Multiresolutional Homogenization Technique in Transient Heat Transfer for Unidirectional Composites

摘要

The paper is devoted to theoretical and computational studies on application of thernwavelet-based homogenization approach in the Finite Element Method modeling ofrntransient heat transfer in unidirectionally heterogeneous media. Multiresolutionalrnhomogenization scheme is proposed for 1D heat transfer problem of periodicrnheterogeneous medium with heat conductivity coefficient and volumetric heatrncapacity defined by some elementary wavelet functions and compared with otherrnmethods – spatial averaging and asymptotic homogenization approach. Symbolicrncomputational comparative studies for various homogenization methods arernperformed and extended on the parameter sensitivity studies related to the interfacernlocation and the contrast between heat conductivity coefficients of compositerncomponents. The results of symbolic homogenization are used in the Finite Elementrnanalysis of the original and homogenized two-component composite. Theoreticalrnand computational analysis shows that effective parameters obtained from waveletbasedrnhomogenization method are significantly different from those obtained usingrnclassical techniques; multiresolutional approach introduces significantly greaterrnrestrictions on original functions defining material properties of the analyzedrnheterogeneous medium.