A Detailed Comparison of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems

In extension to a former work, a detailed comparison of the absolute nodal coordinate formulation (ANCF) and the floating frame of reference formulation (FFRF) is performed for standard static and dynamic problems, both in the small and large deformation regimes. Special emphasis is laid on converged solutions and on a comparison to analytical and numerical solutions from the literature. In addition to the work of previous authors, the computational performance of both formulations is studied for the dynamic case, where detailed information is provided, concerning the different effects influencing the single parts of the computation time. In case of the ANCF finite element, a planar formulation based on the Bernoulli-Euler theory is utilized, consisting of two position and two slope coordinates in each node only. In the FFRF beam finite element, the displacements are described by the rigid body motion and a small superimposed transverse deflection. The latter is described by means of two static modes for the rotation at the boundary and a user-defined number of eigenmodes of the clamped-clamped beam. In numerical studies, the accuracy and computational costs of the two formulations are compared for a cantilever beam, a pendulum, and a slider-crank mechanism. It turns out that both formulations have comparable performance and that the choice of the optimal formulation depends on the problem configuration. Recent claims in literature that the ANCF would have deficiencies compared with the FFRF thus can be refuted.

[1]  A. Shabana,et al.  DEVELOPMENT OF SIMPLE MODELS FOR THE ELASTIC FORCES IN THE ABSOLUTE NODAL CO-ORDINATE FORMULATION , 2000 .

[2]  A. Mikkola,et al.  Description of Elastic Forces in Absolute Nodal Coordinate Formulation , 2003 .

[3]  H. Irschik,et al.  Vibrations of the elasto-plastic pendulum , 2003 .

[4]  J. Gerstmayr,et al.  A 3D Finite Element Method for Flexible Multibody Systems , 2006 .

[5]  Horst Czichos,et al.  Hütte : die Grundlagen der Ingenieurwissenschaften , 1989 .

[6]  R. Y. Yakoub,et al.  Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications , 2001 .

[7]  Aki Mikkola,et al.  A two-dimensional shear deformable beam element based on the absolute nodal coordinate formulation , 2005 .

[8]  Johannes Gerstmayr,et al.  Analysis of Stress and Strain in the Absolute Nodal Coordinate Formulation , 2006 .

[9]  P. Likins,et al.  Floating reference frames for flexible spacecraft , 1977 .

[10]  Ahmed A. Shabana,et al.  Dynamics of Multibody Systems , 2020 .

[11]  Johannes Gerstmayr,et al.  On the Accuracy and Computational Costs of the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation in Deformable Multibody Systems , 2007 .

[12]  Johannes Gerstmayr,et al.  On the correct representation of bending and axial deformation in the absolute nodal coordinate formulation with an elastic line approach , 2008 .

[13]  A. Shabana,et al.  Use of the Finite Element Absolute Nodal Coordinate Formulation in Modeling Slope Discontinuity , 2003 .

[14]  A. Mikkola,et al.  Studies on the Stiffness Properties of the Absolute Nodal Coordinate Formulation for Three-Dimensional Beams , 2003 .

[15]  A. Shabana,et al.  Equivalence of the floating frame of reference approach and finite element formulations , 1998 .

[16]  A. Shabana,et al.  EFFICIENT INTEGRATION OF THE ELASTIC FORCES AND THIN THREE-DIMENSIONAL BEAM ELEMENTS IN THE ABSOLUTE NODAL COORDINATE FORMULATION , 2005 .

[17]  Franz Ziegler,et al.  Mechanics of solids and fluids , 1991 .

[18]  Johannes Gerstmayr,et al.  Analysis of Thin Beams and Cables Using the Absolute Nodal Co-ordinate Formulation , 2006 .

[19]  B. D. Veubeke,et al.  The dynamics of flexible bodies , 1976 .

[20]  H. Ashley.  Observations on the dynamic behavior of large flexible bodies in orbit. , 1967 .

[21]  Oleg Dmitrochenko,et al.  Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation , 2003 .

[22]  K. Hjelmstad.  Fundamentals of Structural Mechanics , 1996 .

[23]  M. Géradin,et al.  Flexible Multibody Dynamics: A Finite Element Approach , 2001 .

[24]  J. C. Simo,et al.  On the Dynamics of Flexible Beams Under Large Overall Motions—The Plane Case: Part II , 1986 .

[25]  Werner Schiehlen,et al.  Multibody System Dynamics: Roots and Perspectives , 1997 .

[27]  E. Reissner.  On one-dimensional finite-strain beam theory: The plane problem , 1972 .

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

[29]  Mohamed A. Omar,et al.  A TWO-DIMENSIONAL SHEAR DEFORMABLE BEAM FOR LARGE ROTATION AND DEFORMATION PROBLEMS , 2001 .

[30]  J. M. Jiménez,et al.  Recursive and Residual Algorithms for the Efficient Numerical Integration of Multi-Body Systems , 2004 .