scholarly journals Massive Parallelization of Multibody System Simulation

10.14311/1686 ◽  
2012 ◽  
Vol 52 (6) ◽  
Author(s):  
Michael Valášek ◽  
Ladislav Mráz
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
The Other ◽  
Algebraic Equations ◽  
Simultaneous Solution ◽  
Cpu Time ◽  
Dynamics Of Multibody Systems ◽  
Linear Algebraic Equations ◽  
Multiple Processors ◽  
Massive Parallelization

This paper deals with the decrease in CPU time necessary for simulating multibody systems by massive parallelization. The direct dynamics of multibody systems has to be solved by a system of linear algebraic equations. This is a bottleneck for the efficient usage of multiple processors. Simultaneous solution of this task means that the excitation is immediately spread into all components of the multibody system. The bottleneck can be avoided by introducing additional dynamics, and this leads to the possibility of massive parallelization. Two approaches are described. One is a heterogeneousmultiscale method, and the other involves solving a system of linear algebraic equations by artificial dynamics.

Kinematics Analysis of Mechanisms Based on Dynamics Multibody Systems in Virtual Assembly Environment

2010 ◽  
Vol 102-104 ◽  
pp. 214-218
Author(s):  
Zhi Xian Zhang ◽  
Jian Hua Liu ◽  
Ru Xin Ning
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Virtual Assembly ◽  
Assembly System ◽  
Prototype System ◽  
Motion Simulation ◽  
Kinematics Analysis ◽  
Simulation Process ◽  
Dynamics Of Multibody Systems ◽  
Kinematics Parameters

In recent years, in view of the absence of kinematics analysis function of mechanisms in the virtual assembly system, the method of kinematics analysis of mechanisms based on dynamics of multibody systems in virtual assembly environment is presented. A mechanism is considered as a multibody system and the kinematics equations are established based on Descartes coordinate system. All the kinematics parameters, just like position, speed and acceleration, can be obtained through solving the kinematics equations. In addition, the realization method of mechanism motion simulation in virtual assembly system is also proposed which contains the hiberarchy, data structure, module classes and simulation process of the system. The method is implemented and validated based on the prototype system VAPP(Virtual Assembly Process Planning).

Globally Independent Coordinates for Real-Time Vehicle Simulation

1998 ◽  
Vol 122 (4) ◽  
pp. 575-582 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
State Space ◽  
Real Time ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Vehicle Simulation ◽  
Generalized Coordinates ◽  
Dynamics Of Multibody Systems ◽  
Improved Performance ◽  
Control Forces

Models of the dynamics of multibody systems generally result in a set of differential-algebraic equations (DAE). State-space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. Therefore, these additional coordinates, together with Cartesian coordinates describing the position and orientation of the chassis, form a set of globally independent coordinates. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization in a state-space formulation, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples with realistic vehicle handling models demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation, yielding real-time for vehicle simulation. [S1050-0472(00)00404-9]

scholarly journals Construction Fragile Digital Watermark Used by a Team of Authors in Executable Files

2020 ◽  
Vol 18 (1) ◽  
pp. 65-73
Author(s):  
I. V. Nechta
Keyword(s):  
Unique Solution ◽  
Digital Watermark ◽  
The Other ◽  
System Of Equations ◽  
Algebraic Equations ◽  
Statistical Research ◽  
Other Hand ◽  
Linear Algebraic Equations ◽  
Software Product ◽  
The One

According to statistical research, a violation of license agreements annually causes huge losses to software companies. On the one hand, illegal copies of the software product are created, on the other hand, some fragments of the programs are used by third parties unauthorized. Another important problem is the violation of the program integrity, for example, in terms of blocking functions of the license key checking. In this regard, the task of construction methods for protecting intellectual property in software applications is highly relevant. Previously known methods solve this problem by means of fragile digital watermarks. Below is presented a method for constructing a fragile digital watermark used in executable files. A model of a developers team creating software product protected by DWM is considered. The application of this method will allow to reveal the fact of the container integrity violation, on the one hand, and, on the other hand, will allow the author, if it is necessary, to confirm his participation in the development and embedding of the DWM. In this method we use mathematical properties of systems of linear algebraic equations, digital signature and cryptographic hash functions. The scheme is based on the Kronecker – Capelli theorem. To find the group password the co-author who is in the group finds one root of the consistent system of linear algebraic equations. The indicated system consists of n equations and contains n + 1 variables. For an outsider who is not in the group, the system of equations does not have a unique solution. The co-author of the group is able to calculate one variable in system based on their passport data. Therefore, the system of equations for such co-author has a unique solution. Various attacks on a protected by the new method are analyzed, and it is shown its efficiency. The constructed method can be applied in companies with a large team of developers.

