Tolerance modelling of heat conduction in bidirectional graded thin walled cellular structures

The aim of this contribution is to present a new method of formulation of simplified model of skeletonal structures. The exact description of the heat conduction leads to PDEs with highly oscillating and discontinuous coefficients. We would like to obtain the simplified models of the tolerance type which is described by PDEs with smooth coefficients. As a method of modelling we used the tolerance averaging. This method could be treated as a certain generalization of the well known homogenization method. However, it is not basis on the limit passage from the microstructure size to zero. This method makes it possible to analyze the effect of microstructure size on the overall i.e. macroscopic behavior of the composite structure. Instead of limit passage, we introduce here the concept of tolerance parameter. Using this concept we could define the slowly varying functions [1], [2]. (© 2012 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)