Elliptical head transition zone
Thread Content
There is instability in the transition zone of the elliptical head; under negative pressure, does this instability exacerbate the situation or counteract it? Could someone please explain this? Images would be great, thank you
Under internal pressure, elliptical heads exhibit a \"tendency to become circular\", while under external pressure they show a \"tendency to become flatter\"; this causes circumferential tensile membrane stresses to arise in the transition zone of the head, with no instability issue. However, compressive membrane stresses exist in its \"spherical portion\", just like in a shell under external pressure; therefore, stability calculations must be performed using the shell theory. For elliptical heads, it is necessary to calculate the equivalent shell radius of their “spherical portion”.
Thank you for your answer. Under internal pressure, the middle part bulges outward to become rounded, while the transition zone flattens inward； And under external pressure, does the transition zone become more flattened, thereby increasing the stress further?
You have ignored the role of the cylinder. Take a close look at the stress analysis section of the pressure vessel training materials; you’ll understand it then.
Thank you for the reply. It would have been better to answer my question directly; I’ll take a look at the books you mentioned later
The external pressure stability check for elliptical heads is performed on their spherical portion. Because the deformation of an elliptical head under external pressure is the opposite of that under internal pressure, external pressure causes the long axis of the head to elongate while the short axis shortens. The elongation of the long axis increases the circumferential diameter of the transition zone, leading to an increase in its circumference and thus the generation of tensile stress in the circumferential direction; therefore, there is no issue of circumferential instability in the transition zone. Therefore, under external pressure, there is no need to check the stability of the transition zone in an elliptical head. However, circumferential and radial compressive stresses are generated in the spherical portion at the center of the head, leading to instability issues; therefore, the external pressure stability verification for an elliptical head involves checking its spherical portion. If the original poster has time, they might want to take a look at pages P105-P108 written by Qi Guosheng and Duan Rui; the analysis there is quite good.
Under internal pressure, stretching occurs； Under external pressure, compression occurs, and instability is exacerbated