1. Reference problem#

1.1. Geometry#

A rectangular plate of width \(a\) and length \(b\), supported on a spring mat.

Figure 1.1-a : Diagram of the plate and springs in the plane \((y,z)\) .

Dimensions:

\(a=1.00m\)

\(b=2.00m\)

\(\mathrm{ep}=0.30m\)

Young’s module: \(2.0E+11\mathit{Pa}\)

Poisson’s ratio: \(0.3\)

Overall spring pad stiffness: \(K\mathrm{=}10000.0N\mathrm{/}m\)

Spring pad stiffness density: \(k=\frac{K}{(ab)}=5000N/{m}^{3}\)

The load is a pressure loading of the form \(P=\mathrm{p.}{(y-b)}^{2}\), with \(p=\mathrm{5N}/{m}^{4}\)

Displacements imposed on the ends of the springs not connected to the plate:

in the time interval \([0,1]\) the displacement is imposed to 0.0 according to \(\mathit{DX}\), \(\mathrm{DY}\) and \(\mathrm{DZ}\),
in the time interval \([1,2]\) the move is imposed to 0.0 according to \(\mathrm{DX}\) and \(\mathrm{DY}\).

Next \(\mathrm{DZ}\) it is imposed by the \(\mathrm{Dz}=(t-1.0)\ast 0.5E-02\) function.

Not applicable for static analysis.