1. Reference problem#

1.1. Geometry#

A cable of length \(2{l}_{0}\) at rest, in the direction \(x\), is subjected to its own weight (gravity in direction \(-Z\)). It is embedded at the \(O\) and \(B\) ends, which are themselves distant from \(\mathrm{2L}\).

_images/1000000000000192000000759F942EEEF5F0D230.png

Initially, \(2{l}_{0}=2L=\mathrm{325m}\)

The cable cross-sectional area is: \(2.2783E-04{m}^{2}\)

1.2. Material properties#

\(E=5.70E+10\mathrm{Pa}\)

\(\nu =0.3\) (B modeling only)

\(\mathrm{ALPHA}:2.3E-5{K}^{-1}\)

\(\mathrm{RHO}:2.844230E+03\mathrm{kg}/{m}^{3}\)

1.3. Boundary conditions and loads#

Embedding in \(O\) and \(B\)

Gravity: \((9.81\mathrm{,0}.0\mathrm{,0}.0,-1.0)\)

The temperature in the cable varies over time, the reference temperature is \(0.°C\).

  • Instant: 0. Temperature \(T=0.°C\)

  • Instant: 1.Temperature \(T=39.26°C\)

We therefore treat:

  • at instant 0, a cable subject to its own weight alone

  • at instant 1, a heavy cable subjected to thermal expansion.