Modeling elastic-plastic buckling of sandwich axisymmetric shells: on the limits of

Advanced Modeling and Simulation in Engineering Sciences

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

Overall	β	COQMULT	r _sphere	QUA8	Ratio
thickness		$\frac{P_{cr}}{P_{euler}^{E = 200000}}$	solution	$\frac{P_{cr}}{P_{euler}^{E = 200000}}$	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