Improved approximations of Fourier coefficients for computing periodic structures with arbitrary stiffness distribution

The local response of a 3D periodic structure subjected to a spatial average of strain is studied. The governing differential equations for small displacement, linear elasticity theory are solved iteratively in Fourier space. Periodic boundary conditions as well as prescribed averages of strain are satisfied exactly a priori due to the use of Fourier series. r, two errors occur in the numerical solution of the problem, which may be evaluated separately. It is shown that one of these errors may be reduced significantly if attenuation factors are used for the Fourier coefficients.