Partitioned analysis of flexible multibody systems using filtered linear finite element deformational modes

Abstract

SUMMARYThis work presents a partitioned finite element formulation for flexible multibody systems, based on the floating frame (FF) approach, under the assumption of small deformations but arbitrarily large rotations of the bodies. In classical FF of reference methods, deformational modes are normally computed by modal analysis. In this approach, free‐floating modes are eliminated from the linear model using projection techniques and substituted by a complete set of non‐linear finite rotations. In this way, all deformational modes are retained, and no modal selection is needed. The main difference between this work and a classical FF of reference formulation is an algebraic separation of pure deformational modes from rigid‐body motions. The proposed methodology presents the following advantages. First, the position and orientation of the FF has no restriction and can be freely located in the body with identical results. Second, the formulation uses only the linear finite element matrices of a classical vibration problem; hence, they can be easily obtained from linear FEM packages. Third, no selection of modes is needed, all deformational modes are retained through the filtering process. And finally, thanks to the use of localized Lagrangian multipliers (LLM), a partitioned system is obtained that can be solved iteratively and in a distributed manner by available scalable solvers. Copyright © 2014 John Wiley & Sons, Ltd.

Accelerating the convergence of AFETI partitioned analysis of heterogeneous structural dynamical systems

“…The variational energy functional derived previously can be further decomposed by dividing the total displacements into deformations and rigid-body motions. This is accomplished by using the projector [46,20]:…”

“…al. for statics [12,15,14], generalized to structural dynamics by Gumaste et al [13] and later extended to multi-body dynamics with large rotations [20].…”

“…A partitioned subdomain interacts with its adjacent subdomains through the interface forces and moments or Lagrange multipliers. The treatment of Lagrange multiplier-connected components of a mechanical system has been addressed by many authors, particularly in multibody dynamics [18,19,20], parallel computation [21,22,23,24,25,26,27,28,29,30,31,32], multistep integration [33,34], contact problems [35,36] and multiphysics simulation [37,38,16,39].…”