Reference problem
=====================


Geometry
---------

We consider a model structure composed of a horizontal square slab :math:`0.5m` thick and :math:`3m` on the side, four vertical posts of length :math:`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 :math:`0.4m\mathrm{\times }0.6m` rectangular cross section.


Material properties
----------------------

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


* :math:`E\mathrm{=}30000\mathit{MPa}`


* :math:`\nu \mathrm{=}0.3`


* :math:`\rho \mathrm{=}2500\mathit{kg}\mathrm{/}{m}^{3}`

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


* :math:`E\mathrm{=}200000\mathit{MPa}`


* :math:`\nu \mathrm{=}0.3`


* :math:`\rho \mathrm{=}7500\mathit{kg}\mathrm{/}{m}^{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.


Initial conditions
--------------------

Nil.