The algorithms for multi-material topology optimization were developed to solve compliance-minimization problems and applied to engineering problems in automotive concepts and lightweight design. Two small-scale problems of a long cantilever and a control arm were studied initially to verify the effectiveness of the developed algorithms and in-house program. Optimal solutions achieved by the multi-material topology optimization method developed were compared to their counterparts obtained by standard single-material topology optimization. To efficiently solve real-world engineering problems, the algorithms were further advanced to incorporate extrusion constraints and to handle multiple load cases. The effectiveness and the efficiency of the proposed method were demonstrated by the study of two real-world engineering problems: (a) the conceptual design of a cross-member for a chassis frame; and (b) the conceptual design of an automotive engine cradle. The two optimization design problems both involved complex geometries, design and non-design domains, prescribed regions with specific material allocations, multiple load cases, and manufacturing extrusion constraints. It was explicitly demonstrated that, for the same weight, the optimum designs achieved by the multi-material topology optimization method were stiffer than those achieved by standard single-material topology optimization.
