I (David Bushnell) set up a case called “zoelly” and ran (using BIGBOSOR4) the linear buckling option (INDIC=1) for an elastic monocoque spherical hemisphere under uniform external pressure. Boundary conditions applied at the equator of the hemisphere are symmetry, with a special modification (circumferential displacement v = 0) applied only for n = 0 and n = 1 circumferential waves in order to prevent rigid body modes.
The radius of the hemisphere is r = 100 inches, and the thickness, t = 1.0 inch. The elastic modulus E is set equal to 16522.712 psi, and the Poisson ratio is 0.3. The external pressure, p = 1.0 psi. These specifications, along with the Zoelly formula, appear in this slide) . The string, “N_0”, means n = 0 circumferential waves (axisymmetric buckling). The elastic modulus E is set equal to 16522.712 psi so that the buckling load factors will be close to 2.0, provided that the BIGBOSOR4 model predicts “classical” buckling approximately according to the Zoelly formula.
In a survey of buckling load factors for n = 0 to n = 19 circumferential waves it is found that the predictions from BIGBOSOR4 are in good agreement with the Zoelly formula (buckling pressure independent of n). The buckling mode shown in this slide resembles that shown in PICTURE (b) of the previous slide except that in this slide the sign of the buckling mode is the opposite of that shown in PICTURE (b) of the previous slide.
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