1. Reference problem

1.1. Geometry

A rectangular parallelepiped modeling concrete, and a line included in this volume modeling the prestress cable:

All dimensions are in meters. The cross-sectional area of the cable is \(A=0.00015{m}^{2}\) The cable is parallel to the \(x\) axis. Its intersection with plane \((\mathrm{Oyz})\) is defined by point \((1.,0.3)\).

1.2. Material properties

\(E=2.1{10}^{11}\mathrm{Pa}\) for cable, and \(E={3.10}^{10}\mathrm{Pa}\) for concrete.

\({\rho }_{c}=2{10}^{4}\mathrm{kg}/{m}^{3}\) for cable, and for concrete, \({\rho }_{b}=3\mathrm{kg}/{m}^{3}\) (non-physical values intended to make the weight of the cable preponderant)

1.3. Boundary conditions and loads

\(\mathrm{DY}=0\) at point \(1001\), \(\mathrm{DZ}=0\) for all nodes on face \(z=0\), and \(\mathrm{DX}=0\) for all nodes on face \(x=0\).

A single load is applied: gravity, with \(g=10m/{s}^{2}\), successively in the direction \(–z\) then \(–x\).

There is also an initial voltage in cable \(N=2.{10}^{5}N\).