Implicit and explicit integration in the solution of the absolute nodal coordinate differential/algebraic equations

2008 ◽  
Vol 54 (4) ◽  
pp. 283-296 ◽  
Author(s):  
Bassam Hussein ◽  
Dan Negrut ◽  
Ahmed A. Shabana
Keyword(s):  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Explicit Integration ◽  
Absolute Nodal Coordinate ◽  
The Absolute ◽  
Implicit And Explicit

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.

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.

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.

Markov Jump Linear System Analysis of a Microgrid Operating in Islanded and Grid Tied Modes

2020 ◽  
Author(s):  
Gilles Mpembele ◽  
Jonathan Kimball
Keyword(s):  
Monte Carlo ◽  
Power Systems ◽  
Power System ◽  
System Analysis ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Markov Jump ◽  
Numerical Application ◽  
Conditional Moments ◽  
Markov Jump Linear Systems

<div>The analysis of power system dynamics is usually conducted using traditional models based on the standard nonlinear differential algebraic equations (DAEs). In general, solutions to these equations can be obtained using numerical methods such as the Monte Carlo simulations. The use of methods based on the Stochastic Hybrid System (SHS) framework for power systems subject to stochastic behavior is relatively new. These methods have been successfully applied to power systems subjected to</div><div>stochastic inputs. This study discusses a class of SHSs referred to as Markov Jump Linear Systems (MJLSs), in which the entire dynamic system is jumping between distinct operating points, with different local small-signal dynamics. The numerical application is based on the analysis of the IEEE 37-bus power system switching between grid-tied and standalone operating modes. The Ordinary Differential Equations (ODEs) representing the evolution of the conditional moments are derived and a matrix representation of the system is developed. Results are compared to the averaged Monte Carlo simulation. The MJLS approach was found to have a key advantage of being far less computational expensive.</div>

scholarly journals Differential-algebraic systems are generically controllable and stabilizable

2021 ◽  
Author(s):  
Achim Ilchmann ◽  
Jonas Kirchhoff
Keyword(s):  
Algebraic Geometry ◽  
Linear Time ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Algebraic Systems ◽  
Linear Time Invariant ◽  
Survey Article ◽  
Link Type ◽  
Invariant Differential ◽  
Time Invariant

AbstractWe investigate genericity of various controllability and stabilizability concepts of linear, time-invariant differential-algebraic systems. Based on well-known algebraic characterizations of these concepts (see the survey article by Berger and Reis (in: Ilchmann A, Reis T (eds) Surveys in differential-algebraic equations I, Differential-Algebraic Equations Forum, Springer, Berlin, pp 1–61. 10.1007/978-3-642-34928-7_1)), we use tools from algebraic geometry to characterize genericity of controllability and stabilizability in terms of matrix formats.

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