A review of flexible multibody dynamics for gradient-based design optimization

Abstract

Design optimization of flexible multibody dynamics is critical to reducing weight and therefore increasing efficiency and lowering costs of mechanical systems. Simulation of flexible multibody systems, though, typically requires high computational effort which limits the usage of design optimization, especially when gradient-free methods are used and thousands of system evaluations are required. Efficient design optimization of flexible multibody dynamics is enabled by gradient-based optimization methods in concert with analytical sensitivity analysis. The present study summarizes different formulations of the equations of motion of flexible multibody dynamics. Design optimization techniques are introduced, and applications to flexible multibody dynamics are categorized. Efficient sensitivity analysis is the centerpiece of gradient-based design optimization, and sensitivity methods are introduced. The increased implementation effort of analytical sensitivity analysis is rewarded with high computational efficiency. An exemplary solution strategy for system and sensitivity evaluations is shown with the analytical direct differentiation method. Extensive literature sources are shown related to recent research activities.

Analytical sensitivity analysis of dynamic problems with direct differentiation of generalized-α time integration

“…This will be carried out with Newton steps. The flexible multibody system is modeled with the floating frame of reference formulation [26,27,28]. The generic index-3 differential-algebraic equation for a flexible multibody system with holonomic constraints is written as follows: m q,t q (t) + d q,t q (t) + k q,t q (t) + J T Φ q,t λ (t) = F ext q, q,t + F v q, q,t ,…”

Modeling, Design and Optimization of Flexible Mechanical Systems

“…Design optimization of multibody dynamics presents challenges in regard to, i.a., sensitivity analysis, high computational effort and transient behavior. Design optimization of rigid multibody systems is handled by [34][35][36][37], while the optimization of flexible multibody dynamics is currently an active research field and reviewed in [38].…”

A comparison of a level set method and the method of moving asymptotes for the topology optimization of flexible components in multibody systems

“…The topology optimization of flexible multibody systems is a challenging task of high interest. Currently, different fullyand weakly-coupled methods are available to provide the gradient, which can be used within a gradient-based optimization process, see also [5,18] for different gradient strategies. In literature, the method of moving asymptotes (MMA) or level set methods (LSM-s) are typically used to perform gradient-based optimization of flexible multibody systems, see [17] for the MMA-algorithm and [3] for a review of level set methods.…”