A GPU Parallelization of the Absolute Nodal Coordinate Formulation for Applications in Flexible Multibody Dynamics

2012 ◽  
Author(s):  
Daniel Melanz ◽  
Naresh Khude ◽  
Paramsothy Jayakumar ◽  
Mike Leatherwood ◽  
Dan Negrut
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Solution Process ◽  
Flexible Multibody Dynamics ◽  
Differential Algebraic Equations ◽  
Implicit Time ◽  
Processing Unit ◽  
Algebraic Equations ◽  
Large Rotation ◽  
Absolute Nodal Coordinate ◽  
The Absolute

The Absolute Nodal Coordinate Formulation (ANCF) has been widely used to carry out the dynamics analysis of flexible bodies that undergo large rotation and large deformation. This formulation is consistent with the nonlinear theory of continuum mechanics and is computationally more efficient compared to other nonlinear finite element formulations. Kinematic constraints that represent mechanical joints and specified motion trajectories can be introduced to make complex flexible mechanisms. As the complexity of a mechanism increases, the system of differential algebraic equations becomes very large and results in a computational bottleneck. This contribution helps alleviate this bottleneck using three tools: (1) an implicit time-stepping algorithm, (2) fine-grained parallel processing on the Graphics Processing Unit (GPU), and (3) enabling parallelism through a novel Constraint-Based Mesh (CBM) approach. The combination of these tools results in a fast solution process that scales linearly for large numbers of elements, allowing meaningful engineering problems to be solved.

A Multibody Dynamical Model for Full Hole Drillstring Dynamics

2013 ◽  
Vol 378 ◽  
pp. 91-96 ◽  
Author(s):  
Zai Bin Cheng ◽  
Wei Jiang ◽  
Ge Xue Ren ◽  
Jian Liang Zhou ◽  
Shi Quan Jiang ◽  
...  
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Differential Algebraic Equations ◽  
Friction Model ◽  
Dynamical Model ◽  
Contact Friction ◽  
Algebraic Equations ◽  
Absolute Nodal Coordinate ◽  
Multibody Dynamic ◽  
The Absolute

The research on drillstring dynamics is necessary for improving drilling efficiency and safety. In this investigation, a multibody dynamical model for 3D full hole drillstring system is presented based on the Absolute Nodal Coordinate Formulation (ANCF). The drillstring is modeled with the ANCF beam element. The absolute nodal coordinate formulation of the beam element as well as the boundary conditions at the top-drive and drill-bit, and the contact/friction model between drillstring and wellbore are also investigated. The dynamic governing equation for full hole drillstring system is given and solved by the backward differentiation formulation (BDF) for differential algebraic equations (DAEs). The developed multibody dynamic solver is capable of analyzing full coupled vibration for the full hole drillstring system. It can play a certain role in drillstring dynamics researches and engineering applications.

Experimental Validation of Flexible Multibody Dynamics Beam Formulations

2013 ◽  
Author(s):  
Olivier A. Bauchau ◽  
Shilei Han ◽  
Aki Mikkola ◽  
Marko K. Matikainen ◽  
Johannes Gerstmayr
Keyword(s):  
Experimental Data ◽  
Absolute Nodal Coordinate Formulation ◽  
Flexible Multibody Dynamics ◽  
Absolute Nodal Coordinate ◽  
Beam Elements ◽  
Beam Experiment ◽  
Geometrically Exact Beam ◽  
Cantilevered Beam ◽  
The Absolute ◽  
Geometrically Exact Beam Formulation

In this paper, the accuracy of the geometrically exact beam formulation and absolute nodal coordinate formulation are studied by comparing their predictions against experimental data referred to as the “Princeton beam experiment.” The experiment deals with a cantilevered beam experiencing coupled flap, lag, and twist deformations. In the absolute nodal coordinate formulation, two different beam elements are used. The first is based on a shear deformable approach in which the element kinematics are described using two nodes. The second is based on a recently proposed approach in which three nodes are used. The numerical results for the geometrically exact beam formulation and the recently proposed three-node absolute nodal coordinate formulation agree well with the experimental data. The two-node beam element predictions are similarly to linear theory. This study suggests that the latest developments of the absolute nodal coordinate formulation must be used to ensure accuracy under complicated loading conditions involving by twist deformation.

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.

A new higher-order locking-free beam element based on the absolute nodal coordinate formulation

2017 ◽  
Vol 232 (19) ◽  
pp. 3410-3423 ◽  
Author(s):  
Haidong Yu ◽  
Chunzhang Zhao ◽  
Bin Zheng ◽  
Hao Wang
Keyword(s):  
Large Deformation ◽  
Cross Section ◽  
Absolute Nodal Coordinate Formulation ◽  
Beam Element ◽  
Higher Order ◽  
Continuity Condition ◽  
Large Rotation ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
The Cross

The beam elements based on the absolute nodal coordinate formulation are widely used in large deformation and large rotation problems. Some of them lead to shear and Poisson locking problems when the continuum mechanics method is employed to deduce the generalized elastic force of the element. To circumvent these locking problems, a new higher-order beam element is proposed that may capture the warping and non-uniform stretching distribution of the cross-section by introducing the trapezoidal cross-section deformation mode and increasing the order of interpolation polynomials in transverse direction. The curvature vectors are chosen as the nodal coordinates of the new element that improve the continuity condition at the element interface. Static and dynamic analyses are conducted to investigate the performance of the new element. Poisson locking phenomena may be eliminated effectively for the new element even when Poisson’s ratio is greater than zero. Meanwhile, the distortion deformation of the cross-section may be described directly. The new element has a better convergence performance compared with the spatial absolute nodal coordinate formulation beam element for that shear locking issue is eliminated. The results also show that the new element fulfills energy conservation and may be applied to the dynamics of both straight and initial curved structures with large deformation.

