2. Benchmark solution#

2.1. Calculation method used for the reference solution#

For this test, we will use two reference solutions, one experimental, resulting from the work of Schwaighofer and Microys [bib2], the other drawn from the work of Batoz in deep shell theory [bib1].

2.2. Benchmark results#

The baseline results are as follows:

Short Cylinder (A and B)	Batoz [bib1]	Experience [bib2]
Move \(w\) to point \(F\)	\(0.35{10}^{\mathrm{-}4}m\)	\(0.6{10}^{\mathrm{-}4}m\)
Move \(w\) to point \(C\)	\(–0.710–3m\)	\(–0.6{10}^{\mathrm{-}3}m\)
Move \(w\) to point \(D\)	\(0.25{10}^{\mathrm{-}4}m\)	\(0.1{10}^{\mathrm{-}3}m\)
Constraint \({\sigma }_{\mathrm{xx}}\) at point \(F\)	\(–0.35\mathit{MPa}\)	\(–0.325\mathit{MPa}\)
Constraint \({\sigma }_{\mathrm{yy}}\) at point \(F\)	\(0.50\mathit{MPa}\)	\(0.60\mathit{MPa}\)

Long Cylinder (C and D)	Batoz [bib1]	Experience [bib2]
Move \(w\) to point \(F\)	\(1.32{10}^{\mathrm{-}3}m\)	\(1.35{10}^{\mathrm{-}3}m\)
Move \(w\) to point \(C\)	\(–2.45{10}^{\mathrm{-}3}m\)	\(–2.46{10}^{\mathrm{-}3}m\)
Move \(w\) to point \(D\)	\(–0.35{10}^{\mathrm{-}3}m\)	\(–0.51{10}^{\mathrm{-}3}m\)
Constraint \({\sigma }_{\mathrm{xx}}\) at point \(F\)	\(1.68\mathit{MPa}\)	\(1.9\mathit{MPa}\)
Constraint \({\sigma }_{\mathrm{yy}}\) at point \(F\)	\(1.8\mathit{MPa}\)	\(1.55\mathit{MPa}\)

2.3. Uncertainties about the solution#

Around 5% for the Batoz solution, probably much more — around 30% - for the experimental solution.

2.4. Bibliographical references#

BATOZ J.L., DHATT G.: Modeling structures by finite elements, Vol. 3, Shells, HERMES.
SCHWAIGHOFER J., MICROYS H.F.: Orthotropic Cylindrical shells under line load, Journal of Applied Mechanics, June 1979, Vol. 46.
GEOFFROY P., Development and evaluation of a finite element for the static and dynamic nonlinear analysis of thin shells, PhD Thesis, Compiègne University of Technology, 27/04/83.