1. Reference problem#
1.1. Geometry#
The geometry used in this test case is a reinforced concrete plate with a thickness of \(e=0.1\text{m}\) and a length of \(l=1\text{m}\).
Figure 1.1-a : Geometry studied
The characteristics of the steel sheets of the reinforced concrete plate are:
Upper sheet: section per linear meter \(=0.05{m}^{\mathrm{²}}/\mathrm{ml}\); eccentricity with respect to the middle sheet: \(+0.03m\),
Lower sheet: section per linear meter \(=0.05{m}^{\mathrm{²}}/\mathrm{ml}\); eccentricity compared to the middle sheet: \(–0.03m\).
1.2. Material properties#
The material characteristics for multi-layer concrete modeling with steel reinforcements (DKT and GRILLE_EXCENTRE) are summarized in the following table.
Modeling |
Young Module \(N/{m}^{\mathrm{²}}\) |
Fish Coefficient |
Density \(\mathrm{kg}/{m}^{3}\) |
Concrete (plate DKT) |
|
0.0 |
2500 |
Steel (GRILLE_EXCENTRE) |
|
0.0 |
7800 |
1.3. Boundary conditions and loads#
On the \(A\) (\(\mathrm{B0X}\)) side of the plate are embedded the movements \({u}_{x}={u}_{y}={u}_{z}=0\), as well as the rotations \({\theta }_{x}={\theta }_{y}={\theta }_{z}=0\). During the modal calculation, displacement \({u}_{y}=0\) is blocked everywhere on the plate. A linear force is applied to the \(\mathrm{B1X}\) side (side opposite \(\mathrm{B0X}\)) in the direction \((0.0\mathrm{,0}.0\mathrm{,1}\mathrm{,0})\) and depends on the value \({F}_{0}={10}^{6}N\).
In the case of dynamic calculation, a sinusoidal linear force is applied on the \(\mathrm{B1X}\) side in the \((0.0\mathrm{,0}.0\mathrm{,1}.0)\) direction. The sine wave frequency is \(20\mathrm{Hz}\). The duration of the request is \(\mathrm{0,1}s\).
1.4. Initial conditions#
In the initial state, displacements and speeds are zero everywhere.