Flexible Multibody Dynamics Based on a Fully Cartesian System of Support Coordinates

1993 ◽  
Vol 115 (2) ◽  
pp. 294-299 ◽  
Author(s):  
N. Vukasovic ◽  
J. T. Celigu¨eta ◽  
J. Garci´a de Jalo´n ◽  
E. Bayo
Keyword(s):  
Multibody Dynamics ◽  
Reference Frames ◽  
Deformable Body ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Body Motion ◽  
Cartesian System ◽  
Flexible Multibody ◽  
Local Reference ◽  
Rigid Multibody

In this paper we present an extension to flexible multibody systems of a system of fully cartesian coordinates previously used in rigid multibody dynamics. This method is fully compatible with the previous one, keeping most of its advantages in kinematics and dynamics. The deformation in each deformable body is expressed as a linear combination of Ritz vectors with respect to a local frame whose motion is defined by a series of points and vectors that move according to the rigid body motion. Joint constraint equations are formulated through the points and vectors that define each link. These are chosen so that a minimum use of local reference frames is done. The resulting equations of motion are integrated using the trapezoidal rule combined with fixed point iteration. An illustrative example that corresponds to a satellite deployment is presented.

Flexible Multibody Dynamics Formulation by Hamilton’s Equations

2010 ◽  
Author(s):  
Martin M. Tong
Keyword(s):  
Multibody Dynamics ◽  
Multibody System ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Body ◽  
Flexible Multibody System ◽  
Generalized Coordinates ◽  
Flexible Multibody ◽  
The Matrix

Numerical solution of the dynamics equations of a flexible multibody system as represented by Hamilton’s canonical equations requires that its generalized velocities q˙ be solved from the generalized momenta p. The relation between them is p = J(q)q˙, where J is the system mass matrix and q is the generalized coordinates. This paper presents the dynamics equations for a generic flexible multibody system as represented by p˙ and gives emphasis to a systematic way of constructing the matrix J for solving q˙. The mass matrix is shown to be separable into four submatrices Jrr, Jrf, Jfr and Jff relating the joint momenta and flexible body mementa to the joint coordinate rates and the flexible body deformation coordinate rates. Explicit formulas are given for these submatrices. The equations of motion presented here lend insight to the structure of the flexible multibody dynamics equations. They are also a versatile alternative to the acceleration-based dynamics equations for modeling mechanical systems.

Finite Element Method of Flexible Multibody Dynamics Based on a New Kind of Floating Frame

1991 ◽  
Author(s):  
You-Fang Lu ◽  
Zhao-Hui Qi ◽  
Bin Wang ◽  
Guan-Min Feng
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Numerical Analysis ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Flexible Multibody ◽  
Floating Frame ◽  
Element Method

Abstract A new kind of floating frame whose parameters do not appear in equations of motion as additional unknowns is defined. Numerical analysis of flexible multibody dynamics is much facilitated by using finite-element iteration of the corresponding equations based on this concept.

A Virtual Body and Joint for Constrained Flexible Multibody Dynamics

1999 ◽  
Author(s):  
D. S. Bae ◽  
J. M. Han ◽  
J. H. Choi
Keyword(s):  
Rigid Body ◽  
Multibody Dynamics ◽  
Reference Frames ◽  
Flexible Multibody Dynamics ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Flexible Body ◽  
Body Dynamics ◽  
Flexible Multibody ◽  
Flexible Body Dynamics

Abstract A convenient implementation method for constrained flexible multibody dynamics is presented by introducing virtual rigid body and joint. The general purpose program for rigid and flexible multibody dynamics consists of three major parts of a set of inertia modules, a set of force modules, and a set of joint modules. Whenever a new force or joint module is added to the general purpose program, the modules for the rigid body dynamics are not reusable for the flexible body dynamics. Consequently, the corresponding modules for the flexible body dynamics must be formulated and programmed again. Since the flexible body dynamics handles more degrees of freedom than the rigid body dynamics does, implementation of the module is generally complicated and prone to coding mistakes. In order to overcome these difficulties, a virtual rigid body is introduced at every joint and force reference frames. New kinematic admissibility conditions are imposed on two body reference frames of the virtual and original bodies by introducing a virtual flexible body joint. There are some computational overheads due to the additional bodies and joints. However, since computation time is mainly depended on the frequency of flexible body dynamics, the computational overhead of the presented method could not be a critical problem, while implementation convenience is dramatically improved.

scholarly journals Multibody dynamics modeling of electromagnetic direct-drive vehicle robot driver

2017 ◽  
Vol 14 (5) ◽  
pp. 172988141773189 ◽  
Author(s):  
Gang Chen ◽  
Weigong Zhang ◽  
Bing Yu
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Direct Drive ◽  
Dynamics Modeling ◽  
Dynamics Model ◽  
Element Mesh ◽  
Flexible Multibody ◽  
Discrete Processing ◽  
Rigid Multibody

