1. Reference problem

1.1. Geometry

Square plate :

Length: \(l=1.0m\)

Thickness: \(e=0.1m\)

1.2. Material properties

Young’s module, \(E=4.388{10}^{10}N/{m}^{2}\)

Poisson’s ratio, \(\nu =0.0\)

Density, \(\rho =2500\mathrm{kg}/\mathrm{m3}\)

1.3. Boundary conditions and loads

On the \(A\) side we include the movements in \(x\) and \(z\), \({u}_{x}={u}_{z}=0.0\), as well as the rotations, \({u}_{\mathrm{Rx}}={u}_{\mathrm{Ry}}={u}_{\mathrm{Ry}}=0.0\). Then, the linear force is applied to the \(B\) side in the \((1.0\mathrm{,0}.0\mathrm{,1}.0)\) direction, which is linear in time:

\(F(t)={F}_{0}\mathrm{.}t\)

where \({F}_{0}\) is the amplitude, \({F}_{0}=1.6166{10}^{5}N\).

1.4. Initial conditions

Initially, travel and speeds were zero everywhere.