r3.07.09 Plate elements: Q4GG modeling

Summary

This document presents the formulation of thick plate elements, used in Q4GG modeling.

For this modeling, two types of finite elements are available, depending on the meshes:

• Quadrangular finite element (Q4G)

• Triangular finite element (T3G)

This thick plate element modeling, like models DKT, DKQ,, DST,,,, DSQ, DKTG, and Q4G [7], is intended for calculations in small deformations and large displacements of thin curved or plane structures. They are plane elements that do not take into account the geometric curvature of structures, unlike shell elements (COQUE_3D) which are curved: this results in parasitic flexures that can be reduced by using more elements in order to be able to correctly approach curved geometries. The formulation is therefore simplified and the number of degrees of freedom is reduced.

Note:

The formulation of the quadrangular element Q4G used in the Q4GG modeling is described in document [7]. Consequently, we are limited here to the case of the triangular element T3G.

Table of Contents

• 1. Introduction
• 2. Formulation
  • 2.1. Geometry of plate elements
  • 2.2. Cinematics
  • 2.3. Finite element support
  • 2.4. Membrane-Flexion
  • 2.5. Transverse distortion
  • 2.6. Calculation of stresses and internal forces
  • 2.7. « Lumped » mass matrix
  • 2.8. Second member corresponding to external work
• 3. Implanting plate elements in Code_Aster
  • 3.1. Description
  • 3.2. Use and developments introduced
  • 3.3. Linear elasticity calculation
  • 3.4. Nonlinear calculation
• 4. Q4GG modeling validation
  • 4.1. SDLS123 — Straight beam with Rayleigh damping (V2.03.123)
  • 4.2. SDNS108 — Dynamic response of a reinforced concrete slab (model GLRC_DAMAGE) supported on 4 sides subjected to a concentrated load: regime of 4.2 elasto-plastic plate (V5.06.108)
• 5. Bibliography