Scaling-up topology optimization with target stress states via gradient-based algorithms - Mauersberger, Michael; Dexl, Florian; Markmiller, Johannes F.C. (Computers & structures, 2025)
•Witness specimens are an appropriate measure to qualify additively manufactured parts.•Gradient-based topology optimization was successfully used for target stress states.•Target stress states need an indirect formulation considering compliant mechanisms.•2D and 3D topology results feature a high precision up to 3.7%. Benchmark artifacts serve as an appropriate mean to represent quality measures in additively manufactured components. Especially witness specimens, which represent structural properties as a subtype of benchmark artifacts, are supposed to reproduce target stress states as they are critical for component failure. This study aims at proposing an approach to effectively scale the results of topology optimized witness specimens with failure-critical target stress states using gradient-based methods. Therefore, possible formulations with analytical sensitivities are derived and implemented in a Matlab framework in order to contextualize the actual formulation within classical approaches consistently. It has been confirmed that gradient-based topology optimization with analytical sensitivities is not appropriate for a direct formulation of failure-critical target stress states. Thus, an indirect formulation based on compliant mechanisms is presented in this paper. It is shown that plausible, functional structures can be produced. Target stresses are achieved in scaled-up results in two and three dimensions with an accuracy up to a relative error of 3.7 %.