2. Reference solution: Shells and grills

2.1. Calculation method

In the reference solution, the thermal field is imposed using the command CREA_RESU option PREP_VARC for multi-layer shells and eccentric grids. The temperature field, linear in thickness, varies from \(20°C\) on the lower side to \(50°C\) on the upper side.

Field EVOL_THER (at the sub-points) is transmitted to the mechanical calculation by the AFFE_VARC keyword of AFFE_MATERIAU.

2.2. Reference quantities and results

The thermal gradient in the thickness imposes a mechanical flexural deformation in the slab. The expansion coefficients of the steel material and the concrete material were deliberately chosen to be very different in order to generate stresses due to differential expansion and thus test the proper functioning of the grid elements at the same time as that of the multilayer shells.

The stresses generated are uniform in the planes parallel to plane \(\mathit{XY}\)

The sizes tested are:

• the vertical movement of node \(\mathit{C5}\) to the middle of edge \(Y=-0.5m\)

• the \({\sigma }_{\mathit{xx}}\) stress on the underside of the concrete

• the \({\sigma }_{\mathit{xx}}\) stress on the upper side of the concrete

• stress \({\sigma }_{\mathit{xx}}\) in the steel layer

For the thermal deformations of field EPVC_ELGA, the analytical references are given by the formula \({\mathit{EPTHER}}_{L}=\mathrm{\alpha }(\mathit{TEMP}-{\mathit{TEMP}}_{\mathit{REF}})\). The mechanical deformation field EPME_ELGA is then validated by the difference between the total deformations and the thermal deformations.

For anelastic deformations EPSP_ELGA, the reference is given by the relationship: anelastic deformation = mechanical deformation — elastic deformation.

The elastic deformations are found from the stress field and the coefficients E and NU.

2.3. Uncertainties about the solution

Nil.