1. Reference problem#

1.1. Geometry#

We consider a model structure composed of a horizontal square slab \(0.5m\) thick and \(3m\) on the side, four vertical posts of length \(3m\) planted in four corners of the slab and four horizontal beams (of the same length) connecting the high ends of the posts together and thus constituting a closed outline. All posts and beams have a \(0.4m\mathrm{\times }0.6m\) rectangular cross section.

1.2. Material properties#

The slab material is isotropic elastic corresponding to concrete whose properties are:

  • \(E\mathrm{=}30000\mathit{MPa}\)

  • \(\nu \mathrm{=}0.3\)

  • \(\rho \mathrm{=}2500\mathit{kg}\mathrm{/}{m}^{3}\)

The material of columns and beams is isotropic elastic corresponding to a steel whose properties are:

  • \(E\mathrm{=}200000\mathit{MPa}\)

  • \(\nu \mathrm{=}0.3\)

  • \(\rho \mathrm{=}7500\mathit{kg}\mathrm{/}{m}^{3}\)

1.3. Boundary conditions and loads#

The slab is based on a carpet of springs whose stiffness is calculated by the RIGI_PARASOL command from 6 specified values. A floor shock absorber mat is also defined, of the A_T_D_N type, whose values are chosen deliberately low in order to remain close to the reference solution, which is calculated by neglecting this damping.

The slab is loaded by a surface pressure whose appearance in time is given by a function.

1.4. Initial conditions#

Nil.