Reanalysis-based fast solution algorithm for flexible multi-body system dynamic analysis with floating frame of reference formulation

In order to improve the computational efficiency of flexible multi-body system dynamic analysis with floating frame of reference formulation (FFRF), a reanalysis-based fast solution algorithm is developed here. The data of FFRF analysis process can be divided into two parts: unchanged mass and stiffness matrices part kept by deformation, and changed mass and stiffness matrices part caused by rigid motion and joint constraints. In the proposed method, the factorization of the unchanged part is reused in the entire solution process via employing the reanalysis concept; and the changed part is treated as structural modification. Meanwhile, the joint constraints are handled with an exact reanalysis method—the Sherman–Morrison–Woodbury (SMW) formula, which is also beneficial for saving the computational cost. Numerical examples demonstrate that the computational efficiency of the proposed method is higher than that of full analysis, especially in large scale problems. Moreover, since the proposed fast FFRF solution algorithm is-based on exact reanalysis methods, there is no theoretical error between the results obtained by the fast solution algorithm and full analysis method.

[1]  Chen Xiang-zi,et al.  Structural modal reanalysis for large, simultaneous and multiple type modifications , 2015 .

[2]  Zhong-Sheng Liu,et al.  Structural modal reanalysis for topological modifications of finite element systems , 2000 .

[3]  P. Eberhard,et al.  Simulation process of flexible multibody systems with non-modal model order reduction techniques , 2011 .

[4]  Timothy A. Davis,et al.  Modifying a Sparse Cholesky Factorization , 1999, SIAM J. Matrix Anal. Appl..

[5]  Jan Holnicki-Szulc,et al.  The virtual distortion method—a versatile reanalysis tool for structures and systems , 2008 .

[6]  Su-huan Chen,et al.  A method for modal reanalysis of topological modifications of structures , 2006 .

[7]  Guangyao Li,et al.  An adaptive time-based global method for dynamic reanalysis , 2013 .

[8]  Christophe Pierre,et al.  Modal Reduction of a Nonlinear Rotating Beam Through Nonlinear Normal Modes , 2002 .

[9]  Hiroyuki Sugiyama,et al.  Spatial joint constraints for the absolute nodal coordinate formulation using the non-generalized intermediate coordinates , 2011 .

[10]  Xin Chen,et al.  An Adaptive Static Reanalysis Method for Structural Modifications Using Epsilon Algorithm , 2009, 2009 International Joint Conference on Computational Sciences and Optimization.

[11]  Peter Benner,et al.  Krylov-Subspace Based Model Reduction of Nonlinear Circuit Models Using Bilinear and Quadratic-Linear Approximations , 2012 .

[12]  Zhengguang Li,et al.  Static reanalysis of structures with added degrees of freedom , 2005 .

[13]  R. Freund.  Krylov-subspace methods for reduced-order modeling in circuit simulation , 2000 .

[14]  Peter Eberhard,et al.  A two-step approach for model reduction in flexible multibody dynamics , 2007 .

[15]  Paolo Tiso,et al.  Nonlinear model order reduction for flexible multibody dynamics: a modal derivatives approach , 2016 .

[16]  Baisheng Wu,et al.  Method of Updating the Cholesky Factorization for Structural Reanalysis with Added Degrees of Freedom , 2014 .

[17]  Z. Bai.  Krylov subspace techniques for reduced-order modeling of large-scale dynamical systems , 2002 .

[18]  Luis E. Suarez,et al.  Dynamic condensation method for structural eigenvalue analysis , 1992 .

[19]  A. Mikkola,et al.  A new locking-free shear deformable finite element based on absolute nodal coordinates , 2007 .

[20]  Guangwei Meng,et al.  Dynamic response reanalysis for modified structures under arbitrary excitation using epsilon-algorithm , 2008 .

[21]  Uri Kirsch,et al.  A unified reanalysis approach for structural analysis, design, and optimization , 2003 .

[22]  Yehia A. Khulief,et al.  On the dynamic analysis of rotors using modal reduction , 1997 .

[23]  Tae-Won Park,et al.  The development of a sliding joint for very flexible multibody dynamics using absolute nodal coordinate formulation , 2008 .

[24]  William W. Hager,et al.  Updating the Inverse of a Matrix , 1989, SIAM Rev..

[25]  Peter Eberhard,et al.  Flexible Multibody Systems With Large Deformations Using Absolute Nodal Coordinates for Isoparametric Solid Brick Elements , 2003 .

[26]  Timothy A. Davis,et al.  Multiple-Rank Modifications of a Sparse Cholesky Factorization , 2000, SIAM J. Matrix Anal. Appl..

[27]  J. Mayo,et al.  Describing Rigid-Flexible Multibody Systems Using Absolute Coordinates , 2003 .

[28]  Su-huan Chen,et al.  A new method of structural modal reanalysis for topological modifications , 2002 .

[29]  Peter W. Likins,et al.  Finite element appendage equations for hybrid coordinate dynamic analysis. , 1972 .

[30]  Ronald L. Huston,et al.  Multibody Dynamics — Modeling and Analysis Methods , 1991 .

[31]  Hu Wang,et al.  A novel Multi-Grid assisted reanalysis for re-meshed finite element models , 2017 .

[32]  J. Sherman,et al.  Adjustment of an Inverse Matrix Corresponding to a Change in One Element of a Given Matrix , 1950 .

[33]  U. Kirsch,et al.  Efficient reanalysis for topological optimization , 1993 .

[34]  A. Shabana.  Definition of the Slopes and the Finite Element Absolute Nodal Coordinate Formulation , 1997 .

[35]  Ahmed A. Shabana,et al.  Application of the Absolute Nodal Coordinate Formulation to Large Rotation and Large Deformation Problems , 1998 .

[36]  Ahmed A. Shabana,et al.  A new multibody system approach for tire modeling using ANCF finite elements , 2016 .

[37]  Matej Sulitka,et al.  Application of Krylov Reduction Technique for a Machine Tool Multibody Modelling , 2014 .

[38]  Gui-Quan Sun,et al.  Mathematical modeling of population dynamics with Allee effect , 2016, Nonlinear Dynamics.

[39]  Raphael T. Haftka,et al.  Fast exact linear and non‐linear structural reanalysis and the Sherman–Morrison–Woodbury formulas , 2001 .

[40]  Uri Kirsch,et al.  Nonlinear and dynamic structural analysis using combined approximations , 2007 .

[41]  Bin Xu,et al.  Modal reanalysis methods for structural large topological modifications with added degrees of freedom and non-classical damping , 2007 .

[42]  Peter Eberhard,et al.  Linear model reduction of large scale industrial models in elastic multibody dynamics , 2014 .

[43]  Nong Zhang,et al.  Dynamic computation of flexible multibody system with uncertain material properties , 2016 .

[44]  Daniel Materna,et al.  Nonlinear reanalysis for structural modifications based on residual increment approximations , 2016 .

[45]  A. Shabana,et al.  Three-dimensional absolute nodal co-ordinate formulation: Plate problem , 1997 .

[46]  Ahmed A. Shabana,et al.  Clamped end conditions and cross section deformation in the finite element absolute nodal coordinate formulation , 2009 .

[47]  Guangyao Li,et al.  An exact reanalysis method for structures with local modifications , 2016 .

[48]  Paolo Tiso,et al.  A modal derivatives enhanced Rubin substructuring method for geometrically nonlinear multibody systems , 2018, Multibody System Dynamics.