1. Reference problem: Shells and grills#

1.1. Geometry and meshes#

We consider a concrete slab with a length \(2m\), a width \(1m\) and a thickness \(10\mathit{cm}\). It comprises a steel sheet oriented along the axis \(X\), composed of bars of diameter \(8\mathit{mm}\) spaced apart by \(20\mathit{cm}\) whose axis is located \(2.5\mathit{cm}\) below the mean plane.

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1.2. Material properties#

For 3D linear thermal calculation (on concrete only) the properties are:

\(\rho {C}_{p}\mathrm{=}0\)

\(\lambda \mathrm{=}2W\mathrm{/}{m}^{2}\mathrm{/}K\)

For mechanical calculation the materials are linear elastic:

Concrete: \(E=30\mathit{GPa}\) steel: \(E=200\mathit{GPa}\)

\(\mathrm{\nu }=0.2\) \(\mathrm{\nu }=0.3\)

\(\mathrm{\alpha }={10}^{-5}{K}^{-1}\) \(\mathrm{\alpha }=2.{10}^{-5}{K}^{-1}\)

In the third calculation in which we want to validate option EPSP_ELGA, we move on to the VMIS_ISOT_TRAC law whose parameters are as follows:

Concrete: D_ SIGM_EPSI: \(1E10\) steel: D_ SIGM_EPSI: \(5E10\)

SKU: \(5E6\) SY: \(1E7\)

1.3. Boundary conditions and loading#

For the thermal calculation, the temperature is imposed on the lower side and the upper side:

\({T}_{\mathit{inf}}\mathrm{=}20°C\) and \({T}_{\text{sup}}\mathrm{=}50°C\)

The initial temperature is \({T}_{\mathit{ini}}\mathrm{=}20°C\)

For mechanical calculation, the slab is simply supported on its two supports parallel to \(Y\):

  • on the edge \(X\mathrm{=}0\): \(\mathit{DX}\mathrm{=}\mathit{DZ}\mathrm{=}0\)

  • on the edge \(X\mathrm{=}\mathrm{1m}\): \(\mathit{DZ}\mathrm{=}0\)

  • for corner \(Y\mathrm{=}\mathrm{-}\mathrm{0.5m}\): \(\mathit{DY}\mathrm{=}0\)

Charging consists in imposing the temperature resulting from the 3D thermal calculation.