Some our papers and presentations which could be helpful and interesting for UM user are presented below.
• papers
• presentations

1. Pogorelov D. Numerical modelling of the motion of systems of solids. Maths Math. Phys., No. 4, pp 501-506, 1995.
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2. Pogorelov D. Some developments in computational techniques in modeling advanced mechanical systems. D.H. van Campen (ed.). Interaction between Dynamics and Control in Advanced Mechanical Systems. Proc. IUTAM Symp. Eindhoven, 21-26 April 1996. Dordrecht: Kluwer Acad. Publ, pp. 313-320, 1997.

Some methods and algorithms for optimal computer-aided modeling of multibody systems are considered. Special approaches to the computerized symbolic generation of motion equations are discussed. The described methods are realized in the program package Universal Mechanism (UM). Their application to modeling technical objects such as a six-legged walking mechanism and spatial cable systems are presented.
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3. Pogorelov D. Differential-algebraic equations in multibody system modeling. Numerical algorithms, pp. 183-194, 1998.

Numerical methods for the efficient integration of both stiff and nonstiff equations of motion of multibody systems having the form of differential-algebraic equations (DAE) of index 3 are discussed. Linear multi-step ABM and BDF methods are considered for the non-iterational integration of nonstiff DAE. The Park method is proposed for integration of stiff equations.

4. Pogorelov D.Y. On numerical methods of modelling large multibody systems. Mechanism and machine theory 34, pp. 791-800, 1999.

Subsystem technique consisting in a preliminary division of a large multibody system (MBS) into several parts is discussed. The method allows a considerable reduction of efforts on all stages of MBS modeling: description of a system, computer-aided generation of the equations and their integration. Synthesis of the equations of motion including differential and algebraic parts is studied. Numerical methods for efficient integration of the resulting equations are considered.

5. Pogorelov D. Multibody System Approach in Simulation of Underwater Cable Dynamics. Programme and Abstracts. EUROMECH 398, Colloquium on Fluid-Structure Interaction in Ocean Engineering, Technical University Hamburg-Harburg, Hamburg, Germany, October 11-14, 1999.

Dynamics of a flexible underwater cable can be successfully simulated using its representation by a chain of rigid bodies connected by hinges with 1,2 or 3 d.o.f. [1]. The hinges with one d.o.f. are used in the case of a plane cable motion, while the hinges with two and three d.o.f. allow to analyze the spatial cable dynamics taking into account bending and torsion (3 d.o.f.) stiffness. Large cable displacements during the motion make the multibody model of the cable more efficient compared with finite element models. Here numeric methods for generation of nonlinear equations of motion and their integration as well as some simulation results for an underwater robot equipped with a supply flexible cable are discussed.

6. Pogorelov D. On Calculation of Jacobian Matrices in Simulation of Multibody Systems. In Werner Schiehlen and Michael Valasek (eds.) Preprints of the NATO Advanced Study Institute on Virtual Nonlinear Multibody Systems, Czech Technical University in Prague, Prague, 2002, pp. 159-164

Integration of stiff equations of motion of multibody systems using implicit numerical methods, calculation of equilibrium positions, linearization of equations, constructing optimal controls and some other important tasks require computations of a Jacobian matrix. Its evaluation by finite differences is about 13 times more expensive than that for the mass matrix of the system. Some algorithms aimed to decreasing the corresponding computational efforts are discussed in the paper. They could improve considerably the efficiency of numerical analysis of large multibody systems.

7. Dmitrotchenko O.N. Efficient Simulation of Rigid-Flexible Multibody Dynamics: Some Implementations and Results. In Werner Schiehlen and Michael Valasek (eds.) Preprints of the NATO Advanced Study Institute on Virtual Nonlinear Multibody Systems, Czech Technical University in Prague, Prague, 2002, pp. 51-56

Known and modified simulation methods, such as composite and articulated ones, as well as different finite-element discretization methods are presented. Effectiveness of simulation of a large system can be estimated for a n-body chain. So, a direct method of implementation of the equations of motion is cubic in n. That is the computational effort is O(n3) for the mass matrix and O(n2) for the vector of generalized forces. The composite body method known for rigid multibody systems allows decreasing the effort to a quadratic one: down to O(n2) and O(n) for the matrices above. An application of the articulated body method for a rigid-flexible multibody system is considered. The method is linear in n for a n-body chain because it does not deal with a global mass matrix at all, but uses a recurrent two-step procedure instead in order to eliminate reaction forces from the equations of motion of separate bodies. Several examples of n-body pendulums (with various number of DOF per joint) were simulated using the Universal Mechanism (UM) software. The results show that the direct method is the fastest up to 10-15 rotational DOF in a chain, the composite method wins for 15 to 30 DOF, and further the articulated method is the best one. For flexible multibody systems, several approaches are discussed in the paper: finite rigid segment method, floating reference frame formulation as well as absolute nodal coordinate formulation. Several examples are shown in the presentation: cantilever beam subjected to large bending, motion of a flexible ellipsograph with a rigid pendulum, conveyor with hanging belt.

