2. Benchmark solution

The analytical reference solution is determined by the theory of beams.

We consider a freestanding embedded beam. The geometric characteristics are those defined in paragraph [§2.1]. The prestressed cable applies a normal compression force \((\mathrm{-}F;\mathrm{0 };0)\) and a bending moment \((\mathrm{0 };–\mathit{eF};0)\) to the free end.

The solution to this problem is as follows:

Stress tensor:

with

Travel:

with the boundary conditions:

When the effects of Poisson are overlooked (

), the travel solution is simplified as follows:

The numerical reference values are calculated using the analytical expressions above, using for \(F\) the overall equilibrium value of the normal force in the cable: