Topology optimization of structures designed with multiphase materials: volume constraint or mass constraint?

Instead of adopting the common idea of using volume constraint in topology optimization, this work is focused on the topology optimization of structures designed with multiphase materials and mass constraint. Related structural optimization models involving mass constraint and material interpolation model are proposed. Based on the study of two types of material interpolation models, i.e. GSIMP and UIM, the former is found to introduce the nonlinearity into the mass constraint which brings numerical difficulties in searching the global optimum of the optimization problem. The adopted UIM model, however, makes the mass constraint linear and design variable separable, which favors the mathematical programming approaches, especially the convex programming methods. Numerical examples show that the presented scheme is reliable and efficient to deal with the structural topology design problems of multiple materials with mass constraint. The mass constraint is proved to be more significant and important than the volume constraint in structural topology optimization.