Multi-Material Topology Optimization Using Variable Density Lattice Structures for Additive Manufacturing

Multi-material lattice structures are used in a range of load-bearing applications for multiple conditions including mechanical and thermal loads. Additive manufacturing processes with multi-material capabilities are well suited to manufacture multi-material structures. In this paper, a multi-material topology optimization approach has been presented using variable-density lattice structures where the geometry of the lattice structure is pre-defined. The objective of the proposed topology optimization method is to design lightweight parts with minimized compliance and thermal energy or improve the heat transfer capability. To facilitate that, a novel interpolation scheme based on the stiffness matrices of the lattice structures has been proposed. This interpolation scheme, unlike the traditional Solid Isotropic Material Penalization (SIMP) interpolation, is observed to perform better in terms of approximating the structure’s load-bearing capacity, primarily due to its formulation on the lattice’s stiffness matrices. This cubic Hermite spline-based interpolation scheme makes it amenable for gradient-based optimization methods. A sequential linear programming method has been used to solve the weighted multi-objective optimization model. A Pareto-frontier study has also been carried out to fully characterize the trade-offs between the two objectives – compliance minimization and thermal energy minimization.