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The paper describes the first exact results in optimal design of three-phaseelastic structures. Two isotropic materials, the "strong" and the "weak" one,are laid out with void in a given two-dimensional domain so that the complianceplus weight of a structure is minimized. As in the classical two-phase problem,the optimal layout of three phases is also determined on two levels: macro- andmicroscopic. On the macrolevel, the design domain is divided into severalsubdomains. Some are filled with pure phases, and others with their mixtures(composites). The main aim of the paper is to discuss the non-uniqueness of theoptimal macroscopic multiphase distribution. This phenomenon does not occur inthe two-phase problem, and in the three-phase design it arises only when themoduli of material isotropy of "strong" and "weak" phases are in certainrelation.

A Note on Optimal Design of Multiphase Elastic Structures