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.

Incremental Finite Element Formulations and Flexible Multibody Dynamics

1999 ◽  
Author(s):  
Marcello Berzeri ◽  
Marcello Campanelli ◽  
A. A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Dynamics ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
Finite Element Formulations

Abstract In this investigation, the performance of two different large displacement finite element formulations in the analysis of flexible multibody systems is investigated. These are the incremental corotational procedure proposed by Rankin and Brogan [8] and the non-incremental absolute nodal coordinate formulation recently proposed [9]. It is demonstrated in this investigation that the limitation resulting from the use of the nodal rotations in the incremental corotational procedure can lead to simulation problems even when very simple flexible multibody applications are considered.

Review of Finite Elements Using Absolute Nodal Coordinates for Large-Deformation Problems and Matching Physical Experiments

2005 ◽  
Author(s):  
Wan-Suk Yoo ◽  
Oleg Dmitrochenko ◽  
Dmitry Yu. Pogorelov
Keyword(s):  
Finite Elements ◽  
Large Deformation ◽  
Equations Of Motion ◽  
Flexible Multibody Dynamics ◽  
Absolute Nodal Coordinates ◽  
Current State ◽  
Physical Experiments ◽  
Spatial Beams ◽  
Nodal Coordinates ◽  
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 the reasonableness and accuracy of the formulation applied to real physical problems and that are compared with experiments having significant geometrical non-linearity. Current and further development directions of the ANCF are also briefly outlined.

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.

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.

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.

Efficient Coupling of Absolute Nodal Coordinate Formulation Flexible Bodies With an Existing Multibody Dynamics Code

2012 ◽  
Author(s):  
Jeff Liu ◽  
Abdel-Nasser A. Mohamed
Keyword(s):  
Multibody Dynamics ◽  
Absolute Nodal Coordinate Formulation ◽  
Sparse Matrix ◽  
Equations Of Motion ◽  
Matrix Solution ◽  
State Equations ◽  
Combined System ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Efficient Coupling

A couple of issues are identified in the process to embed absolute nodal coordinate formulation (ANCF) flexible bodies in an existing multibody dynamics code. (1) The generalized coordinates of ANCF must be solved together with those of the rest of the mechanism in a combined system of the equations of motion. (2) The various constraints, joints, and forces elements supported in the multibody dynamics code must be extended to the ANCF flexible bodies without major code restructuring. This paper describes two novel techniques that were devised to solve these issues. The first is the idea of interface triad. We will demonstrate how to construct the interface triad such that all exiting constraints, joints, and forces elements are automatically supported. The second idea is to represent the equations of motion of the ANCF body as a user-defined subroutine element representing a set of implicit general state equations subroutine (GSESUB). By treating each ANCF body modularly as a user-defined subroutine, not only all existing integration options of its host solver, e.g., HHT or DAE index-1, 2, and 3, etc., are automatically supported, but also the existing features such as parallel computing and sparse matrix solution of the existing multibody dynamics software are supported with minimum programming. Numerical examples are presented to demonstrate the efficiency and the success of these two techniques.

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