1. Reference problem#
1.1. Geometry#
Side of the plate (square) \(a=\mathrm{0,04 }m\).
Position of the reference points under the contact surface (\(m\))
\(x\) |
|
|
|
\(A\) |
0 |
0 |
0 |
\(B\) |
0.00125 |
0 |
0 |
\(C\) |
0.005 |
0 |
0 |
\(D\) |
0.0075 |
0 |
0 |
\(E\) |
0.01125 |
0 |
0 |
\(R\) |
0.03875 |
0 |
0 |
1.2. Material properties#
Plaque:
Poisson’s ratio: \(\mathrm{0,2}\)
Young’s module: \(\mathrm{1,3}\ast {10}^{11}{\mathit{N.m}}^{-2}\)
Building (only if it is modelled by elements of the same size as the plate):
Poisson’s ratio: \(0.2\)
Young’s module: \({10}^{16}{\mathit{N.m}}^{-2}\)
The coefficient of friction under the rigid plane is \(\mu =1\) .
1.3. Boundary conditions and loads#
The frame, when it has a dimension \(N-1\) in relation to the dimension of the plate, is blocked:
by a complete installation.
The frame, when it is of the same size as the plate, is blocked:
in plane \(x=\mathrm{40 }\mathrm{mm}\) for trips according to \(x\) (symmetry of the problem);
by embedding its underside.
The plate is stuck:
in plane \(x=\mathrm{40 }\mathrm{mm}\) for trips according to \(x\) (symmetry of the problem);
next \(Y\) to the node located at the intersection of the plane of symmetry, the contact face and the plane \(Z=0\) to prevent rigid body movements.
In 3D, to get back to a 2D problem:
the next move \(Z\) is blocked for all nodes.
The plate is subjected to two distributed pressures:
a vertical acting on the top side: \(f=–5\ast {10}^{7}{\mathit{N.mm}}^{-2}\);
a horizontal acting on the face initially in \(x=0\), \(F=15\ast {10}^{7}{\mathit{N.mm}}^{-2}\).