scholarly journals Comparison of Selected Formulations for Multibody System Dynamics with Redundant Constraints

2016 ◽  
Vol 63 (1) ◽  
pp. 93-112 ◽  
Author(s):  
Marcin Pękal ◽  
Janusz Fraczek
Keyword(s):  
System Dynamics ◽  
Multibody Systems ◽  
Solution Method ◽  
Integration Method ◽  
Multibody System ◽  
The Other ◽  
Direct Integration ◽  
Redundant Constraints ◽  
Direct Integration Method ◽  
Integration Errors

Abstract This paper compares selected optimization-based methods for the analysis of multibody systems with redundant constraints. The following numerical schemes are examined: direct integration method, Udwadia-Kalaba formulation, two types of least-squares block solution method and Udwadia-Phohomsiri formulation. In order to compare efficiency of the algorithms, a series of simulations is performed on two exemplary McPherson struts. In the first variant, the mechanism has no redundant constraints whereas the other is overconstrained. Three constraint stabilization schemes are also compared in terms of integration errors.

Dynamic Simulation of Dielectric Elastomer Actuated Multibody Systems

2016 ◽  
Author(s):  
T. Schlögl ◽  
S. Leyendecker
Keyword(s):  
Finite Element ◽  
Multibody Systems ◽  
Multibody System ◽  
Humanoid Robots ◽  
Differential Algebraic Equations ◽  
Rigid Bodies ◽  
Integration Scheme ◽  
Artificial Muscles ◽  
Algebraic Equations ◽  
Energy Behavior

A three-dimensional electro-mechanically coupled finite element model for dielectric elastomers is used to actuate multibody systems. This setting allows exploring the complex behavior of humanoid robots that are driven by artificial muscles instead of electrical drives. The coupling between the finite element muscle model and the rigid bodies is formulated at configuration level, where Lagrange multipliers account for constraint forces, leading to differential algebraic equations of index-3. A well-chosen set of redundant configuration variables for the multibody system avoids any rotational degrees of freedom and leads to linear coupling constraints. As a result, the coupling between the artificial muscles and the multibody system can be formulated in a very modular way that allows for easy future extension. The applied structure preserving time integration scheme provides excellent long time energy behavior. In addition, the index-3 system is solved directly with numerical accuracy, avoiding index reduction approximations.

Dynamics of Multibody Systems With Variable Kinematic Structure

1986 ◽  
Vol 108 (2) ◽  
pp. 167-175 ◽  
Author(s):  
Y. A. Khulief ◽  
A. A. Shabana
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Kinematic Structure ◽  
The Finite Element Method ◽  
Flexible Bodies ◽  
Generalized Coordinates ◽  
Structure Changes ◽  
Dynamics Of Multibody Systems ◽  
Analysis Scheme ◽  
Deformation Modes

The problem of predicting the dynamic behavior of a general multibody system subject to kinematic structure changes is addressed using a mixed set of Lagrangian coordinates. Changes in the kinematic structure may occur smoothly or accompanied by a change in the system momenta. The finite element method is employed to estimate the modal characteristics of flexible bodies. An automated pieced-interval computational scheme that accounts for the change in the dynamic characteristics due to the imposition of new sets of constraints on the boundaries of flexible components is developed. The resulting change in the deformation modes and the associated change in basis of the configuration space requires a new set of generalized coordinates for each subinterval of the analysis. A numerical example is used to demonstrate the analysis scheme developed in this paper.

DYNAMICS OF MULTIBODY SYSTEMS WITH UNILATERAL CONSTRAINTS

1999 ◽  
Vol 09 (03) ◽  
pp. 473-478 ◽  
Author(s):  
M. WÖSLE ◽  
F. PFEIFFER
Keyword(s):  
Contact Problem ◽  
Multibody Systems ◽  
Mathematical Formulation ◽  
Three Dimensional ◽  
Differential Algebraic Equations ◽  
Mathematical Form ◽  
Algebraic Equations ◽  
Unilateral Constraints ◽  
Stick Slip ◽  
Dynamics Of Multibody Systems

