2. Reference solution

2.1. Calculation method used for the reference solution

Finite element calculation with Samcef Version 7.0 (Mecanl).

2.2. Reference solution

Variation of tensions on the skin along the meridian section for internal pressure \({p}_{0}\) [bib2]

Variation of tensions on the skin along the meridian section in the vicinity of the ruin for internal pressure \({p}_{\mathrm{max}}\) [bib2]

Variation in azimuthal stress \({\sigma }_{\theta \theta }\) on the upper skin along the meridian section in the vicinity of the ruin for internal pressure \({p}_{\mathrm{max}}\) . Geometric linear calculation.

Variation in azimuthal stress \({\sigma }_{\theta \theta }\) on the lower skin along the meridian section in the vicinity of the ruin for internal pressure \({p}_{\mathrm{max}}\) . Geometric linear calculation.

Variation in azimuthal stress \({\sigma }_{\theta \theta }\) on the upper skin along the meridian section in the vicinity of the ruin for internal pressure \({p}_{\mathrm{max}}\) . Geometric nonlinear calculation.

Variation in azimuthal stress \({\sigma }_{\theta \theta }\) on the lower skin along the meridian section in the vicinity of the ruin for internal pressure \({p}_{\mathrm{max}}\) . Geometric nonlinear calculation.

Discretization used for the reference solution. Definition of axes

Geometric nonlinear calculation: \(\mathrm{pression}={p}_{\mathrm{max}}\)

Skin	Meridian length \((\mathrm{inch})\)	Knot position
	0.0	1	26.223
Superior	46.298	73	—26.688
	137.9	137	24.103
	0.0	1	25.231
	16.491	27	27.909
Lower	35.518	57	—12.711
	52.707	87	—8.1652
	134.76	137	25.103

Geometric linear calculation: \(\mathrm{pression}={p}_{\mathrm{max}}\)

Skin	Meridian length \((\mathrm{inch})\)	Knot position
	0.0	1	26.2
Superior	45.1	71	—30.7
	138	137	24.0
	0.0	1	25.231
	22.833	37	29.899
Inferior	32.981	53	—16.127
	52.707	87	—13,756
	134.76	137	25.008

Movement field (point \(A\) , lower skin)

Calculus… geometric	Meridian length \((\mathrm{inch})\)	Node position	Pressure	Displacement \({U}^{Z}\) \((\mathrm{inch})\)
Linear	0.0	1	\(0.5\mathrm{pmax}\)	0.100945
	0.0	1	\(\mathrm{pmax}\)	0.370468
Nonlinear	0.0	1	1	\(0.5\mathrm{pmax}\)	0.0990524
	0.0	1	\(\mathrm{pmax}\)	0.244347

2.3. Uncertainty about the solution

Uncertainty less than \(\text{2 \%}\) (linear regime), less than \(\text{5 \%}\) (elasto-plastic regime).

2.4. Bibliographical references

• LARSEN, P.K., POPOV, E.P., E.P., Elastic-plastic analysis of thick-walled pressure vessels with sharp discontinuities, Trans. ASME Applied Mechanics, pp 1016-1019, 1971

• NYSSEN, C., Finite element modeling of the nonlinear behavior of aerospace structures, doctoral thesis, University of Liège, 1979