Analysis of multibody systems experiencing large elastic deformations

This study presents an approach based on the floating frame of reference method to model complex three-dimensional bodies in a multibody system using solid and plate elements. Unlike most of the formulations based on the floating frame of reference method, which assume small or moderate deformations, the present formulation allows large elastic deformations within each frame by using the corotational form of the updated Lagrangian description of motion. The implicit integration scheme is based on the Generalized-α method, and kinematic joints are invoked in the formulation through the coordinate partitioning method. A triangular element with three nodes and a solid wedge element with six nodes have been developed to facilitate the modeling of three-dimensional bodies with arbitrary geometry. Various numerical examples have been considered to demonstrate the robustness of the present approach.

[1]  O. C. Zienkiewicz,et al.  An alpha modification of Newmark's method , 1980 .

[2]  K. M. Liew,et al.  Non-linear substructure approach for dynamic analysis of rigid-flexible multibody systems , 1994 .

[3]  J. Gerstmayr.  Strain Tensors in the Absolute Nodal Coordinate and the Floating Frame of Reference Formulation , 2003 .

[4]  A. Banerjee,et al.  Dynamics of an Arbitrary Flexible Body in Large Rotation and Translation , 1989 .

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

[6]  G. E. O. Widera,et al.  Large reference displacement analysis of composite plates. Part II: Computer implementation , 1993 .

[7]  I. Sharf.  Geometric Stiffening in Multibody Dynamics Formulations , 1995 .

[8]  A. Shabana,et al.  Large reference displacement analysis of composite plates part I: Finite element formulation , 1993 .

[9]  T. R. Kane,et al.  Dynamics of a cantilever beam attached to a moving base , 1987 .

[10]  Olivier A. Bauchau,et al.  On the Modeling of Shells in Multibody Dynamics , 2000 .

[11]  A. Shabana,et al.  Total Lagrangian formulation for the large displacement analysis of rectangular plates , 1990 .

[12]  J. Mayo,et al.  Geometrically non-linear formulation of flexible multibody systems in terms of beam elements: Geometric stiffness , 1996 .

[13]  A. Tessler,et al.  A C o -anisoparametric three-node shallow shell element , 1990 .

[14]  T. Kane,et al.  Dynamics of a Plate in Large Overall Motion , 1989 .

[15]  Johannes Gerstmayr,et al.  The comparative analysis of the fully nonlinear, the linear elastic and the consistently linearized equations of motion of the 2D elastic pendulum , 2004 .

[16]  A. Erdman,et al.  Dynamics of Flexible Beams and Plates in Large Overall Motions , 1992 .

[17]  A. Shabana,et al.  Nonlinear Finite Element Formulation for the Large Displacement Analysis of Plates , 1990 .

[18]  Jintai Chung,et al.  A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method , 1993 .

[19]  S. Atluri,et al.  Dynamic analysis of planar flexible beams with finite rotations by using inertial and rotating frames , 1995 .

[20]  Tamer M. Wasfy,et al.  Computational strategies for flexible multibody systems , 2003 .

[21]  C. Rankin,et al.  An element independent corotational procedure for the treatment of large rotations , 1986 .

[22]  Erdogan Madenci,et al.  Nonlinear elastic deformations of moderately thick laminated shells subjected to large and rapid rigid-body motion , 1996 .

[23]  Oskar Wallrapp,et al.  Representation of geometric stiffening in multibody system simulation , 1991 .

[24]  Y. Vetyukov.  CONSISTENT APPROXIMATION FOR THE STRAIN ENERGY OF A 3D ELASTIC BODY ADEQUATE FOR THE STRESS STIFFENING EFFECT , 2004 .

[25]  Farid Amirouche,et al.  Influence of Geometric Nonlinearities in the Dynamics of Flexible Treelike Structures , 1989 .

[26]  B. J. Hsieh,et al.  Non-Linear Transient Finite Element Analysis with Convected Co--ordinates , 1973 .

[27]  T. Tsang,et al.  A novel approach to the dynamic analysis of highly deformable bodies , 1996 .

[28]  Ahmed A. Shabana,et al.  Flexible Multibody Dynamics: Review of Past and Recent Developments , 1997 .

[29]  Daniel García-Vallejo,et al.  Study of the Geometric Stiffening Effect: Comparison of Different Formulations , 2004 .

[30]  Edward L. Wilson,et al.  Incompatible Displacement Models , 1973 .

[31]  Michał Kleiber,et al.  Computational aspects of nonlinear structural systems with large rigid body motion , 2001 .

[32]  Robert V. Whitman,et al.  Seismic risk analysis of discrete system of sites , 1977 .

[33]  Arun K. Banerjee,et al.  Contributions of Multibody Dynamics to Space Flight: A Brief Review , 2003 .

[34]  E. M. Bakr,et al.  Geometrically nonlinear analysis of multibody systems , 1986 .

[35]  E. Haug,et al.  Geometric non‐linear substructuring for dynamics of flexible mechanical systems , 1988 .

[36]  E. Madenci,et al.  DYNAMIC RESPONSE OF THIN COMPOSITE SHELLS EXPERIENCING NON-LINEAR ELASTIC DEFORMATIONS COUPLED WITH LARGE AND RAPID OVERALL MOTIONS , 1996 .

[37]  Sung-Soo Kim,et al.  A CRITERION ON INCLUSION OF STRESS STIFFENING EFFECTS IN FLEXIBLE MULTIBODY DYNAMIC SYSTEM SIMULATION , 1997 .

[38]  Thomas J. R. Hughes,et al.  Improved numerical dissipation for time integration algorithms in structural dynamics , 1977 .

[39]  E. Haug,et al.  Generalized Coordinate Partitioning for Dimension Reduction in Analysis of Constrained Dynamic Systems , 1982 .

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

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

[42]  E. Wilson,et al.  A non-conforming element for stress analysis , 1976 .