Direct Differentiation of the Floating Frame of Reference Formulation via Invariants for Gradient-Based Design Optimization

This paper applies the analytical differentiation of the equations of motion of flexible multibody systems modeled with the floating frame of reference formulation based on invariants. This leads to an efficient sensitivity analysis with the direct differentiation method and enables efficient design optimization of flexible multibody systems. The main results are the analytical derivatives of the equation terms of the floating frame of reference formulation in terms of inertia shape integrals or invariants. The introduced sensitivity analysis is applied and verified with a slider–crank mechanism modeled with beam elements. After numerical studies to assess the speedup, design optimization is carried out using the lightweight design formulation.