Homogenization-based finite element analysis of unidirectional composites by classical and multiresolutional techniques

Computational studies of unidirectional transient problems in multiresolutional periodic heterogeneous media using homogenization technique and the finite element method are documented below. This homogenization method, being the extension of the classical two-scale asymptotic approach and based on the wavelet representation for composite parameters, is used here to calculate effective material parameters of a composite. Efficiency of this method is compared against asymptotic homogenization technique and simple spatial averaging of material properties using the FEM solution for some transient heat transfer and free vibration problems. On the other hand, a comparison with the solutions obtained for a multiresolutional decomposition of material parameters for composites is also made. Numerical results show that the homogenized parameters resulting from the new approach are bounded by spatial averages and by asymptotic method results; this result is valid also for the eigenvalues of a periodic and simply supported composite beam. The multiresolutional homogenization proposed appears to be especially efficient in case of smaller numbers of periodicity cells in the structure, while increased number of cells needs application of an asymptotic homogenization method. Further computational studies are necessary in this area, but the application of the multiresolutional technique is natural because of multiscale character of composites. Moreover, this method may be very efficient in common symbolic-FEM programs implementation.