1. Reference problem#
1.1. Geometry#
We consider a rectangular structure with dimensions \(L\mathrm{=}\mathrm{5m}\) along \((\mathrm{0x})\) and \(l\mathrm{=}\mathrm{1m}\) along \((\mathrm{0y})\).
The coordinates of the points are given in the following table:
Point |
\(A\) |
|
|
|
|
|
|
Abscissa (\(m\)) |
0 |
0 |
5 |
5 |
0 |
1.875 |
1.875 |
Ordered (\(m\)) |
0 |
0 |
0 |
1 |
1 |
0.5 |
0 |
1.2. Material properties#
Only the material parameters on which the solution depends are given here, knowing that the command file contains other data that play no role in the solution of the problem at hand.
Liquid water |
\(\rho\): density (\({\mathrm{kg.m}}^{-3}\)) |
1000 |
Material coefficients |
\(r\): homogenized density (\({\mathrm{kg.m}}^{-3}\)) \(E\): Young’s modulus (\(\mathrm{Pa}\)) \(\nu\): Poisson’s ratio (–) \(b\): Biot coefficient (—) |
1600 225,000,000 0.4 1 |
Constants |
\({P}_{0}\): atmospheric pressure (\(\mathrm{Pa}\)) \(g\): acceleration due to gravity (\({m}^{2.}{s}^{-1}\)) |
100000 10 |
1.3. Boundary conditions and loads#
On \([\mathrm{AD}]\), conditions \({u}_{x}={u}_{y}=0\) and \(\mathrm{M.n}=0\) are imposed.
On \([\mathrm{AB}]\), conditions \({u}_{y}=0\) and \(\mathrm{M.n}=0\) are imposed.
On \([\mathrm{DC}]\), conditions \({u}_{y}=0\) and \(\mathrm{M.n}=0\) are imposed.
On \([\mathrm{BC}]\), conditions \(\sigma \cdot n=0\) and \(p={P}_{0}=100000\mathrm{Pa}\) are imposed.
We assume gravity oriented along the \((\mathrm{0x})\) axis such as \(\overrightarrow{g}=-g\overrightarrow{x}\).