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Optimization of properties of multicomponent isotropic composites. (English) Zbl 0545.73005

We suggest a method for the calculation of the extremal conductivity of composites under some natural assumptions concerning their microstructure. The method is based on the principle of consecutive assembling of binary mixtures by addition of infinitely small amounts of one of the initial compounds to the already assembled isotropic composite. This process is assumed to produce an optimal isotropic binary mixture at each step, (which is performed by the Hashin-Shtrikman procedure). We are seeking a suitable sequence of compounds to be added to the mixture in order to minimize its resultant conductivity. A solution is given to corresponding optimization problems for both finite number and infinite number of initial compounds taken in prescribed concentrations. We also describe the microstructure of the optimal composites. The results can be used for the optimal design of elastic and heat-conducting constructions.

MSC:

74P99 Optimization problems in solid mechanics
74E30 Composite and mixture properties
74A15 Thermodynamics in solid mechanics
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References:

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