Stress in ellipsoidal head of pressure vessel DANotes.xlsx

The stresses in a pressurised thin axisymmetric shell of revolution is considered so that the behaviour of dished ends can be appreciated. The shell is formed conceptually by rotating the meridian, a curved line of selected shape lying in the r-z meridional plane, about the z-axis. The resulting surface of revolution is has a uniform thickness and the resulting shell is loaded by an internal pressure p. These shells are similar to thin cylinders in that radial stresses are negligible and the membrane stresses are calculated in two orthoginal directions:

• the circumferential or hoop stress
• the meridional stress (analogous to axial stress in cylinder theory)

A alternative calculation method is available here.

This calculation was very useful in understanding the deflection and stresses in a pressure vessel head finite element model (see below). ExcelCalcs Consultancy services available here.

Calculation Reference
Pressure Vessel Design Manual, Moss

Stresses In Plates and Shells

Pressure Vessel Handbook

Shells of Revolution