1. Introduction#

Shell and plate elements are particularly used to model thin structures where the relationships between dimensions (thickness/characteristic length) are much less than \(1\mathrm{/}10\) (thin shells) or in the order of \(1\mathrm{/}10\) (thick shells). For very thin cases, we recommend not to exceed a \(1/500\) ratio in order to avoid digital locking problems that will underestimate travel and therefore give false results.

These models can be used in linear and non-linear mechanics, under hypotheses of small deformations and small displacements or even hypotheses of large displacements and large rotations, depending on the models. Thin shell modeling is also available in transient linear thermal.

Two categories of thin structural elements are described in this document:

The elements of**plates*, which are planar. The curvature of the structure to be represented is not taken into account and it is therefore necessary to use a large number of elements in order to correctly approach the geometry of the structure (facet aspect).

The elements of**shells*, which are curved.

Triangle and quadrangle planar plate elements are described in the reference documentation [R3.07.03]) and include the following models:

  • DKT: mesh TRIA3élément DKT, mesh QUAD4éléments DKQ (geometric linear);

  • DKTG: mesh TRIA3élément DKT, mesh QUAD4éléments DKQ (geometric linear or nonlinear);

  • DST: mesh TRIA3élément DST, mesh QUAD4élément DSQ (geometric linear);

  • Q4G: QUAD4élément Q4G mesh (geometric linear).

  • Q4GG: TRIA3élément T3G mesh, QUAD4éléments Q4G mesh (geometric linear)

Curved shell elements from 3D models with shell kinematics are grouped under the following models:

  • COQUE_3D: TRIA7et QUAD9 mesh, 3D structure with any geometry ([R3.07.04] in geometric linear, [R3.07.05] in geometric nonlinear and [R3.03.07] with subsequent pressures);

  • COQUE_AXIS: mesh SEG3, shells with symmetry of revolution around the axis \(\mathrm{0Y}\) ([R3.07.02] in geometric linear);

The conventional membrane elements are grouped under the model MEMBRANE and may have as geometric support meshes TRIA3, QUAD4, TRIA6, QUAD8, TRIA7 and QUAD9. They are membrane elements with simple membrane stiffness (no rotational degree of freedom). There is no eccentricity. Membrane models can also be used in large transformations.

There are specific plate elements to represent reinforcement sheets:

  • GRILLE_EXCENTRE: TRIA3ou QUAD4 (geometric linear) meshes. This modeling corresponds to plate elements DKTorthotropes with 3 or 4 nodes eccentric with respect to the average concrete sheet, (only one reinforcement direction). Concrete can be modelled by plate elements DKTou DST with 3 knots. The reinforced concrete structure is then represented by the superposition of models GRILLE_EXCENTRE and that used for concrete (DKTou DST).

  • GRILLE_MEMBRANE: meshes TRIA3, QUAD4, TRIA6ou QUAD8 (doc [R3.08.07]): they are reinforcement elements (a single reinforcement direction) working only as a membrane (no degree of freedom of rotation). There is no eccentricity.