8. Kovalev R. Optimizing Multibody Systems: Some Implementations and Results. In Werner Schiehlen and Michael Valasek (eds.) Preprints of the NATO Advanced Study Institute on Virtual Nonlinear Multibody Systems, Czech Technical University in Prague, Prague, 2002, pp. 107-112

Optimization of multibody systems is presented as a multicriteria optimization problem. The problem of forming goal function is still open due to wide variety of conflicting criteria, which as a rule has to be reduced to a scalar function. Implementation of an approach for optimizing dynamic systems based on the analytic hierarchy process for getting the scalar goal function is considered. The developed approach is implemented in program package for simulation of multibody system dynamics.

9. Yazykov V.N. Some Results of Wheel-Rail Contact Modelling. In Werner Schiehlen and Michael Valasek (eds.) Preprints of the NATO Advanced Study Institute on Virtual Nonlinear Multibody Systems, Czech Technical University in Prague, Prague, 2002, pp. 236-241

Research of railway vehicle dynamics by means of mathematical models is the necessary stage for providing the vehicles with improved characteristics. Many problems such as dynamic stability, computation of wheel wear and others can be successfully solved by using a computer-aided multibody model of the vehicle. Significant part of the model is the description of forces at contact between wheel and rail. Computation of these forces is one of the most CPU time-consuming operations during the simulation process. Mathematical models of the contact forces often lead to stiff equations of motion because of high contact stiffness. In this paper an approximate non-stiff method for computing the non-elliptical contact problem and some results of its implementation are presented.

10. R. Kovalev, V. N. Yazykov, G. S. Mikhalchenko and D. Yu. Pogorelov Railway Vehicle Dynamics: Some Aspects of Wheel-Rail Contact Modeling and Optimization of Running Gears. Mechanics Based Design of Structures and Machnines. Vol. 31, Number 3, 2003, pp. 315-334

A significant part of a computer-aided model of a railway vehicle is the description of forces at contact between wheel and rail. Computation of these forces is one of the most time-consuming CPU operations during the simulation process. Mathematical models of the contact forces often lead to stiff equations of motion because of high contact stiffness. In this article, an approximate, nonstiff method for computing the nonelliptical contact problem and some results of its implementation are presented. Optimization of multibody systems is presented as a multicriteria optimization problem. The problem of forming objective function is still open due to wide variety of conflicting criteria, which have to be reduced to a scalar function. Implementation of an approach for optimizing dynamic systems based on the analytic hierarchy process for getting the scalar objective function is presented. The application of the developed approach to railway vehicle dynamics is considered.
Article abstract on www.dekker.com

11. E. Kreuzer and U. Wilke. Mooring Systems - A Multibody Dynamic Approach. Multibody System Dynamics 8: 279-297, 2002.

A method for simulating the motion behaviour of moored floating offshore structures in the time domain is presented. The interaction between the fluid and the floating structure is considered using linear potential theory. The hydrodynamic forces acting on the mooring lines are computed using a modified Morison equation. A complete three-dimensional model of the structure and the mooring lines is generated using a multibody system approach including a subsystem technique. The model results in a large number of degrees of freedom. In order to illustrate a practical application of this method, an analysis of a moored ponton in a random sea is presented. Different configurations of the system are examined in order to evaluate the motion behaviour and the restoring forces. Comparisons are made with the natural frequencies of the damped system.
Article abstract on www.kluweronline.com

12. O.N. Dmitrochenko and D. Yu. Pogorelov. Generalization of Plate Finite Elements for Absolute Nodal Coordinate Formulation. Multibody System Dynamics 10 (1): 17-43, August 2003.

