Integral Equations Solution for Reinforced Mode I Cracks Opened by Internal Pressure

Abstract

The problem of a series of collinear Mode I cracks loaded by a uniform internal pressure is solved by an integral equations technique. By superimposing the solution for an arbitrarily loaded Mode I crack with the solution for an edge loaded infinite strip, a system of integral equations is developed by making the superposition satisfy the required boundary conditions. Solving the integral equations by a least-squares Ritz method gives boundary values which may then be used with the Green’s functions solutions to calculate stress intensity factors for the cracks and the stress and displacement fields in the reinforcement and the cracked regions. By changing the boundary conditions at the reinforcement interface, integral equations modeling other situations such as imperfect bonding may be obtained.