Topology optimization with geometric constraints for additive manufacturing based on coupled fictitious physical model

Abstract

The combination of topology optimization and laser powder bed fusion (LPBF), a kind of metal additive manufacturing, has attracted attention because of its ability to manufacture complex optimal structures with metal materials. However, LPBF must satisfy geometric constraints, e.g., overhang constraint and closed cavity exclusion constraint. Several previous studies proposed the fictitious physics model (FPM) to describe and consider these constraints. However, there exists a problem where the objective of the mechanical model (MM) describing physical phenomena conflicts with that of the FPM, resulting in poor convergence. To solve the convergence problem, we propose a coupled fictitious physics model (CFPM) in this paper. In the CFPM, the material constant in the MM is varied in the regions that violate the geometric constraints defined by the FPM such that the objective function of the MM worsens. Then, the objective of the FPM is integrated into that of the MM, potentially improving convergence. This paper formulates the CFPM and performs sensitivity analysis on representative optimization problems considering geometric constraints for LPBF. In addition, we verify through numerical examples whether the CFPM can lead to an optimal structure that satisfies the geometric constraints and can improve convergence. The proposed method to couple the two models can also be applied to topology optimization considering various geometric constraints in other manufacturing requirements.