Dynamic analysis of balance rope under multiple constraints with friction

2021 ◽  
pp. 095440622098659
Author(s):  
Ning Zhang ◽  
Guohua Cao ◽  
Fang Yang
Keyword(s):  
Dynamic Analysis ◽  
Absolute Nodal Coordinate Formulation ◽  
Vertical Motion ◽  
Differential Algebraic Equations ◽  
Multiple Constraints ◽  
Lateral Vibration ◽  
Algebraic Equations ◽  
Absolute Nodal Coordinate ◽  
Constraint Equations ◽  
Forced Responses

Dynamic model of balance rope under multiple constraints with friction is established via using non-equal-length element division method (NEL-EDM) based on absolute nodal coordinate formulation. Then, the natural frequency of balance rope under multiple constraints is derived by the proposed method. The KDP generalized-alpha scheme is expanded to differential algebraic equations (DAEs) with friction constraint equations and used to solve the DAEs proposed by this paper. Compared with the frequencies, lateral vibration displacements at four observation points, the analysis of the NEL-EDM is carried out by MATLAB, ANSYS, and RECURDYN software, and the feasibility of NEL-EDM is verified. The frequencies of balance rope with installed bushing constraints will occur frequency veering phenomenon when the balance rope moves up and down with the conveyance. Last, free responses of the balance rope under multiple constraints due to the effects of conveyance vertical motion, and those of in-plane excitation on forced responses of balance rope under multiple constraints with friction are investigated.

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.

Three Dimensional Absolute Nodal Coordinate Formulation for Beam Elements: Implementation and Applications

2000 ◽  
Vol 123 (4) ◽  
pp. 614-621 ◽  
Author(s):  
Refaat Y. Yakoub ◽  
Ahmed A. Shabana
Keyword(s):  
High Speed ◽  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Three Dimensional ◽  
Large Rotation ◽  
Absolute Nodal Coordinate ◽  
Incremental Methods ◽  
Beam Elements ◽  
High Speed Forming ◽  
The Absolute

This part of these two companion papers demonstrates the computer implementation of the absolute nodal coordinate formulation for three-dimensional beam elements. Two beam elements that relax the assumptions of Euler-Bernoulli and Timoshenko beam theories are developed. These two elements take into account the effect of rotary inertia, shear deformation and torsion, and yet they lead to a constant mass matrix. As a consequence, the Coriolis and centrifugal forces are identically equal to zero. Both beam elements use the same interpolating polynomials and have the same number of nodal coordinates. However, one of the elements has two nodes, while the other has four nodes. The results obtained using the two elements are compared with the results obtained using existing incremental methods. Unlike existing large rotation vector formulations, the results of this paper show that no special numerical integration methods need to be used in order to satisfy the principle of work and energy when the absolute nodal coordinate formulation is used. These results show that this formulation can be used in manufacturing applications such as high speed forming and extrusion problems in which the element cross section dimensions significantly change.

A New Plate Element Based on the Absolute Nodal Coordinate Formulation

2001 ◽  
Author(s):  
Aki M. Mikkola ◽  
Ahmed A. Shabana
Keyword(s):  
Absolute Nodal Coordinate Formulation ◽  
Mass Matrix ◽  
Body Motion ◽  
Deformation Analysis ◽  
Plate Element ◽  
Large Rotation ◽  
Shell Elements ◽  
Absolute Nodal Coordinate ◽  
Plates And Shells ◽  
The Absolute

Abstract In this investigation, a method for the finite rotation and large deformation analysis of plates is presented. The method, which is based on the absolute nodal coordinate formulation, leads to a plate element capable of representing exact rigid body motion. In this method, continuity conditions on all the displacement gradients are imposed. Therefore, non-smoothness of the plate mid-surface at the nodal points is avoided. By developing such a plate element, a constant mass matrix is obtained, and as a consequence, the centrifugal and Coriolis forces are equal to zero. Generalization of the formulation to the case of shell elements is discussed. Numerical results are presented in order to demonstrate the use of the proposed method in the large rotation and deformation analysis of plates and shells.

A Parallel GPU Implementation of the Absolute Nodal Coordinate Formulation With a Frictional/Contact Model for the Simulation of Large Flexible Body Systems

2011 ◽  
Author(s):  
Naresh Khude ◽  
Dan Melanz ◽  
Ilinca Stanciulescu ◽  
Dan Negrut
Keyword(s):  
Frictional Contact ◽  
Absolute Nodal Coordinate Formulation ◽  
Analytical Framework ◽  
Computational Effort ◽  
Contact Model ◽  
Flexible Body ◽  
Processing Unit ◽  
Absolute Nodal Coordinate ◽  
Deformable Bodies ◽  
The Absolute

This contribution discusses how a flexible body formalism, specifically, the Absolute Nodal Coordinate Formulation (ANCF), is combined with a frictional/contact model using the Discrete Element Method (DEM) to address many-body dynamics problems; i.e., problems with hundreds of thousands of rigid and deformable bodies. Since the computational effort associated with these problems is significant, the analytical framework is implemented to leverage the computational power available on today’s commodity Graphical Processing Unit (GPU) cards. The code developed is validated against ANSYS and FEAP results. The resulting simulation capability is demonstrated in conjunction with hair simulation.

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