r4.07.05 Homogenization of a network of beams immersed in a fluid

Summary:

This note describes a model obtained by a homogenization method to characterize the vibratory behavior of a periodic network of tubes bathed by an incompressible fluid. Next, the development of a finite element associated with this homogenized model is presented.

The tubes are modelled by Euler beams and the fluid by a potential model.

This modeling is available in command AFFE_MODELE by choosing 3D model_ FAISCEAU.

Table of Contents

• 1. Introduction
• 2. Initial physical problem
  • 2.1. Problem description
  • 2.2. Modeling hypotheses
• 3. Homogenized problem
  • 3.1. Homogenized problem obtained
  • 3.2. Matrix problem
• 4. Solving the cellular problem
  • 4.1. Problem to be solved
  • 4.2. Equivalent problem to define \({\chi }_{\alpha }\)
  • 4.3. Put into practice in Code_Aster
• 5. Choice of the finite element for the homogenized problem
  • 5.1. Choice of finite elements
  • 5.2. Reference finite elements
  • 5.3. Choice of Gauss points
  • 5.4. Addition of traction and twisting problems
  • 5.5. Integration of this finite element into the Code_Aster
• 6. Use in Code_Aster
  • 6.1. The necessary data
  • 6.2. Orientation of the axes of the beams
  • 6.3. Modal calculation
• 7. Characterization of the homogenized model spectrum
  • 7.1. Heterogeneous model
  • 7.2. Homogeneous model
• 8. Conclusion
• 9. Bibliography
• 10. Description of document versions