1. Introduction

Modeling MEMBRANE makes it possible to represent the mechanical behavior of a membrane that is possibly anisotropic in linear and only isotropic in non-linear. It makes it possible to model structural elements whose flexural stiffness is negligible.

Elements GRILLE_MEMBRANE make it possible to represent the possibly non-linear behavior of reinforcing bars in a reinforced concrete structure. The main constraint is that the reinforcing bars must be periodically distributed over a surface, and all oriented in the same direction. However, it should be noted that crossed reinforcing bars can be modeled by superimposing two GRILLE_MEMBRANE models (see later).

The elements of type GRILLE_MEMBRANE complement the reinforcement modeling possibilities in Code_Aster, in addition to the GRILLE_EXCENTRE modeling. The differences between models GRILLE_MEMBRANE and GRILLE_EXCENTRE are shown below.

Recall that modeling GRILLE_EXCENTRE is based on shell kinematics DKT with a single layer in the thickness [R3.07.03]. This base DKT implies the presence of degrees of freedom of rotation at the nodes of the elements GRILLE_EXCENTRE: while it allows the concept of eccentricity, it is useless when there is no need for an eccentricity (in this case it makes the model unnecessarily heavier), because not only do the degrees of freedom of rotation extend the vector of unknowns, but it is also necessary to block a significant number of these degrees of freedom by double multiplier of Lagrange). Modeling GRILLE_MEMBRANE is a modeling based on « surface » kinematics, it does not require any degrees of freedom other than the usual movements (on the other hand, of course, this modeling does not allow the concept of eccentricity to be used).

Modeling GRILLE_EXCENTRE, based on DKT, requires supporting geometric elements such as triangle or linear quadrangle; modeling GRILLE_MEMBRANE is developed from triangular or quadrangle, linear or quadratic surface geometric supports.

For both types of modeling, on the other hand, only one reinforcement direction is available per finite element. This makes it possible to model any type of reinforcement with several directions, by superimposing one element per direction; the calculation cost generated by these duplications is low: no duplication of degrees of freedom (therefore constant matrix inversion cost), duplication of elementary calculations (but they remain simple, but they remain simple, in reduced number in 3D, in reduced number in 3D — surface elements versus volume elements) — and elementary calculations for structures with large numbers of degrees of freedom (compared) are of low cost. at the cost of reversal).