Stress concentration around a cylindrical hole in arbitrary thick plates

Based on the Kane-Mindlin plate theory, a stress function method is used to investigate the stress concentration around a cylindrical hole in elastic plates of arbitrary thickness. An explicit formula for stress concentration factor K is obtained. The effects of hole radius, plate thickness and materials properties are discussed. It is found that K in a finite thick plate is greater than that in both plane stress and plane strain states. As the ratio of plate thickness over hole radius, B/R, increasing from zero to infinity, K increases from its plane stress value to a peak value, and then decreases monotonously to its plane value again when the limit of plane strain is approached. The results also show that Poisson's ratio has strong effect on stress concentration factors, while no effect of the elastic modulus of the material can be found. Comparison of the present solution with three-dimensional finite element results from ANSYS 5.4 shows good agreement.