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Let’s say I have an irregularly shaped bearing with a cross section that looks like the angled surface of a conical frustum, shown below.

enter image description here

If a bending moment is applied which causes the inside diameter to ‘cave outwards’, how would I perform a static loading failure analysis to see at what bending moment the shape would cave outwards? How would I determine the second moment of area and distance from centroid values required to apply the bending stress formula sigma = My/I? Or is there a manufacturing method in the form of some sheet metal bending formula that would be more helpful in looking at failure mode in a cylindrical cross section instead of a planar one.

EDIT: The end goal is to have the curved surface completely vertical, as if it was the surface area of a rod. If there is an easier method of calculating the forces required, let me know!

juggling_pro
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This is a typical case of stresses on shells and plates and obviously lends itself to analyzing using polar coordinates.

If your element is a thin shell and is loaded in a way that only membrane stresses are involved there are some formulas in references such as Roark's formulas for stress and strain. Otherwise you may need to use FEM and define your loading.

kamran
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