IMPROVED HYBRID SOLID ELEMENT WITH A TRACTION-FREE CYLINDRICAL SURFACE

New 8‐node solid elements with two parallel faces and one traction‐free cylindrical surface are derived using the assumed stress hybrid model. Six new expressions of stress components are developed by using four stress functions and cylindrical co‐ordinates, so that the normal stress σz on the plane perpendicular to the two parallel faces varies as a parabola, and the assumed stress field satisfies the equilibrium equations as well as the traction‐free conditions over the cylindrical boundary. The assumed stress field also satisfies the compatibility conditions when the new element is degenerated into the 2‐dimensional case. Examples have clearly demonstrated that these present special elements are far superior in predicting the stress concentration factors, the distributions of circumferential stresses and the normal stress σz. Copyright © 1990 John Wiley & Sons, Ltd