Abstract
In this chapter, problems associated with multifunctional requirements with respect to effective characteristics of composites consisting of two components as well as composites with holes or technological inclusions have been studied. In the process of investigation, a strong dependence of the optimal topology of the distribution of materials in the microstructure of composites on the form of the target functions has been detected. The study of transformations of the optimal topology of the composite microstructure with a change in the weight coefficient from \(\omega = 0\) (maximization of the heat transfer) up to \(\omega = 1\) (maximization of the mechanical moduli) has been conducted. Moreover, a set of alternatives optimal in the Pareto sense has been constructed. The considered examples clearly indicate the inability to achieve the best/required properties simultaneously in both cases, which is caused by conflicting criteria in the target function. In addition, nonlinear dynamics of the size-dependent Euler-Bernoulli beams embedded into temperature field with topologically optimized microstructure is studied.
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