We propose a way to generate new finite elements in the absolute nodal coordinate formulation (ANCF) and use a generalization of displacement fields and degrees of freedom (d.o.f.) of ordinary finite elements used in structural mechanics. Application of this approach to 16- and 12-d.o.f. rectangle plate elements as well as to 9-d.o.f. triangle element gives, accordingly, 48-, 36- and 27-d.o.f. ANCF plate elements. We perform a thorough study of a 48-d.o.f. Hermitian element. Its shape function set is a Cartesian product of sets of one-dimensional shape functions for beam elements. Arguments of the shape functions are decoupled, that is why an explicit calculation of terms of equations of motion leads to single integration only. We develop several models of elastic forces of different complexity with their Jacobian matrices. Convergence and accuracy of the finite element is demonstrated in geometrically nonlinear static and dynamic test problems, as well as in linear analysis of natural frequencies.
Article abstract on www.kluweronline.com

13. Wan-Suk Yoo, Jeong-Han Lee, Su-Jin Park, Jeong-Hyun Sohn, Dmitry Pogorelov, Oleg Dmitrochenko. Large Deflection Analysis of a Thin Plate: Computer Simulations and Experiments. Multibody System Dynamics 11 (2): 185-208, March 2004.

Many previous studies have conducted computer-aided simulations of elastic bodies undergoing large deflections and deformations, but there have not been many attempts to validate their numerical results. The subject of this paper is a thin clamped plate undergone large vibration due to attached end-point weight. The main aim of this paper is to show the validity of the absolute nodal coordinate formulation (ANCF) by comparing to the real experiments. Large oscillations of thin plates are studied in the paper with taking into account effects of an attached end-point weight and aerodynamic damping forces. The physical experiments are carried out using a high-speed camera and data acquisition system. For numerical modeling of the plate, the absolute nodal coordinate formulation is used.
Article abstract on www.kluweronline.com

14. Pogorelov D.Yu. On Approximate Jacobian Matrices in Simulation of Stiff Multibody Systems. XXI International Congress of Theoretical and Applied Mechanics (ICTAM), Warsaw, Poland, August 15-21, 2004.

Simulation of stiff multibody systems requires Jacobian matrices (JM) of equations of motion. Evaluation of the JM by finite differences is a very CPU time-consuming operation. Use of approximate JM taking into account stiff forces reduces considerably the computational efforts. Analytic expressions for the corresponding matrices are obtained. Block-diagonal approximations of the JM are introduced to apply implicit solvers to the scheme of the articulated body algorithm as well as to simulate system of thousands of bodies undergoing contact interactions. Models of a fright coach and a ballast system illustrate implementation of the developed approaches.
Article on ICTAM web site

15. Dmitrochenko O.N., Pogorelov D.Yu., Su-Jin Park, Wan-Suk Yoo. Simulation of Con-strained Rigid and Elastic Bodies Without Constraint Equations. XXI International Congress of Theoretical and Applied Mechanics (ICTAM), Warsaw, Poland, August 15-21, 2004.

Equations of motion of connected rigid and elastic bodies usually contain an algebraic part for constraint equations (DAE). Although methods of reliable solving DAE are well known, it is worth to avoid them if possible. A rigid body is usually modeled by Newton-Euler equations using any triplet of orientation angles. We consider large displacement finite-element (FE) approaches for simulation of elastic bodies. In the large rotation vector formulation, which uses rotation angles, the generalized coordinates for both rigid and elastic bodies are compatible and we can apply the assembling procedure to obtain ordinary differential equations instead of DAE. The recently introduced absolute nodal coordinate formulation (ANCF) uses finite slopes instead of rotation angles. When a rigid body is attached to ANCF FE without restrictions for relative orientation (revolute joint in 2D, spherical joint in 3D) we still can directly use the assembling procedure. If there are such restrictions we develop new rigid-body elements that employ ANCF nodal slopes as generalized coordinates. These elements can be easily assembled with elastic ones.
Article on ICTAM web site

16. Agapov D.G., Pogorelov D.Yu., Bidulya A. Simulation of Track Ballast. XXI International Congress of Theoretical and Applied Mechanics (ICTAM), Warsaw, Poland, August 15-21, 2004.

Railway ballast simulation algorithms are presented in the paper. The ballast is a system of planar rigid bodies with both convex and non-convex shapes. Contacts of interacting bodies are computed as force elements, which consist of a viscous-elastic normal part and a dry friction tangential part with sliding and sticking modes. Collision detection consists of two levels: neighbor and far ones. The far collision level detects contacts of polygon hulls by the linked linear list method. The neighbor collision level is an approach for detecting polygon penetrations by the sensitivity cell method. Simplified Jacobian matrices are used to accelerate the integration of stiff equations of motion. The ballast model can include up to some thousands of bodies and allows simulating processes of the ballast laying, compaction and so on. Some simulation results are presented.
Article on ICTAM web site

17. Yazykov V.N., Pogorelov D.Yu., Mikhalchenko G.S. Railway Vehicle Simulation Using Non-Elliptical Wheel-Rail Contact Model. XXI International Congress of Theoretical and Applied Mechanics (ICTAM), Warsaw, Poland, August 15-21, 2004.

