1. Reference problem

1.1. Geometry

The cylinder has an inner radius \({R}_{1}=10m\), an outer radius \({R}_{2}=20m\), a height \(h\mathrm{=}1m\). The circumferential frame has a cross section per unit length of \(e=1{m}^{2}/\mathrm{ml}\).

1.2. Material properties

The material characteristics of concrete (hollow cylinder) are \(E=2E+10\mathrm{Pa}\) and \(\nu =0.2\); those of steel (circumferential reinforcement) \(E=2E+11\mathrm{Pa}\), \(\nu =0\), \({E}_{t}=2.E+09\) (tangent module), \({\sigma }_{y}=2.E+11\mathrm{Pa}\) (very high plasticity constraint to remain in the elastic domain).

The reinforcing sheet has its main vertical direction and a cross section per linear meter of \(1m\).

1.3. Boundary conditions and loading

We are only interested in an angular section of the cylinder.

The following conditions are imposed:

1. a zero normal displacement on the lateral faces of the angular cylinder section (\(\mathrm{SG}\) and \(\mathrm{SD}\) in the schematic figure) (zero ortho-radial displacement)

2. zero vertical displacement on the bottom face of the cylinder section (simple support)

3. an imposed pressure of \({10}^{6}\mathrm{Pa}\) on the inner face of the cylinder section (\(\mathrm{SI}\)) (in the schematic figure) (internal pressure)

Schematic designation of cylinder surfaces