2. Benchmark solution

2.1. Calculation method used for the reference solution

A loading path is reproduced on an element in each of the 3 domains (elastic, plastic, limit) of a unidirectional behavior relationship (local direction \(y\)). The parameters are described in the attached Figure 1.

The charging path comprises 12 steps defined as follows:

2.2. Benchmark results

Direct calculations on the limit curve of the behavioral relationship:

\({F}_{y}={k}_{\mathrm{el}}\cdot {U}_{y}\) if \({U}_{y}<{d}_{e}\)

\({F}_{y}={k}_{\mathrm{el}}\cdot {d}_{e}+{k}_{\mathrm{pl}}({U}_{y}-{d}_{e})\) if \({U}_{y}\in \left[{d}_{e},{d}_{l}\right]\)

\(\begin{array}{}\mathrm{Vari}={U}_{y}-{d}_{e}\\ \mathrm{Varimax}={d}_{l}-{d}_{e}\end{array}\)

\({F}_{y}={k}_{\mathrm{el}}\cdot {d}_{e}+{k}_{\mathrm{pl}}({d}_{l}-{d}_{e})+{k}_{G}({U}_{y}-{d}_{l})\) if \(\mathrm{Vari}=\mathrm{Varimax}\)

2.3. Uncertainty about the solution

Exact solution: \(\mathrm{Fy}\) imposed and \(\mathrm{Uy}\) deduced directly from relationships in [§2.2].

2.4. Bibliographical references

Note HM-77/94/368, G. DEVESA. « Dynamic study of conductor failure and frost discharge on an experimental medium voltage line ».