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# Principal Stress of a 2:1 Ellipsoid

## Principal Stress of a 2:1 Ellipsoid

(OP)
Hello,
I am currently carrying out an FEA study using ANSYS of a cylindrical pressure vessel with an ellipsoidal head, in order to verify the results produced by ANSYS I want to do the hand calcs, however can not find equations for the max principal stress of an internally pressurised ellipsoid. Any help would be greatly appreciated.
The vessel is made from 304L stainless steel, For this specific grade of stainless steel, the density is 7900 kg/m^3, with a Young’s Modulus of 198 GPa, yield stress of 243 MPa, and ultimate tensile stress of 546 MPa.
The maximum internal radius is 1070mm, the minimum internal radius is 535mm and the thickness is 30mm. The vessel will be subject to an internal pressure of 1MPa.
Thanks in advance for any help, this has been driving me crazy, and I have joined this forum solely to ask this question 🤣

### RE: Principal Stress of a 2:1 Ellipsoid

Timoshenko discusses elliptical heads to some extent in Theory of Plates and Shells. Just glancing through there, he comes up with membrane solutions out in the head and allowances for continuity stresses at the head-to-cylinder junction. I don't know that those results would necessarily be that useful for your application. That is, if you do your analysis right and he did his derivations right, I would expect you might still have considerable variations between the two, so it'd be hard to verify anything.

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