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Formula for buckling pressure of an elastic, perfect spherical shell

E = Young's modulus
h = uniform thickness
R = radius
nu = Poisson ratio

From:
Zoelly, R., 1915. Ueber ein Knickungaproblem and der Kugelschale. Thesis, Zurich, Switzerland.

NOTE: Actual spherical shells that have small imperfections buckle at a much, much lower pressure than the "classical" buckling pressure given by this formula. For example, see the second and third slide after this slide.

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