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.

Performance of the Incremental and Non-Incremental Finite Element Formulations in Flexible Multibody Problems

1999 ◽  
Vol 122 (4) ◽  
pp. 498-507 ◽  
Author(s):  
Marcello Campanelli ◽  
Marcello Berzeri ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Systems ◽  
Large Displacement ◽  
Body Motion ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Finite Element Formulations

Many flexible multibody applications are characterized by high inertia forces and motion discontinuities. Because of these characteristics, problems can be encountered when large displacement finite element formulations are used in the simulation of flexible multibody systems. 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 in an earlier article (Rankin, C. C., and Brogan, F. A., 1986, ASME J. Pressure Vessel Technol., 108, pp. 165–174) and the non-incremental absolute nodal coordinate formulation recently proposed (Shabana, A. A., 1998, Dynamics of Multibody Systems, 2nd ed., Cambridge University Press, Cambridge). It is demonstrated in this investigation that the limitation resulting from the use of the infinitesmal nodal rotations in the incremental corotational procedure can lead to simulation problems even when simple flexible multibody applications are considered. The absolute nodal coordinate formulation, on the other hand, does not employ infinitesimal or finite rotation coordinates and leads to a constant mass matrix. Despite the fact that the absolute nodal coordinate formulation leads to a non-linear expression for the elastic forces, the results presented in this study, surprisingly, demonstrate that such a formulation is efficient in static problems as compared to the incremental corotational procedure. The excellent performance of the absolute nodal coordinate formulation in static and dynamic problems can be attributed to the fact that such a formulation does not employ rotations and leads to exact representation of the rigid body motion of the finite element. [S1050-0472(00)00604-8]

Use of Plasticity Theory in Flexible Multibody System Dynamics

2003 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Dynamics ◽  
Plasticity Theory ◽  
Position Vector ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Return Algorithm ◽  
Finite Element Formulations

The objective of this investigation is to develop a general nonlinear finite deformation formulation for the elastic-plastic analysis of flexible multibody systems. The Lagrangian plasticity theory based on J2 flow theory is used to account for the effect of plasticity in flexible multibody dynamics. In addition, it is demonstrated that the principle of objectivity that is an issue when existing finite element formulations using ratetype constitutive equations are used can be fully satisfied when the stress and strain rate are directly calculated in the Lagrangian descriptions using the absolute nodal coordinate formulation employed in this investigation. This is attributed to the fact that, in the finite element absolute nodal coordinate formulation, the position vector gradients can completely define the state of rotation and deformation within the element. As a consequence, the numerical algorithm used to determine the plastic deformations such as the Radial Return Algorithm becomes much simpler when the absolute nodal coordinate formulation is used as compared to existing finite element formulations that employ incrementally objective algorithms. Several numerical examples are presented in order to demonstrate the use of the formulations presented in the paper.

Application of Plasticity Theory and Absolute Nodal Coordinate Formulation to Flexible Multibody System Dynamics

2003 ◽  
Vol 126 (3) ◽  
pp. 478-487 ◽  
Author(s):  
Hiroyuki Sugiyama ◽  
Ahmed A. Shabana
Keyword(s):  
Finite Element ◽  
Absolute Nodal Coordinate Formulation ◽  
Plasticity Theory ◽  
Position Vector ◽  
Element Formulation ◽  
Absolute Nodal Coordinate ◽  
Flexible Multibody ◽  
The Absolute ◽  
Return Algorithm ◽  
Finite Element Formulations

The objective of this investigation is to develop a nonlinear finite element formulation for the elastic-plastic analysis of flexible multibody systems. The Lagrangian plasticity theory based on J2 flow theory is used to account for the effect of plasticity in flexible multibody dynamics. It is demonstrated that the principle of objectivity that is an issue when existing finite element formulations using rate-type constitutive equations are used is automatically satisfied when the stress and strain rate are directly calculated in the Lagrangian descriptions using the absolute nodal coordinate formulation employed in this investigation. This is attributed to the fact that, in the finite element absolute nodal coordinate formulation, the position vector gradients can completely define the state of rotation and deformation within the element. As a consequence, the numerical algorithm used to determine the plastic deformations such as the radial return algorithm becomes much simpler when the absolute nodal coordinate formulation is used as compared to existing finite element formulations that employ incrementally objective algorithms. Several numerical examples are presented in order to demonstrate the use of the formulations presented in the paper.

Comparison of Finite Element Solutions of Non-Rational B-Spline and ANCF Elements in the Analysis of Flexible Multibody Systems

2011 ◽  
Author(s):  
Hiroki Yamashita ◽  
Hiroyuki Sugiyama
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Flexible Multibody Systems ◽  
Numerical Convergence ◽  
Absolute Nodal Coordinate ◽  
B Spline ◽  
Numerical Examples ◽  
The Third

In this investigation, comparison of finite element solutions obtained using the B-spline approach and the absolute nodal coordinate formulation (ANCF) is performed. Furthermore, equivalence of the two formulations with different orders of polynomials and degrees of continuity is demonstrated by several numerical examples. The degree of continuity can be easily controlled in B-spline elements by changing knot multiplicities, while continuity conditions associated with higher order derivatives need to be imposed to achieve C2 and higher continuities in ANCF elements. In order to compare element performances of the third and quartic B-spline and ANCF elements, the three-node quartic ANCF beam element is developed. It is demonstrated in several numerical examples that use of B-spline and ANCF elements with same orders and continuities leads to identical results. Furthermore, effects of polynomial orders and continuities on the accuracy and numerical convergence are demonstrated.

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