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.

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.

Sliding Joint Constraints for the Analysis of Flexible Multibody Systems Using Intermediate Coordinates

2011 ◽  
Author(s):  
Ryo Honda ◽  
Hiroki Yamashita ◽  
Hiroyuki Sugiyama
Keyword(s):  
Multibody Dynamics ◽  
Absolute Nodal Coordinate Formulation ◽  
Rigid Bodies ◽  
Computer Algorithms ◽  
Arc Length ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Sliding Joint ◽  
Joint Constraints ◽  
The Absolute

In this investigation, formulations of sliding joint constraints for flexible bodies modeled using the absolute nodal coordinate formulation are developed using intermediate coordinates. Since modeling of prismatic and cylindrical joints for flexible bodies requires solutions to moving boundary problems in which joint definition points are moving on flexible bodies, arc-length coordinates are introduced for defining time-variant constraint definition points on flexible bodies. While this leads to a systematic modeling procedure for sliding joints, specialized formulations and implementations are required in general multibody dynamics computer algorithms. For this reason, intermediate coordinates are introduced to derive a mapping between the generalized gradient coordinates used in the absolute nodal coordinate formulation and the intermediate rotational coordinates used for defining the orientation constraints with rigid bodies. With this mapping, existing joint constraint libraries formulated for rigid bodies can be employed for the absolute nodal coordinate formulation without significant modifications. It is also demonstrated that the intermediate coordinates and arc-length coordinates introduced for modeling sliding joint constraints can be systematically eliminated from the equations of motion and standard differential algebraic equations used in general multibody dynamics computer algorithms can be obtained. Several numerical examples are presented in order to demonstrate the use of the formulation developed in this investigation.

A Numerical Approach to Solving Flexible Multibody Systems Using the Absolute Nodal Coordinate Formulation

1999 ◽  
Author(s):  
R. Y. Yakoub ◽  
A. A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Sparse Matrix ◽  
Mass Matrix ◽  
Numerical Approach ◽  
Absolute Nodal Coordinates ◽  
Absolute Nodal Coordinate ◽  
Velocity Transformation ◽  
Flexible Multibody ◽  
Nodal Coordinates ◽  
The Absolute

Abstract By utilizing the fact that the absolute nodal coordinate formulation leads to a constant mass matrix, a Cholesky decomposition of the mass matrix can be used to obtain a constant velocity transformation matrix. This velocity transformation can be used to express the absolute nodal coordinates in terms of the generalized Cholesky coordinates. In this case, the inertia matrix associated with the Cholesky coordinates is the identity matrix, and therefore, an optimum sparse matrix structure can be obtained for the augmented multibody equations of motions. The implementation of a computer procedure based on the absolute nodal coordinate formulation and Cholesky coordinates is discussed in this paper. A flexible four-bar linkage is presented in this paper in order to demonstrate the use of Cholesky coordinates in the simulation of the small and large deformations in flexible multibody applications. The results obtained from the absolute nodal coordinate formulation are compared to those obtained from the floating frame of reference formulation.

Three-Dimensional Solid Brick Element Using Slopes in the Absolute Nodal Coordinate Formulation

2013 ◽  
Vol 9 (2) ◽  
Author(s):  
Alexander Olshevskiy ◽  
Oleg Dmitrochenko ◽  
Chang-Wan Kim
Keyword(s):  
Finite Element ◽  
Finite Elements ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Test Problems ◽  
Absolute Nodal Coordinate ◽  
Highly Nonlinear ◽  
Brick Element ◽  
The Absolute

The present paper contributes to the field of flexible multibody systems dynamics. Two new solid finite elements employing the absolute nodal coordinate formulation are presented. In this formulation, the equations of motion contain a constant mass matrix and a vector of generalized gravity forces, but the vector of elastic forces is highly nonlinear. The proposed solid eight node brick element with 96 degrees of freedom uses translations of nodes and finite slopes as sets of nodal coordinates. The displacement field is interpolated using incomplete cubic polynomials providing the absence of shear locking effect. The use of finite slopes describes the deformed shape of the finite element more exactly and, therefore, minimizes the number of finite elements required for accurate simulations. Accuracy and convergence of the finite element is demonstrated in nonlinear test problems of statics and dynamics.

Study on Elastic Forces of the Absolute Nodal Coordinate Formulation for Deformable Beams

1999 ◽  
Author(s):  
Yoshitaka Takahashi ◽  
Nobuyuki Shimizu
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Equations Of Motion ◽  
Nonlinear Function ◽  
Absolute Nodal Coordinates ◽  
Large Rotation ◽  
Inertia Effects ◽  
Absolute Nodal Coordinate ◽  
Elastic Forces ◽  
The Absolute

Abstract There are three basic finite element formulations which are used in the dynamics of flexible beams. These are the floating frame of reference approach, the finite segment method and the large rotation vector approach. Recently, the absolute nodal coordinate formulation was proposed by A.A.Shabana et al. In this procedure, there is no need to transform the element matrices since the equations of motion are defined in terms of absolute nodal coordinates. The mass matrix becomes constant, whereas the stiffness matrix becomes nonlinear function of time, even in case of linear elastic problems. One possible method to avoid such cumbersome of the absolute nodal coordinate formulation in calculating clastic forces is to assume the infinitesimal deformation theory against beams undergoing large rotation. In this paper, a new formulation to calculate the elastic forces and add the rotary inertia effects in the expression of the inertia forces. This formulation is based on the assumption that the deformations within each element remain very small. The expression of the resulting clastic force is simple, and the need for performing coordinate transformation is avoided. As the method assumes that the deformation of the beam from a selected beam axis is very small, a large number of finite elements is required for large deformation problems. However, the formulation has been found to be efficient for large rotation and medium deformation problems. Numerical examples are demonstrated for this formulation by using planar flexible pendulum problems.

