Multiresolutional Homogenization Technique in Transient Heat Transfer for Unidirectional Composites

摘要

The paper is devoted to theoretical and computational studies on application of the wavelet-based homogenization approach in the Finite Element Method modeling of transient heat transfer in unidirectionally heterogeneous media. Multiresolutional homogenization scheme is proposed for 1D heat transfer problem of periodic heterogeneous medium with heat conductivity coefficient and volumetric heat capacity defined by some elementary wavelet functions and compared with other methods – spatial averaging and asymptotic homogenization approach. Symbolic computational comparative studies for various homogenization methods are performed and extended on the parameter sensitivity studies related to the interface location and the contrast between heat conductivity coefficients of composite components. The results of symbolic homogenization are used in the Finite Element analysis of the original and homogenized two-component composite. 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 original functions defining material properties of the analyzed heterogeneous medium.