Topology Optimization of Multibody Structures Considering Inertial Loads Using an Equivalent Static Displacement Framework

Topology optimization (TO) of dynamic structures has traditionally been constrained to single-body components and simplified harmonic load assumptions. Extending TO to multibody dynamic systems (MBS) remains challenging due to complex coupling between inertia, mass distribution, and joint constraints. This paper presents an inertia-aware topology optimization framework that integrates mass moment of inertia (MMI) constraints within an enhanced Equivalent Static Displacement (ESD) methodology. Building upon the authors’ previously developed ESD framework, the proposed approach — termed Inertia-Augmented Equivalent Static Displacement (IA-ESD) — explicitly incorporates inertial effects arising from accelerations and joint interactions. The approach enables dynamically consistent optimization by coupling design-dependent inertia tensors with equivalent static displacements derived from nonlinear multibody dynamics. Case studies involving an MBB beam and a piston–connecting rod assembly demonstrate that accounting for MMI constraints yields lighter, stiffer, and dynamically balanced multibody topologies. The proposed method establishes a foundation for inertia-aware structural design with applications in aerospace, automotive, and robotics engineering.