1. Reference problem#

1.1. Geometry#

_images/100013D0000069D500004B73FCB24D9EA571DA94.svg

Side of the plate (square) \(a=\mathrm{0,04 }m\).

Position of the reference points under the contact surface (\(m\))

\(x\)

\(y\)

\(z\)

\(A\)

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 \(x=0\), \(F=15\ast {10}^{7}{\mathit{N.mm}}^{-2}\).