Fourier series for computing the response of periodic structures with arbitrary stiffness distribution

A method based on Fourier series is presented, which allows to calculate the local stress–strain response of a three-dimensional periodic structure subjected to a spatial average of strain. The periodicity allows the reduction of the problem to that of a Representative Volume Element (RVE). The solution operator (which can easily be calculated in Fourier space) is defined for a simplified problem, and it is shown that this operator may also be used for the original problem. In order to illustrate the use of this procedure, an example problem is presented. A global error is defined and calculated for the example problem.