7. Summary of results

• De **placements*: regardless of the modeling used (DKT or DST) the results are satisfactory, the maximum error is less than \(\text{0.7\%}\).

• Plane constraints: the results are more accurate with modeling DKT, the error is less than \(\text{1\%}\) except for \(\mathrm{SIXY}\) (QUAD4) where the error is \(\text{5\%}\). For modeling DST the error is higher (\(\text{<8\%}\)) with a significant difference over \(\mathrm{SIXX}\) (\(\text{28\%}\)) for mesh TRIA3.

• Cross shear: regardless of the modeling used (DKT or DST), the results obtained with quadrangular meshes are closer to the reference solution than those obtained with triangular meshes. In the first case the error on the \(\mathrm{SIXZ}\) component is less than \(\text{15\%}\), and the error on \(\mathrm{SIYZ}\) is less than \(\text{3\%}\), while in the second case, the error on \(\mathrm{SIXZ}\) is \(\text{35\%}\) and that on \(\mathrm{SIYZ}\) is between \(\text{2\%}\) and \(\text{24\%}\). Apart from the lower precision of triangular meshes because of their anisotropy, the difference that remains with quadrangular meshes is due to the difference in the modeling of transverse shear: in the reference, a transverse shear correction coefficient of 5/6 is used. In Code_Aster, we calculate the shear distribution in the thickness, which is assumed to be parabolic in each layer.