A logarithmic complexity divide-and-conquer algorithm for multi-flexible-body dynamics including large deformations

2014 ◽  
Vol 34 (1) ◽  
pp. 81-101 ◽  
Author(s):  
Imad M. Khan ◽  
Kurt S. Anderson
Keyword(s):  
Large Deformations ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Divide And Conquer Algorithm ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Logarithmic Complexity

New and Extended Applications of the Divide-and-Conquer Algorithm for Multibody Dynamics

2014 ◽  
Vol 9 (4) ◽  
Author(s):  
Jeremy J. Laflin ◽  
Kurt S. Anderson ◽  
Imad M. Khan ◽  
Mohammad Poursina
Keyword(s):  
Multibody Dynamics ◽  
Large Deformations ◽  
Multibody System ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Ongoing Research ◽  
Flexible Bodies ◽  
Computational Burden ◽  
Divide And Conquer Algorithm ◽  
Model Fidelity

This work presents a survey of the current and ongoing research by the authors who use the divide-and-conquer algorithm (DCA) to reduce the computational burden associated with various aspects of multibody dynamics. This work provides a brief discussion of various topics that are extensions of previous DCA-based algorithms or novel uses of this algorithm in the multibody dynamics context. These topics include constraint error stabilization, spline-based modeling of flexible bodies, model fidelity transitions for flexible-body systems, and large deformations of flexible bodies. It is assumed that the reader is familiar with the “Advances in the Application of the DCA to Multibody System Dynamics” text as the notation used in this work is explained therein and provides a summary of how the DCA has been used previously.

Multi-Flexible-Body Simulations Using Interpolating Splines in a Divide-and-Conquer Scheme

2013 ◽  
Author(s):  
Imad M. Khan ◽  
Woojin Ahn ◽  
Kurt Anderson ◽  
Suvranu De
Keyword(s):  
Equations Of Motion ◽  
Linear Equations ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Divide And Conquer Algorithm ◽  
Large Rotations ◽  
Floating Frame ◽  
Interpolating Splines ◽  
Divide And Conquer Scheme ◽  
Logarithmic Complexity

A new method for modeling multi-flexible-body systems is presented that incorporates interpolating splines in a divide-and-conquer scheme. This algorithm uses the floating frame of reference formulation and piece-wise interpolation spline functions to construct and solve the non-linear equations of motion of the multi-flexible-body systems undergoing large rotations and translations. We compare the new algorithm with the flexible divide-and-conquer algorithm (FDCA) that uses the assumed modes method and may resort to sub-structuring in many cases [1]. We demonstrate, through numerical examples, that in such cases the interpolating spline-based approach is comparable in accuracy and superior in efficiency to the FDCA. The algorithm retains the theoretical logarithmic complexity inherent to the divide-and-conquer algorithm when implemented in parallel.

Development of a New Multi-Flexible Body Dynamics (MFBD) Platform: A Relative Nodal Displacement Method for Finite Element Analysis

2005 ◽  
Author(s):  
Dae Sung Bae
Keyword(s):  
Rigid Body ◽  
Reference Frame ◽  
Large Deformations ◽  
Shape Function ◽  
Rigid Body Motion ◽  
Body Motion ◽  
Flexible Body ◽  
Element Analysis ◽  
Body Dynamics ◽  
Flexible Body Dynamics

Recently the analysis of multi flexible body dynamics has been a hot issue in the area of the computational dynamics research. There have been two main streams of research. One is the extension of conventional FEA theory for the multi flexible body systems, using either the total Lagrangian or updated Lagrangian method. The other is the extension of the multi body dynamics theory. The latter is the topic of this research. One essential requirement of a shape function in FEA theory is ability to represent the rigid body motion. This research proposes to use the moving reference frame to represent the rigid body motion. Therefore, the shape function does not need to have ability to represent the rigid body motion. The moving reference frame covers the rigid body. Since the nodal displacements are measured relative to its adjacent moving nodal reference frame, they are still small for a truss structure undergoing large deformations if the element sizes are small. As a consequence, many element formulations developed under small deformation assumptions are still valid for structures undergoing large deformations, which significantly simplifies the equations of equilibrium. Several numerical examples are analyzed to demonstrate the efficiency and validity of the proposed method.

Model Transitions and Optimization Problem in Multi-Flexible-Body Modeling of Biopolymers

2011 ◽  
Author(s):  
Mohammad Poursina ◽  
Imad Khan ◽  
Kurt S. Anderson
Keyword(s):  
Optimization Problem ◽  
Computational Cost ◽  
Divide And Conquer ◽  
Flexible Body ◽  
Basic Form ◽  
Divide And Conquer Algorithm ◽  
Time Optimal ◽  
Logarithmic Complexity ◽  
Algorithm Implementation ◽  
Fidelity Model

This paper presents an efficient algorithm for the simulation of multi-flexible-body systems undergoing discontinuous changes in model definition. The equations governing the dynamics of the transitions from a higher to a lower fidelity model and vice versa are formulated through imposing/removing certain constraints on/from the system. Furthermore, the issue of the non-uniqueness of the results associated with the transition from a lower to a higher fidelity model is dealt with as an optimization problem. This optimization problem is subjected to the satisfaction of the impulse-momentum equations. The divide and conquer algorithm (DCA) is applied to formulate the dynamics of the transition. The DCA formulation in its basic form is time optimal and results in linear and logarithmic complexity when implemented in serial and parallel, respectively. As such, it reduces the computational cost of formulating and solving the optimization problem in the transitions to the finer models. Necessary mathematics for the algorithm implementation is developed and a numerical example is given to validate the method.

