Stress analysis at knuckle of variable thickness in torispherical end vessels using axisymmetric shell finite element

This paper presents minimization of stress concentration in cylindrical pressure vessels with torispherical heads by employing variable thickness in the knuckle region. If uniform thickness is used, the stress field in the knuckle region controls the design, as stress concentration occurs in this region. The ratio of crown radius to knuckle radius and the thickness ratio of the crown or cylinder to thickness at the mid position of the knuckle (7) are used as geometric parameters. Each ratio of crown to knuckle radii (β= R d/Rk has five sets of knuckle to cylinder thickness ratio (γ = hk/hc)· The variable thickness in knuckle region was obtained by B-spline curve method. Using two nodes axisym-metric shell finite elements, the analysis is carried out for 35 cases with different values of β and γ when subjected to uniform internal pressure. The results are presented in the form of stress indices of axial, hoop and von Mises stresses at inner and outer surfaces and the deformation for each value of β. The intensity of hoop and axial stresses and the displacement are considerably reduced at the knuckle portion when γ is varying from lower value (γ = 1.0) to higher value (γ = 3) by this method.