Collaborative dynamics modeling of flexible multibody and rigid multibody for an electromagnetic direct-drive vehicle robot driver is proposed in the article. First, spatial dynamic equations of the direct-drive vehicle robot driver are obtained based on multibody system dynamics. Then, the shift manipulator dynamics model and the mechanical leg dynamics model are established on the basis of the multibody dynamics equations. After establishing a rigid multibody dynamics model and conducting finite element mesh and finite element discrete processing, a flexible multibody dynamics modeling of the electromagnetic direct-drive vehicle robot driver is established. The comparison of the simulation results between rigid and flexible multibody is performed. Simulation and experimental results show the effectiveness of the presented model of the electromagnetic direct-drive vehicle robot driver.

A TUTORIAL PRESENTATION OF ALTERNATIVE SOLUTIONS TO THE FLEXIBLE BEAM ON RIGID CART PROBLEM

2005 ◽  
Vol 29 (3) ◽  
pp. 357-373 ◽  
Author(s):  
R. G. Langlois ◽  
R. J. Anderson
Keyword(s):  
Rigid Body ◽  
Multibody Dynamics ◽  
Flexible Multibody Dynamics ◽  
Beam Theory ◽  
General Purpose ◽  
Rigid Body Dynamics ◽  
Body Motion ◽  
Flexible Beam ◽  
Euler Beam ◽  
Flexible Multibody

A classical planar problem in forward flexible multibody dynamics is thoroughly investigated. The system consists of a damped flexible beam cantilevered to a rigid translating cart. The problem is solved using three distinctly different conventional approaches presented in roughly the chronological order in which they have been applied to flexible dynamic systems. First, a modal superposition formulation based on Bernoulli-Euler beam theory is developed. Second, an alternative solution is developed drawing exclusively on methods for rigid body dynamics combined with a knowledge of the theoretical modal behaviour of continuous beams. Third, a formulation based on the conventional finite element method using four-degree-of-freedom planar beam elements is adapted to include the rigid body motion of the cart. The relative merits of the three formulations are discussed and numerical simulation results generated using each of the three formulations are compared with each other and with a solution from a general-purpose flexible multibody dynamics formulation that is briefly outlined. The relative accuracy and efficiency of the methods and the challenges associated with generalizing each formulation are discussed.

Discontinuous Galerkin Method and Dual-SLERP for Time Integration of Flexible Multibody Dynamics

2020 ◽  
Vol 15 (9) ◽  
Author(s):  
Shilei Han ◽  
Olivier A. Bauchau
Keyword(s):  
Discontinuous Galerkin ◽  
Multibody Dynamics ◽  
Time Integration ◽  
Flexible Multibody Dynamics ◽  
Differential Algebraic Equations ◽  
Body Motion ◽  
Motion Field ◽  
Algebraic Equations ◽  
Time Step ◽  
Flexible Multibody

Abstract A novel time-discontinuous Galerkin (DG) method is introduced for the time integration of the differential-algebraic equations governing the dynamic response of flexible multibody systems. In contrast to traditional Galerkin methods, the rigid-body motion field is interpolated using the dual spherical linear scheme. Furthermore, the jumps inherent to time-DG methods are expressed in terms of a parameterization of the relative motion from one time-step to the next. The proposed scheme is third-order accurate for initial value problems of both rigid and flexible multibody dynamics.

Verification of Absolute Nodal Coordinate Formulation in Flexible Multibody Dynamics via Physical Experiments of Large Deformation Problems

2005 ◽  
Vol 1 (1) ◽  
pp. 81-93 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Su-Jin Park ◽  
Oleg N. Dmitrochenko ◽  
Dmitry Yu. Pogorelov
Keyword(s):  
Large Deformation ◽  
Multibody Dynamics ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Geometrical Nonlinearity ◽  
Flexible Multibody Dynamics ◽  
Absolute Nodal Coordinate ◽  
Spatial Beams ◽  
Flexible Multibody ◽  
Large Deformation Problems

A review of the current state of the absolute nodal coordinate formulation (ANCF) is proposed for large-displacement and large-deformation problems in flexible multibody dynamics. The review covers most of the known implementations of different kinds of finite elements including thin and thick planar and spatial beams and plates, their geometrical description inherited from FEM, and formulations of the most important elements of equations of motion. Much attention is also paid to simulation examples that show reasonableness and accuracy of the formulations applied to real physical problems and that are compared with experiments having significant geometrical nonlinearity. Current and further development directions of the ANCF are also briefly outlined.

Sign in / Sign up

Export Citation Format

Share Document