Topology and material optimization of anisotropic materials including a filter to smooth fiber pathways

Abstract A three‐dimensional topology optimization of anisotropic materials including the optimization of the local material orientation based on thermodynamic principles is presented. To this end, the topology is parameterized by a continuous density variable with penalization of intermediate densities (SIMP) [1]. The material orientation is defined by the rotation of a given anisotropic base material and the rotation is parameterized by a set of three Euler angles. A novel filtering technique is presented to provide a smoothing of the material orientation, i.e. the fiber paths. The influence of the filter parameter on the maximum allowed fiber path curvature is shown. The constraint on the maximum fiber curvature also influences the results for the optimal topology. Corresponding numerical results for the simultaneous optimization of the topology and local material optimization for the two‐dimensional and three‐dimensional case will be presented.