Material interpolation schemes in topology optimization problems involving coupled structural and thermal optimization

In traditional topology optimization (considering one discipline, and having only concentrated loads) one can often choose to ignore the physical interpretation of the intermediate densities when the optimization results lead to black-and-white topologies anyway. On the contrary, when two or more physical phenomena are involved, for example when structural and thermal optimization processes are combined, or when distributed loads are imposed, intermediate densities can constitute part of the optimal solution. In this study, we analyze a variety of distinct material interpolation schemes and their influence on the optimized topology. A first case study considers tree structures and how to cope with the blurred transition areas at the top. A second case study solves coupled structural and thermal optimization problems. The physical interpretation of the schemes is discussed and the effective properties of the intermediate densities are analyzed.

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