TOPOLOGY OPTIMIZATION OF ADDITIVE MANUFACTURING COMPONENTS WITH LATTICE STRUCTURES FOR MULTIPHYSICS APPLICATIONS

This paper aims to optimize additive manufacturing parts containing lattice structures by means of topology optimization. The proposed method relies on numerical homogenization to model the behavior of the mesoscale lattices inside the macroscale component with an equivalent material model. While the topology of the unit cell is fixed a priori, the material constitutive model is considered to be a function of multiple size parameters of the lattice struts and the orientation of the lattice cell. Both the size parameters and the orientation are considered as design fields in the design domain of the optimization in order to optimize the distribution of orthotropic lattice structures while adapting their orientation to the macroscale loads. In addition, the shape of the macroscale part is described by a separate level set function. Besides avoiding the appearance of degenerate lattice structures, the strict control over the macroscale shape permits the inclusion of different manufacturing constraints. The design fields describing the lattice geometry and macroscale shape are parametrized explicitly by filtering sets of independent optimization variables. This explicit design parametrization allows one to simultaneously optimize the shape of the macroscale part and the lattice structures inside the part. Moreover, the optimization problem is expressed and solved as a standard nonlinear programming problem, which allows one to easily adopt the formulation for different design problems. This interesting feature is illustrated in the numerical examples which deal with different physical problems, and several objective and constraint functions.