A Numerical Method for Computing the Response of Periodic Structures with Arbitrary Stiffness Distribution

Abstract

A method based on Fourier series is presented, which allows to calculate the local stress-strain response of a periodic structure subjected to an applied (spatial average) strain field. The periodicity allows the reduction of the problem to that of a Representative Volume Element (R.V.E.), which can be solved by transferring it into Fourier space. - First, a review of Fourier series as a particular method of solving the set of differential equations is given. Second, the solution operator is calculated in Fourier space. Third, a related problem is studied, in which the material is homogeneous and fourth, the solution for the problem with arbitrary stiffness distribution is presented as well as the algorithm for the numerical calculation of the desired fields. Finally, example problems are studied, and the results are compared to those obtained by the method of Discrete Fourier Transforms (Muller, 1996).