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Table 3 Sphere under external pressure: the calculated buckling loads for the different cases

From: Modeling elastic-plastic buckling of sandwich axisymmetric shells: on the limits of "shell" models and analytical solutions

Overall β COQMULT r sphere QUA8 Ratio
thickness   P cr P euler E = 200000 solution P cr P euler E = 200000 QUA8/
(mm)      COQMULT
3 0.0001 0.80 0.80 0.022 0.30
3 0.001 0.80 0.80 0.0 0.56
3 0.01 0.80 0.80 0.256 0.94
3 0.1 0.82 0.82 0.82 0.99
3 1. 1.00 1.0 1.00 1.00
11 0.0001 0.286 0.286 0.022 0.078
11 0.001 0.286 0.286 0.073 0.25
11 0.01 0.294 0.294 0.257 0.87
11 0.1 0.364 0.364 0.369 0.98
11 1. 1.00 1.0 1.00 0.996
51 0.0001 0.065 0.065 0.0015 0.023
51 0.001 0.066 0.066 0.0092 0.13
51 0.01 0.075 0.075 0.066 0.85
51 0.1 0.160 0.160 0.165 0.97
51 1. 1.00 1.0 1.00 0.96