1. Reference problem#

1.1. Geometry#

Piping bent in plane \(\mathrm{XY}\). The straight sections are \(L=1m\) in length.

The radius of curvature of the elbow is: \({R}_{c}=1.25m\)

The tubular section has an average radius \({r}_{\mathit{moy}}=395.5\mathit{mm}\) and a thickness \(e=\mathrm{77mm}\).

1.2. Material properties#

The material is elastoplastic with isotropic linear work hardening.

\(E=2.E11\mathrm{Pa}\)

\(\nu =0.3\)

Elasticity limit \(\mathrm{SIGY}={200.10}^{6}\mathrm{Pa}\)

Work hardening module \(\text{D\_SIGM\_EPSI}={2.10}^{10}\mathrm{Pa}\)

1.3. Boundary conditions and loads#

Embedding in \(A\) (blocked beam degrees of freedom, but free ovalization degrees of freedom).

Moment \(\mathrm{MZ}\) imposed in growing \(D\):

Increment 1

\(\mathrm{Mz}=3086702.1520853\mathrm{Nm}\)

10 equal increments up to:

1.4. Initial conditions#

Not applicable.