14. Summary of results

The very good results obtained for models \(A\) and \(B\) are explained by the fact that the reference solutions belong to the space generated by the finite elements chosen. Only numerical rounding errors remain.

Satisfactory results have been obtained for plate and shell models in space \(C,D,E,F,G,H,I,J\) and \(K\). For the latter, a chained thermo-elastic calculation was carried out. The results with modeling DKT (\(E,F,G,H,I,J\)) show that quadrangle elements behave better than triangle elements. It is necessary to have a sufficiently fine discretization with these plane elements in order to be able to correctly model the circular geometry of the cylindrical shell. In fact, discretizing the geometry of the cylinder by plane or parabolic facets is not consistent and induces parasitic flexure which decreases with the fineness of the mesh. Thus, multiplying the number of elements by two over the height of the structure causes the relative maximum error to fall from 5.48% (case presented here) to 2.8%. The results with modeling COQUE_3D (\(C\) and \(D\)) are very good except for gravity with the triangle element.

Calculations with modeling DKTG (\(K\)) give the same results as with modeling DKT.