Abstract
It is not difficult to motivate, from a practical point of view, the kind of situations we would like to deal with and analyze. We have selected a typical example in heat conduction, but many other examples are as valid as this one. Suppose we have two very different materials at our disposal: the first, with conductivity α 1 = 1, is a good and expensive conductor; the other is a cheap material, almost an insulator with conductivity coefficient α 0 = 0. 001. These two materials are to be used to fill up a given design domain Q, which we assume to be a unit square for simplicity (Fig. 1.1), in given proportions t 1, t 0, with t 1 + t 0 = 1. Typically, t 1 < t 0 given that the first material is much more expensive than the second. We will take, for definiteness, t 1 = 0. 4, t 0 = 0. 6. The thermal device is isolated all over ∂ Q, except for a small sink Γ 0 at the middle of the left side where we normalize temperature to vanish, and there is a uniform source of heat all over Q of size unity. The mixture of the two materials is to be decided so that the dissipated energy is as small as possible.
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Pedregal, P. (2016). Motivation and Framework. In: Optimal Design through the Sub-Relaxation Method. SEMA SIMAI Springer Series, vol 11. Springer, Cham. https://doi.org/10.1007/978-3-319-41159-0_1
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