A flexible natural coordinates formulation (FNCF) for the efficient simulation of small‐deformation multibody systems

Abstract

SummaryThis paper introduces the novel flexible natural coordinates formulation to model small‐deformation multibody dynamics. The main contribution of this work is its resulting constant mass matrix and quadratic constraint equations devoid of any other nonlinearities. These properties are similar to those of a natural coordinates formulation for rigid multibody systems with the addition of constant damping and stiffness matrices to model the flexibility under the assumption of small deformations. As such, it is a straightforward extension to natural coordinates while maintaining its beneficial properties. The main concept of the current approach is to introduce ample redundancy in the set of generalized coordinates to simplify the kinematics ensuring the aforementioned properties and the similarity to a natural coordinates approach. This is not achievable by standard techniques that introduce redundancy. Not only does this offer a very simple equation structure but also interesting properties toward the development of system‐level model order reduction techniques for flexible multibody systems as well as a straightforward parameter gradient extraction. The formulation accuracy is validated with a floating frame of reference implementation.