Structural sensitivity analysis of flexible multibody systems modeled with the floating frame of reference approach using the adjoint variable method

For the efficient analysis and optimization of flexible multibody systems, gradient information is often required. Next to simple and easy-to-implement finite difference approaches, analytical methods, such as the adjoint variable method, have been developed and are now well established for the sensitivity analysis in multibody dynamics. They allow the computation of exact gradients and require normally less computational effort for large-scale problems. In the current work, we apply the adjoint variable method to flexible multibody systems with kinematic loops, which are modeled using the floating frame of reference formulation. Thereby, in order to solve ordinary differential equations only, the equations of motion are brought into minimal form using coordinate partitioning, and the constraint equations at position and velocity level are incorporated in the adjoint dynamics. For testing and illustrative purposes, the procedure is applied to compute the structural gradient for a flexible piston rod of a slider–crank mechanism.