2. Benchmark solution

2.1. Calculation method used for the reference solution

The reference solution was obtained with a finite shell element DKT24 (4x6 mesh) at 4 nodes with 6 degrees of freedom per node in Total Lagrangian Formulation. This solution is described in detail in [bib2].

2.2. Benchmark results

\({W}_{A}\) \(\times {10}^{-\mathrm{3m}}\)	Charge \(P\) (\(\mathrm{KN}\))	Charge \(P/\mathrm{Pmax}\)		\({W}_{A}\) \(\times {10}^{-\mathrm{3m}}\)	Charge \(P\) (\(\mathrm{KN}\))	Charge \(P/\mathrm{Pmax}\)		\({W}_{A}\) \(\times {10}^{-\mathrm{3m}}\)	Charge \(P\) (\(\mathrm{KN}\))	Charge \(P/\mathrm{Pmax}\)
0.0	0.000	0.0000		0.0000		—16.4	0.480	0.8000		—14.0	—0.295	—0.295	—0.295	—0.295	—0.4916
—1.7	0.150	0.2500		0.2500		—16.7	0.415	0.6916		—14.3	—0.345	—0.345	—0.345	—0.345	—0.5750
—3.5	0.265	0.4416		0.4416		—16.9	0.350	0.5833		—15.0	—0.370	—0.370	—0.370	—0.6166
—4.9	0.345	0.5750		—17.0	—17.0	0.290	0.4833		—16.1	—16.1	—0.380	—0.380	—0.6333
—6.8	0.410	0.6833		0.6833		—17.3	0.375	—0.375	—0.375	—0.375	—0.6250
—8.4	0.475	0.7916		—7916		—17.1	0.150	0.2500		—18.7	—0.350	—0.350	—0.350	—0.350	—0.350	—0.350	—0.350	—0.350	—0.5833
—9.8	0.520	0.8666			—17.0	0.090	0.1500		—20.3	—0.3	—0.305	—0.305	—0.305	—0.5083
—11.1	0.555	0.9250		9250		—16.8	—16.8	—0.230	—0.230	—0.230	—0.3833
—12.2	0.580	0.9666		—666		—16.4	—0.035	—0.0583		—23.5	—23.5	—0.120	—0.120	—0.2000
—13.1	0.595	0.9916		0.9916		—16.0	—0.085	—0.1416		—25.2	0.025	0.025	0.0416
—14.0	0.600	1.0000		1.0000		—15.3	—0.130	—0.2166		—26.8	1.0000	0.210	0.210	0.3500
—14.9	0.585	0.9750		0.9750		—14.8	—0.155	—0.2583		—28.5	0.9750	0.445	0.445	0.7416
—15.5	0.565	0.9416			—14.2	—0.195	—0.3250
—16.1	0.525	0.8750		—8750		—14.0	—0.240	—0.4000

2.3. Uncertainty about the solution

Less than 2%, digital solution

2.4. Bibliographical references

1. HAMMADI Fodil: Formulation and evaluation of finite elements with C° continuity of geometry for the linear and non-linear analysis of shells.

2. JAAMEI S.,: Study of various Lagrangian formulations for the nonlinear analysis of thin elasto-plastic plates and shells in large displacements and rotations, Doctoral thesis, University of Technology of Compiègne 1986.