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.

Modeling Rotorcraft Dynamics With Finite Element Multibody Procedures

2009 ◽  
Author(s):  
Olivier A. Bauchau
Keyword(s):  
Finite Element ◽  
Multibody Dynamics ◽  
Equations Of Motion ◽  
Maximum Efficiency ◽  
Flexible Bodies ◽  
Modal Reduction ◽  
Nonlinear Finite Element Methods ◽  
Deformable Bodies ◽  
Joint Element ◽  
Key Aspects

This paper describes a multibody dynamics approach to the modeling of rotorcraft systems and reviews the key aspects of the simulation procedure. The multibody dynamics analysis is cast within the framework of nonlinear finite element methods, and the element library includes rigid and deformable bodies as well as joint elements. No modal reduction is performed for the modeling of flexible bodies. The structural and joint element library is briefly described. The algorithms used to integrate the resulting equations of motion with maximum efficiency and robustness are discussed. Various solution procedures, static, dynamic, stability, and trim analysis, are presented. Post-processing and visualization issues are also addressed. Finally, the paper concludes with selected rotorcraft applications.

Rational Finite Elements and Flexible Body Dynamics

2010 ◽  
Vol 132 (4) ◽  
Author(s):  
Peng Lan ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Elements ◽  
Computer Aided Design ◽  
Large Deformations ◽  
Absolute Nodal Coordinate Formulation ◽  
Finite Rotations ◽  
Flexible Bodies ◽  
Absolute Nodal Coordinate ◽  
Computer Aided ◽  
Curve Representation ◽  
Aided Design

The goal of this study is to develop the dynamic differential equations of the first finite element based on the rational absolute nodal coordinate formulation (RANCF) and to demonstrate its use in the nonlinear dynamic and vibration analysis of flexible bodies that undergo large displacements, including large deformations and finite rotations. New RANCF elements, which correctly describe rigid body displacements, will allow representing complex geometric shapes that cannot be described exactly using nonrational finite elements. Developing such rational finite elements will facilitate the integration of computer aided design and analysis and will allow for developing analysis models that are consistent with the actual geometry. In order to demonstrate the feasibility of developing RANCF finite elements, an Euler–Bernoulli beam element, called in this investigation as the cable element, is used. The relationship between the nonrational absolute nodal coordinate formulation (ANCF) finite elements and the nonrational Bezier curves is discussed briefly first in order to shed light on the transformation between the control points used in the Bezier curve representation and the ANCF gradient coordinates. Using similar procedure and coordinate transformation, the RANCF finite elements can be systematically derived from the computer aided design geometric description. The relationships between the rational Bezier and the RANCF interpolation functions are obtained and used to demonstrate that the new RANCF finite elements are capable of describing arbitrary large deformations and finite rotations. By assuming the weights of the Bezier curve representation to be constant, the RANCF finite elements lead to a constant mass matrix, and as a consequence, the Coriolis and centrifugal inertia force vectors are identically equal to zero. The assumption of constant weights can be used to ensure accurate representation of the geometry in the reference configuration and also allows for the use of the same rational interpolating polynomials to describe both the original geometry and the deformation. A large strain theory is used to formulate the nonlinear elastic forces of the new RANCF cable element. Numerical examples are presented in order to demonstrate the use of the RANCF cable element in the analysis of flexible bodies that experience large deformations and finite rotations. The results obtained are compared with the results obtained using the nonrational ANCF cable element.

A Large Deformation Finite Element for Pipes Conveying Fluid Based on the Absolute Nodal Coordinate Formulation

2007 ◽  
Author(s):  
Michael Stangl ◽  
Johannes Gerstmayr ◽  
Hans Irschik
Keyword(s):  
Finite Element ◽  
Large Deformation ◽  
Absolute Nodal Coordinate Formulation ◽  
Equations Of Motion ◽  
Directional Derivatives ◽  
Absolute Nodal Coordinate ◽  
Lagrange’S Equations ◽  
The Absolute ◽  
Lagrange's Equations ◽  
Conveying Fluid

A novel pipe finite element conveying fluid, suitable for modeling large deformations in the framework of Bernoulli Euler beam theory, is presented. The element is based on a third order planar beam finite element, introduced by Berzeri and Shabana, on basis of the absolute nodal coordinate formulation. The equations of motion for the pipe-element are derived using an extended version of Lagrange’s equations of the second kind for taking into account the flow of fluids, in contrast to the literature, where most derivations are based on Hamilton’s Principle or Newtonian approaches. The advantage of this element in comparison to classical large deformation beam elements, which are based on rotations, is the direct interpolation of position and directional derivatives, which simplifies the equations of motion considerably. As an advantage Lagrange’s equations of the second kind offer a convenient connection for introducing fluids into multibody dynamic systems. Standard numerical examples show the convergence of the deformation for increasing number of elements. For a cantilever pipe, the critical flow velocities for increasing number of pipe elements are compared to existing works, based on Euler elastica beams and moving discrete masses. The results show good agreements with the reference solutions applying only a small number of pipe finite elements.

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