Stress Concentration Around a Patched Hole in an Axi-Symmetrically Loaded Plate

摘要

This paper examines the efficiency of an adhesively bonded reinforcement patch in reducing the stress concentration around a hole in a plate, as a function of hole size. Differential equations are derived for the radial and tangential displacements in the plate and reinforcement assuming only in plane stresses without out of plane bending. Imposition of angular independence leads to distinct load transfer lengths for radial and tangential adhesive shear (beta(gamma)-1 and beta(theta)-1 respectively), and zero tangential displacement reduces the problem to a patched circular hole with axisymmetric loading. Four boundary conditions permitted analytic solutions in terms of modified Bessel functions. A stress concentration factor (SCF) is defined as the tangential stress in the plate at the hole boundary, compared to that far away in the plate but still under the reinforcement. Plotting SCF against hole radius normalised by Beta(gamma)-1 leads to an analytic function with a single (non-dimensional) parameter h, depending on the thicknesses and moduli of the components. SCF approaches two in the limit of small holes indicating that the reinforcement is ineffective in that limit. SCF approaches 1/h in the large hole limit. For the typical repair geometry where h approximately equal 1, SCF falls to 1.6 when the hole radius reaches beta(gamma) -1, and 1.3 by 3beta(gamma)-1. The related problem of a circular reinforcement bonded on a large (unholed) plate is briefly examined. This indicates how the normalisation stress for SCF relates to that applied beyond the patch.