Lightweight topology optimization of process-induced anisotropic structures under stiffness and strength constraints

In topology optimization (TO) for additive manufacturing (AM), considering the anisotropy of formed materials induced by layer-by-layer AM processes is an emerging challenge. Based on this special process-related anisotropic constitutive relationship, a lightweight TO framework that considers both strength and stiffness requirements is proposed and explored in this work. Firstly, by introducing a print-off angle variable related to the anisotropy, the classical transversely isotropic model is extended to simulate the process-related anisotropic constitutive behavior. Then, based on the Hoffman failure criterion, a process-related anisotropic failure strength measurement is established. Furthermore, to achieve effective strength control, a global aggregation strategy based on the P-norm and error correction techniques is constructed. On this basis, the classical volume minimization is extended to include both anisotropic strength and stiffness constraints. Additionally, to address the convergence difficulties caused by the angle periodicity, an adaptive adjustment strategy for the angle variation is applied. The sensitivities related to the density and angle variables are derived in detail to adapt to gradient-based optimization algorithms. Typical numerical examples validate the effectiveness of the proposed method. The results reveal the inherent trade-off between lightweight, structural safety, and stiffness performance in the design. By effectively utilizing the process-induced anisotropy, the proposed algorithm reduces material usage while ensuring structural stiffness and strength requirements.