2. Benchmark solution

2.1. Calculation method

The formulas used are from BPEL 83. They are also found in NFEN1992 -1-1 October 2005, AFCEN ETC -C2010, with a few small variations.

\({\mathrm{\sigma }}_{p}\left(x\right)={\mathrm{\sigma }}_{\mathit{pi}}\left(x\right)\left(1.0\phantom{\rule{2em}{0ex}}-\phantom{\rule{2em}{0ex}}\mathrm{\Delta }{\mathrm{\sigma }}_{p}\left(\mathrm{\mu },t\right)\right)\)

\(\mathrm{\Delta }{\mathrm{\sigma }}_{p}\left(\mathrm{\mu },t\right)={k}_{1}.{\mathrm{\rho }}_{1000}{\left(\frac{t}{1000}\right)}^{\frac{3}{4}\left(1-\mathrm{\mu }\right)}.{e}^{\frac{10\mathrm{\mu }-7.5}{{k}_{2}}}\) with \(\mathrm{\mu }=\frac{{\mathrm{\sigma }}_{\mathit{pi}}\left(x\right)}{{f}_{\mathit{prg}}}\), \(t\) is in hours.

To be able to apply these formulas, the deformation must remain constant. \({\mathrm{\sigma }}_{\mathit{pi}}\) is the initial stress that corresponds to the initial deformation.

Validation will therefore be done on the “a” and “b” models, with these formulas. The test case “c” will be a non-regression test case because we simulate retension of the cable, so the deformation will vary over time.

2.2. Reference quantities and results

The quantity tested will be the stress in the cable, at various times.

2.3. Uncertainty about the solution

No uncertainty, the reference solution is analytical.

2.4. Bibliographical references

beep [1] BPEL.

NF-EN-1992 [2] NF EN 1992-1-1 October 2005.

afcen [3] AFCEN ETC -C 2010.