Topology optimization for dynamic flexible multibody systems using the Flexible Natural Coordinates Formulation

This work proposes a fully-coupled topology optimization methodology to optimize the struc-tural components of flexible multibody systems. It employs the Adjoint Variable Method (AVM) and the Flexible Natural Coordinates Formulation (FNCF) to achieve constant Jacobians in the reduced mass, stiffness, and damping matrix when computing the sensitivity information. Although a fully-coupled approach is inherently computationally more expensive than a method based on equivalent static load, the use of FNCF can reduce the computational time of a fully -coupled approach by only computing these terms once per design iteration, as opposed to for each timestep. The methodology is demonstrated through two optimization cases on a slider -crank multibody system and compared with the commonly used equivalent static load approach. The second case showcases the inter-component and system-level optimization capabilities of the fully-coupled approach by minimizing the deformation energy of two flexible bodies while only optimizing one body's structural design.