal pressure and internal shear at hole boundary. The von Mises stress, tangential, radial and shear stress distribution is presented in polar coordinate. Plane stress finite element model for some cases are presented and results are compared with present method. The results are in close conformation.