r3.06.04 Fourier elements for axisymmetric structures

Summary

Fourier elements are intended to calculate the response of structures with axisymmetric geometry stressed by non-axisymmetric loads broken down into Fourier series.

In this document, we present a general theory of Fourier Analysis with the coupling of symmetric and antisymmetric modes in the anisotropic case. The case of isotropic materials, or orthotropic materials with axis \(\mathit{Oz}\), where the modes are decoupled, is studied separately.

Fourier elements can be used in*Code_Aster* based on modeling AXIS_FOURIER. The support cells for these elements are triangles and quadrangles of degrees 1 and 2.

• 1. Introduction
• 2. Anisotropic Fourier analysis
  • 2.1. General theory
  • 2.2. Coupling and decoupling symmetric and antisymmetric modes
  • 2.3. Stress calculation
• 3. Calculation of the stiffness matrix
  • 3.1. General case
  • 3.2. Calculation of \({K}_{l}^{g}\) in the isotropic case
• 4. Loads
• 5. Conclusion and Perspectives
• 6. Bibliography
• 7. Description of document versions