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Buckling modes as a function of Cassini ovaloidal shape

This slide is from the same paper as the previous slide.

kc = c/a is a dimensional parameter. The meridian shape of the shell depends on the value of this parameter. The following cases are possible:
• 0 < kc < 1/√2 – convex meridian,
• kc = 1/√2 – plano-convex meridian,
• 1/√2 < kc < 1 – concavo-convex meridian.

in which the Cassini shape is given by:
r(x) = y(x) = sqrt[sqrt(4c2x2 + a2) − (c2 + x2)]

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