# STRESS CONCENTRATION FACTORS IN THICK WALLED CYLINDERS WITH ELLIPTICAL CROSS-BORES

### Abstract

Computer simulations were conducted to determine the elastic stress concentration factors in the vicinity of

an elliptical cross-bore in a closed ended thick walled cylinder. The orientation of the elliptical cross-bore

with respect to the meridional plane was varied. Various cross-bore to cylinder bore radius ratios and

various geometries of the elliptical cross-bore were investigated. A three-dimensional finite element method

(FEM) computer programme in FORTRAN code was developed and used to carry out the investigations. The

displacement formulation was used. Cylinder geometries of thickness ratios k = 2.0, 2.25 and 2.5 were

considered. Cylinder length was taken to be 9 times the wall thickness to avoid the end effects. The

maximum stress concentration factor was experienced when the major axis of the elliptical cross-bore lay in

the meridional plane. The minimum stress concentration factor was experienced when the major axis of the

elliptical cross-bore lay in the transverse plane. For an elliptical cross-bore of cross-sectional area equivalent

to that of a circular cross-bore of cross-bore to cylinder bore radius ratio of d = 0.15, the stress concentration

factor (SCF) was a constant at 2.1 for angle of rotation (AOR) of 74.5°. For an elliptical cross-bore of crosssectional

area equivalent to that of a circular cross-bore of d = 0.20, the SCF was a constant at 2.1 for AOR =

73°. For an elliptical cross-bore of cross-sectional area equivalent to that of a circular cross-bore of d = 0.25,

the SCF was a constant at 2.1 for AOR = 72.5°. When the elliptical cross-bore had its major axis perpendicular

to the cylinder axis the SCF was a minimum, i.e., 2.0 and below. The SCF for a circular cross-bore was 3.0.

Therefore an elliptical cross-bore offered the lowest SCF when compared to a circular cross-bore. The

information on SCF constants obtained will enable quick design of thick walled cylinders with elliptical crossbore.