WCCM V -- Authors' Guidelines for Full Paper Submission

The paper is devoted to theoretical and computational studies on application of the multiresolutional wavelet-based homogenization approach in the Finite Element Method modeling of heterogeneous media. Multiresolutional homogenization scheme is proposed for 1D elastostatic equilibrium problem of periodic heterogeneous medium with Young modulus defined by some elementary wavelet functions and compared with the classical method; some new example of non-homogenizable periodic heterogeneous structure is shown in the context of the wavelet-based algorithm. Next, symbolic computational comparative studies for various homogenization methods are performed and used in the Finite Element analysis of the original and homogenized two, three and five-bays periodic composite beams. Theoretical and computational analysis shows that effective parameters obtained from waveletbased homogenization method are significantly different from those obtained using classical techniques; multiresolutional approach introduces significantly greater restrictions on the original functions defining material properties of analyzed heterogeneous medium. The eigenvalues obtained for periodic composite beams show that the responses of both classical and wavelet-based homogenized beams approximate well the real structural response – multiresolutional technique is more efficient for smaller numbers of the periodicity cells in the structure. The method can be extended on homogenization-based modeling of other structures and can be implemented for the forced and even stochastic vibrations.