Considering Kinematic Stability in Truss Topology Optimization via a Singular Disturbance Scenario

Kinematic instability remains a major challenge in truss topology optimization, as unstable nodes can undermine both structural performance and numerical accuracy. In engineering practice, kinematic stability is typically enforced only after optimizing the force distribution -by adding unstrained members or iteratively modifying the layout until stability conditions are satisfied. From an optimization standpoint, however, such post-hoc corrections can be detrimental: initial design proposals optimized without stability considerations may lead to suboptimal or inefficient final structures. This motivates the further development of optimization approaches that inherently ensure kinematic stability, producing more efficient and practically realizable truss designs. We introduce the Singular Disturbance Scenario (SDS) approach, which differs from established methods such as the Nominal Lateral Force (NLF) and Nominal Disturbing Force (NDF) approaches. Unlike NLF and NDF-which rely on multiple disturbance scenarios computed implicitly during optimization-we precompute a single scenario solely from the ground structure, whose forces are included in the optimization model but become active only at nodes selected in the design. This scenario is obtained by solving a separate optimization problem that determines nodal forces designed to constrain every degree of freedom. It builds on the predefined ground structure, leveraging its member directions and spanned planes. We benchmark SDS against a conventional workflow that first optimizes for load cases and subsequently restores stability through heuristic post-processing. The results demonstrate that SDS integrates stability considerations directly into the optimization process, producing truss designs that were kinematically stable across all evaluated instances.