Topology Optimization with Limits on Joint Loads
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Additive manufacturing (AM) and topology optimization (TO) together enable complex, lightweight components tailored to specific performance targets. In this setting, bolted joints remain indispensable, as for assembly, maintenance, and overcoming AM build‑volume limits, and they often become the critical regions of the structure. In connections with multiple bolted joints, loads can be distributed across the joints and thus relieve an overloaded connection. Designing a structure that keeps every joint within its limit is difficult, especially when normal and shear forces act simultaneously. Prior studies have integrated connection elements into topology optimization. However, explicit constraints on joint loads under combined loading have received limited attention. This work includes a joint load constraint in topology optimization for bolted joints. Bolts are implicitly represented as in the VDI 2230 model class I. The required preload is computed from internal forces at the interface, and is limited by the allowable preload of the bolt. Adjoint sensitivities of the joint load constraint are derived for efficient gradient‑based optimization. The constraint is implemented in a simple 2D TO code in Matlab. Two 2D examples, a cantilever and an engine transmission crossmember, demonstrate substantial reductions in joint loads and allow a reduction in the number of bolts while keeping all joints below their limits. The constraint steers designs to reduce shear loads at the joints, with an expected trade‑off of increased compliance. The formulation is computationally inexpensive (one additional adjoint solve per constraint) and is readily extendable to 3D and to models with explicit preload. Further, it can be used to synthesize compliant mechanisms.
