Topology optimization for 3D printing-driven anisotropic components accounting for stress and displacement constraints

Concrete 3D printing produces a layered macrostructure with different properties in three orthogonal directions, while new techniques allow printing at different orientations. Can printing with spatially variable layer-to-layer interface orientations produce lighter structures while stress and displacement limits are met? To address this question, this study first establishes the connection between experimentally measured properties of printed concrete samples, which inherently capture interlayer effects, and parameters of orthotropic elasticity and orthotropic yielding. Building upon this connection, a topology optimization framework is built that minimizes weight with respect to both the material distribution and spatially variable layer orientation, while simultaneously addressing both stress and displacement constraints. This framework is implemented via the Augmented Lagrangian approach together with the Method of Moving Asymptotes, and sensitivities are calculated using the adjoint method to reduce the computational cost. To expedite convergence without constraint violations, this study further introduces the concept of offset tolerances. Convergence is further expedited by introducing a cubic term in the displacement constraints that accelerates convergence at large constraint violations and by introducing a densityweighted change norm for the orientation angles to eliminate the effect of inconsequential orientation variations in regions of negligible density. This diverse framework enables investigation of fixed vs. variable orientation and tension-compression asymmetry vs. symmetry in achieving low weights. It further enables investigation of the relative effect of stress vs. displacement constraints in minimizing weight.