r3.08.07 Elements MEMBRANE and GRILLE_MEMBRANE

Summary:

This document describes the formulation and implementation of elements MEMBRANE and GRILLE_MEMBRANE in*Code_Aster*. Elements MEMBRANE make it possible to model any linear membrane behavior or a non-linear behavior of isotropic membranes. Elements GRILLE_MEMBRANE are finite elements more specifically dedicated to the representation of steel reinforcements in a mass (for civil engineering applications such as reinforced concrete). The main characteristics of these elements are as follows:

• membrane elements, without torsional stiffness;

• no degrees of freedom of rotation, but in return no possibility of eccentricity;

• surface geometric support (triangle, quadrangle; linear or quadratic, and biquadratic only for MEMBRANE);

Elements GRILLE_MEMBRANE make it possible to model the non-linear behavior of reinforcing bars.

• 1. Introduction
• 2. Linear formulation of the elements of MEMBRANE
• 3. Nonlinear formulation of the elements of MEMBRANE
  • 3.1. Differential geometry
  • 3.2. Assumptions
  • 3.3. Equations governing the movement of membranes
  • 3.4. Finite element discretization
  • 3.5. Expressing coded elements in code_aster
• 4. Formulation of the elements of GRILLE_MEMBRANE
• 5. Mass matrix
• 6. Bibliography
• 7. Description of document versions