scholarly journals Coupled simulation of elastohydrodynamics and multi-flexible body dynamics in piston-lubrication system

2019 ◽  
Vol 11 (12) ◽  
pp. 168781401989585 ◽  
Author(s):  
Seongsu Kim ◽  
Juhwan Choi ◽  
Jin-Gyun Kim ◽  
Ryo Hatakeyama ◽  
Hiroshi Kuribara ◽  
...  
Keyword(s):  
Cylinder Block ◽  
Flexible Body ◽  
Asperity Contact ◽  
Lubrication System ◽  
Film Pressure ◽  
Oil Film ◽  
Piston Skirt ◽  
Body Dynamics ◽  
Flexible Body Dynamics ◽  
Oil Film Pressure

In this work, we propose a robust modeling and analysis technique of the piston-lubrication system considering fluid–structure interaction. The proposed schemes are based on combining the elastohydrodynamic analysis and multi-flexible body dynamics. In particular, multi-flexible body dynamics analysis can offer highly precise numerical results regarding nonlinear deformation of the piston skirt and cylinder bore, which can lead to more accurate results of film thickness for gaps filled with lubricant and of relative velocity of facing surfaces between the piston skirt and the cylinder block. These dynamic analysis results are also used in the elastohydrodynamic analysis to compute the oil film pressure and asperity contact pressure that are used as external forces to evaluate the dynamic motions of the flexible bodies. A series of processes are repeated to accurately predict the lubrication characteristics such as the clearance and oil film pressure. In addition, the Craig–Bampton modal reduction, which is a standard type of component mode synthesis, is employed to accelerate the computational speed. The performance of the proposed modeling schemes implemented in the RecurDyn™ multi-flexible body dynamics environment is demonstrated using a well-established numerical example, and the proposed simulation methods are also verified with the experimental results in a motor cycle engine (gasoline) which has a four cycle, single cylinder, overhead camshaft (OHC), air cooled.

A Recursive Implementation Method With Implicit Integrator for Multibody Dynamics

2001 ◽  
Author(s):  
H. J. Cho ◽  
H. S. Ryu ◽  
D. S. Bae ◽  
J. H. Choi ◽  
B. Ross
Keyword(s):  
Equations Of Motion ◽  
Flexible Body ◽  
Differential Algebraic Equation ◽  
Dynamic Correction ◽  
Body Dynamics ◽  
Mode Method ◽  
Numerical Integrators ◽  
Flexible Body Dynamics ◽  
Body Concept ◽  
Implementation Method

Abstract A recursive implementation method for the equations of motion and kinematics is presented. Computational structure of the kinematic and dynamic equations is exploited to systematically implement a dynamic analysis program RecurDyn. A differential algebraic equation solution method with implicit numerical integrators is discussed. Virtual body concept is introduced for the flexible body dynamics. The accuracy of the flexible body solutions is estimated by an error measure and is improved by the dynamic correction mode method. Several examples are solved to demonstrate the efficiency of the proposed methods.

Generalized Constraint and Joint Reaction Forces in the Inverse Dynamics of Spatial Flexible Mechanical Systems

1994 ◽  
Vol 116 (3) ◽  
pp. 777-784 ◽  
Author(s):  
D. C. Chen ◽  
A. A. Shabana ◽  
J. Rismantab-Sany
Keyword(s):  
Inverse Dynamics ◽  
Mechanical Systems ◽  
Flexible Body ◽  
Body Dynamics ◽  
Joint Reaction Forces ◽  
Flexible Body Dynamics ◽  
Reaction Forces ◽  
Applied Forces ◽  
Generalized Constraint ◽  
Joint Reaction

In both the augmented and recursive formulations of the dynamic equations of flexible mechanical systems, the inerita, constraints, and applied forces must be properly defined. The inverse dynamics is a commonly used approach for the force analysis of mechanical systems. In this approach, the system is kinematically driven using specified motion trajectories, and the objective is to determine the driving forces and torques. In flexible body dynamics, however, a force that acts at a point on the deformable body is equipollent to a system, defined at another point, that consists of the same force, a moment that depends on the relative deformation between the two points, and a set of generalized forces associated with the elastic coordinates. Furthermore, a moment in flexible body dynamics is no longer a free vector. It is defined by the location of its line of action as well as its magnitude and direction. The joint reaction and generalized constraint forces represent equipollent systems of forces. Both systems in flexible body dynamics are function of the deformation. In this investigation, a procedure is developed for the determination of the joint reaction forces in spatial flexible mechanical systems. The mathematical formulation of some mechanical joints that are often encountered in the analysis of constrained flexible mechanical systems is discussed. Expressions for the generalized reaction forces in terms of the constraint Jacobian matrices of the joints are presented. The effect of the elastic deformation on the reaction forces is also examined numerically using the spatial flexible multibody RSSR mechanism that consists of a set of interconnected rigid and elastic bodies. The procedure described in this investigation can also be used to determine the joint torques and actuator forces in kinematically driven spatial elastic mechanism and manipulator systems.

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