u3.12.03 Modeling COQUE_3D

Summary:

The modeling COQUE_3D presented here corresponds to a formulation of the general kinematics of shells and plates, of the Naghdi-Reissner type, where the generalized constraints are obtained from the laws of three-dimensional behavior of the constituent materials [R3.07.04]. Unlike the DKT - DST models, Q4G corresponding to the formulations of plate elements developed by J.L. BATOZ [bia1] _ which use plane finite elements, the COQUE_3D modeling makes it possible to perform calculations of shell structures of any shape, with a good approximation of the geometry. In addition, this modeling is capable of representing the large rotations of structures [R3.07.05] under the hypothesis of small deformations.

The degrees of freedom are the movements and the rotations, taken at the nodes of the elements.

The nonlinear behavior is discretized by \(\mathit{P2}\) polynomials, which allows precise calculation of the constraints.

It can be used for three-dimensional shell structure problems in linear and nonlinear mechanical analysis.

This formulation also exists for slice problems, or revolution problems. It is based on 1D elements: (see [U3.12.02]).

Thermomechanical calculations are linked using the finite elements of thermal shells (see [U3.22.01]).

• 1. Discretization
  • 1.1. Degrees of freedom
  • 1.2. Support mesh for stiffness, mass matrices, etc.
  • 1.3. Cargo support mesh
• 2. Assignment of characteristics
• 3. Supported loads
• 4. Nonlinear possibilities
  • 4.1. Law of behavior
  • 4.2. Deformations
• 5. Examples of implementation: test cases
• 6. Bibliography