In couplings of machines and mechanisms, backlash and friction phenomena are always occurring. Whether stick–slip phenomena take place depends on the structure of such couplings. These processes can be modeled as multibody systems with a time-varying topology. Making use of Lagrange multiplier methods with a mathematical formulation of the contact problem is very efficient for large systems with many constraints. In the following, the differential-algebraic equations are transformed into a resolvable mathematical form by means of the contact laws in equation form. Ultimately we get a nonlinear system of equations for the three-dimensional contact problem with dependent constraints. For its solution, the homotopy method will be used and applied to a simple mechanical system.

scholarly journals On the cosimulation of multibody systems and hydraulic dynamics

2020 ◽  
Vol 50 (2) ◽  
pp. 143-167
Author(s):  
Jarkko Rahikainen ◽  
Francisco González ◽  
Miguel Ángel Naya ◽  
Jussi Sopanen ◽  
Aki Mikkola
Keyword(s):  
Numerical Integration ◽  
Multibody Systems ◽  
Multibody System ◽  
Physical Nature ◽  
The Other ◽  
Numerical Examples ◽  
Complex Engineering ◽  
Coupling Variables ◽  
Mechanical Devices ◽  
Accuracy And Stability

Abstract The simulation of mechanical devices using multibody system dynamics (MBS) algorithms frequently requires the consideration of their interaction with components of a different physical nature, such as electronics, hydraulics, or thermodynamics. An increasingly popular way to perform this task is through co-simulation, that is, assigning a tailored formulation and solver to each subsystem in the application under study and then coupling their integration processes via the discrete-time exchange of coupling variables during runtime. Co-simulation makes it possible to deal with complex engineering applications in a modular and effective way. On the other hand, subsystem coupling can be carried out in a wide variety of ways, which brings about the need to select appropriate coupling schemes and simulation options to ensure that the numerical integration remains stable and accurate. In this work, the co-simulation of hydraulically actuated mechanical systems via noniterative, Jacobi-scheme co-simulation is addressed. The effect of selecting different co-simulation configuration options and parameters on the accuracy and stability of the numerical integration was assessed by means of representative numerical examples.

Globally Independent Coordinates for Real-Time Vehicle System Simulation

1998 ◽  
Author(s):  
Radu Serban ◽  
Edward J. Haug
Keyword(s):  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Algebraic Equations ◽  
Generalized Coordinates ◽  
Constraint Manifold ◽  
Vehicle System ◽  
Dynamics Of Multibody Systems ◽  
Improved Performance ◽  
Cartesian Coordinate ◽  
Control Forces

Abstract Models of the dynamics of multibody systems generally result in a set of differential–algebraic equations (DAE). State–space methods for solving the DAE of motion are based on reduction of the DAE to ordinary differential equations (ODE), by means of local parameterizations of the constraint manifold that must be often modified during a simulation. In this paper it is shown that, for vehicle multibody systems, generalized coordinates that are dual to suspension and/or control forces in the model are independent for the entire range of motion of the system. In addition to the immediate advantage of avoiding the computationally expensive redefinition of local parameterization, the existence of globally independent coordinates leads to efficient algorithms for recovery of dependent generalized coordinates. A topology based approach to identify efficient computational sequences is presented. Numerical examples demonstrate the improved performance of the proposed approach, relative to the conventional Cartesian coordinate formulation.

Improved Differential Nullspace Matrix Method for the Dynamic Analysis of Multibody Systems

2018 ◽  
Author(s):  
Keisuke Kamiya
Keyword(s):  
Lagrange Multipliers ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Computational Time ◽  
Algebraic Equations ◽  
Accurate Analysis ◽  
Dynamics Of Multibody Systems ◽  
General Dynamics ◽  
Novel Method ◽  
Rigid Multibody Systems

This paper presents a novel method for motion analysis of rigid multibody systems. In general, dynamics of multibody systems is described by differential algebraic equations with Lagrange multipliers. For efficient and accurate analysis, it is desirable to eliminate the Lagrange multipliers and dependent variables. Methods called nullspace method and Maggi’s method eliminate the Lagrange multipliers by using the nullspace matrix for the constraint Jacobian. In a previous report, the author presented a method in which the nullspace matrix is obtained by solving a differential equation together with the equation of motion of the system. In that method QR decomposition is used. In this report, reduction in computational time with the LU decomposition is attempted. In addition, treatment of singular configurations for accurate analysis is presented. Validity of the presented method is confirmed via numerical examples.

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