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 cross-sectional 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 cross-bore.