Discrete multi-material topology optimization under total mass constraint

A novel approach to computing the discrete solution to the challenging multi-material topology optimization problem under total mass constraint is studied in this paper. The challenge of the problem lies in the incompressibility constraint on the summation of the usage of the total materials, which significantly increases the associated computational difficulty, and is seldom studied before; a few previous studies focus on respective mass constraint on each used material, whose solution lies in a strictly feasible space and is easier to compute. Solution to the optimization problem is derived on a theoretical finding that the iterative density update in a two-material optimization problem is totally determined by the rankings of the elemental compliances, which only involves an FE analysis computation, and can be efficiently achieved. Based on this theoretical insight, a practical regulated iterative numerical approach is then devised to find the solution to the multi-material topology optimization problem by solving a series of two-material subproblems. Various 2D and 3D numerical examples demonstrate its capability in providing structure of better compliance as compared with results obtained using latest approach based on density interpolation. (C) 2018 Elsevier Ltd. All rights reserved.