Multi-joint topology optimization for stiffness constrained design problems

Topology optimization (TO) has been used extensively in industry to develop structurally efficient designs for many years. Traditional applications of TO are confined to a single candidate material, leaving implementations of structurally beneficial multi-material designs mainly up to designer experience. To address this, advanced tools capable of considering multiple candidate materials in optimization such as multi-material TO (MMTO) have been developed. However, MMTO is limited by the assumption of perfect joining between dissimilar materials, which introduces the potential for artificially high performance, and requires joining to be added manually in post-processing. Multi-joint topology optimization (MJTO) methods have been introduced to address these concerns by incorporating dissimilar material joining directly within the optimization loop, thereby considering the impact of joints on structural performance, and reducing the amount of manual interpretation required. However, previous implementations of MJTO are confined to mass or volume constrained compliance minimization problems. These problems do not offer a use case in practical level design, as they require mass targets to be defined a priori, and do not incorporate any functional design constraints. In this work, the MJTO problem is extended to include capability for mass minimization subject to stiffness constraints, offering a new problem type which is more applicable to practical design problems. A new joint material modeling approach is also introduced which addresses the discrepancy between physical joint thickness and finite element size by leveraging numerical homogenization techniques. Multiple case studies are included to demonstrate the effectiveness of the new MJTO algorithm for practical design problems.