1. Introduction

Fourier analysis is intended to calculate the response of structures with axisymmetric geometries subjected to non-axisymmetric loads. In this case, it is necessary to develop Fourier serial loads. Generally, convergence is achieved for 4 or 5 harmonics, but the speed of this convergence depends on the nature of the load: the more regular the loading, the more rapidly the corresponding series converges. The most unfavorable case is that of a concentrated force for which practice shows that it is necessary to go beyond it (at least 7 harmonics).

In Code_Aster, the decomposition of the load into Fourier series is assumed to have been done beforehand by the user. Code_Aster allows you to calculate the responses to this loading, harmonic by harmonic (modeling AXIS_FOURIER), and globally after recombining the harmonics with each other (operator COMB_FOURIER).

In a first chapter, the general framework of anisotropy will be presented, with emphasis on the decoupling of modes in the orthotropic case. The second chapter explains the calculation of the stiffness matrix in the isotropic case.

For the use of Fourier elements in*Code_Aster*, refer to the Fourier modeling user manual [U2.07.01].