A Unified Flexible Multibody Dynamics Framework for Integrated Sizing and Shape Optimization of Nonlinear Truss Systems

Integrated sizing and shape optimization of structural layouts often encounters inherent computational difficulties under nonlinear structural responses and transient buckling criteria. These challenges primarily stem from disjointed sub-problems and localized numerical constraints. This work proposes an integrated optimization methodology utilizing a unified flexible multibody dynamics (FMBD) architecture, with the globally convergent method of moving asymptotes (GCMMA) serving as the mathematical programming solver. By leveraging time-domain dynamic relaxation, complex structural phenomena—including localized post-buckling trajectories and structure-mechanism structural transitions—are mapped into standard kinematic displacement bounds, which are subsequently resolved via the gradient-based solver. Comparative analyses against classic static benchmarks demonstrate that the method’s dynamic and geometric nonlinear characteristics allow the design to naturally circumvent various failure modes associated with ideal results under actual loading, yielding outcomes that better align with engineering requirements. Furthermore, the use of displacement constraints avoids the overly restrictive limitations that buckling criteria often impose on the design space; the ability to simultaneously accommodate and rapidly implement both structural and mechanical configurations expands the optimization space, resulting in significantly lighter structures and mechanisms. This method offers a versatile, stable, and complementary computational pathway for the conceptual design and early-stage exploration of integrated size and shape optimization for structures and mechanisms.