Topology Optimization of Multibody Systems Undergoing Dynamic Loading Using an Equivalent Static Displacement Method

Dynamic multibody systems (MBS)—such as piston–connecting rod assemblies in internal combustion engines—pose significant challenges in topology optimization due to their nonlinear contact interfaces, lack of fixed supports, and time-varying loads. Traditional equivalent static load (ESL) methods often struggle with these scenarios, as they rely on displacement fields ill-suited to free-floating or accelerating bodies.This research introduces a novel Equivalent Static Displacement (ESD) methodology that converts reaction forces from dynamic simulations into equivalent nodal displacements, enabling efficient static topology optimization without neglecting essential contact and inertial effects. To address non-equilibrium systems (where no fixed supports exist), a boundary condition (BC) sub-optimization framework is proposed, systematically minimizing the discrepancy between dynamic and static strain energy distributions. By integrating this BC sub-optimization with ESD, designers can accurately capture real interface loads, iterating only on physically meaningful static constraints.The work further extends ESD to support multiple load cases simultaneously, implementing duty-cycle weighting and demonstrating concurrent topology optimization for MBS components under diverse operating conditions. Results on a crank-slider mechanism (piston–rod subassembly) show significant mass savings and robust structural performance, illustrating the potential for broader applications in automotive, aerospace, and robotics. By bridging high-fidelity dynamic simulation with static-based optimization, this method significantly expands the scope and fidelity of topology optimization for complex, contact-rich mechanical systems.