Sensitivity Analysis of Flexible Multibody Systems Based on the Motion Formalism and the Discrete Adjoint Method

The combination of analysis and optimization methods in mechanical engineering, also known as design optimization, has great potential in product development. Robust sensitivity analyses that provide reliable and efficient objective function gradients play a key role in design optimization. This paper presents a discrete adjoint method for the sensitivity analysis of flexible mechanical systems. The ultimate goal is to be able to relate the physical properties of beam cross-sections to the dynamic behavior of the system, which is key to design realistic flexible elements. The underlying flexible multibody formulation is one that supports large-amplitude motion, beams with sophisticated composite cross-sections, and kinematic joints. A summary of the kinematic and dynamic foundations of the forward equations is presented first. Then, a discrete adjoint method, along with meaningful examples and validation, is presented. The method has proven to provide extremely accurate and reliable sensitivities.