کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
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499313 | 863039 | 2009 | 13 صفحه PDF | دانلود رایگان |
This paper proposes a closed form expression for the sensitivity of the macroscopic heat conductivity tensor for two-dimensional problems to topological microstructural changes of the underlying material. The sensitivity formula is remarkably simple. It is derived by applying the concept of topological derivative within a variational multi-scale framework for steady-state heat conduction where the macroscopic temperature gradient and heat flux are defined as volume averages of their microscopic counterparts over a representative volume element (RVE) of material. The classical Fourier law is assumed to hold at the scale referred to as microscopic (the RVE). The derived sensitivity – a symmetric second order tensor field over the RVE domain – measures how the estimated macroscopic conductivity tensor changes when a small circular inclusion is introduced at the micro-scale. The proposed formula finds potential application in the design and optimisation of heat conducting materials.
Journal: Computer Methods in Applied Mechanics and Engineering - Volume 198, Issues 5–8, 15 January 2009, Pages 727–739