An approximate model of wheel-rail contact, which does not lead to stiff equations of motion and can be used for non-elliptical contact area, is considered. The elastic Winkler foundation model is employed to find the contact patch configuration and the distribution of the normal pressure. The foundation modulus is determined with the help of the half space method. The FASTSIM algorithm, which was adapted for non-elliptical contact area, is applied for solving the tangential contact problem. An analytical solution of the tangential problem for a slice of the contact patch in the formulation of Kalker's simplified theory is used in the model. Results of contact problem solution and wheel wear prediction for a locomotive equipped with radial steering bogies using an algorithm based on the model are given.
Article on ICTAM web site

18. Nikolay Lysikov, Roman Kovalev, Gennadiy Mikheev. Stress Load and Durability Analysis of Railway Vehicles Using Multibody Approach. Transport Problems. International Scientific Journal. Volume 2, Issue 3, P. 49-56, 2007.

The present paper describes the CAE-based approach for durability analysis that is being implemented in Universal Mechanism software to predict the fatigue damage of parts of mechanical systems. The approach predicts fatigue strength of structural components of machines and mechanisms based on results of simulation their dynamics taking into account real working conditions. An application the developed software to a stress load and durability analysis is considered.
Transport Problems web site

19. Soshenkov S. N., Mezrin A. M. Integral evaluation of wheel profile forming during wear simulation in a wheel-rail system. Journal of Friction and Wear. Volume 29, Number 5, P. 369-380, 2008.

An integral characteristic (the forming coefficient) supplementing local characteristics of worn out profiles is suggested based on analysis of the wear profile of worn out railway wheels obtained from tribodynamic simulation. This characteristic allows classification of the profiles of worn out wheels according to type of wear (wear forming). Based on the technique suggested, the possibility is demonstrated of predicting future wear profiles using profile pairs obtained by tribodynamic simulation, thereby reducing simulation time. This technique allows minimizing the amount of turning in the central wear-off area during the restoration of wheel profiles.
Paper on SpringerLink web site
Journal of Friction and Wear

20. Kovalev, R., Lysikov, N., Mikheev G., Pogorelov, D., Simonov, V., Yazykov, V., Zakharov, S., Zharov, I., Goryacheva, I., Soshenkov, S., Torskaya, E.: Freight car models and their computer-aided dynamic analysis. Multibody System Dynamics 22 (4), 399–423 (2009)

Computer models of freight cars with three-piece and Y25 bogies are considered and compared. Efficient numeric methods for simulation of vehicle models in the presence of frictional contacts are discussed. Some simulation results on derailment safety analysis and influence of track gauge value on freight-car dynamics are presented. Methods of stress loading and durability analysis based on computer simulation and some results are presented. A tribodynamic model of railway vehicle-track interaction and results of computation of wheel and rail profile wear are discussed.
Paper on SpringerLink web site

21. Dmitry Agapov, Roman Kovalev. Contact Simulation for Convex Polyhedrons in Materials of Multibody Dynamics 2009, 29th June - 2nd July 2009, Warsaw, Poland.

Contact interaction is a central problem in many virtual reality and physically based simulations. An approach for simulation of contact interaction between two arbitrary polyhedrons is presented in this paper. This approach treats nondeformable 3D objects with small overlaps at the contact. The presented approach consists of two parts: a collision detection for arbitrary polyhedrons and then a contact force calculation. Collision detection deals with generalized three-dimensional clipping algorithm by Cyrus and Beck. Contact force calculation is based on a point-plane model and computed as a sum of normal viscous-elastic and tangential dry friction forces. Several examples of application of this approach for simulation of multibody system dynamics are given.
Presentation (zip archive, 119 Mb)
Abstracts (pdf, 271 Kb)

22. Dmitry Pogorelov, Vitaly Simonov, Roman Kovalev, Vladislav Yazykov, Nikolay Lysikov. Simulation of Freight Car Dynamics: Mathematical Models, Safety, Wear. 2nd International Conference on Recent Advances in Railway Engineering (ICRARE-2009), Iran university of science and Technology, Tehran, I.R. Iran, September 27-28, 2009.

Mathematical models of freight cars, numerical methods, simulation results and some related topics such as safety, durability, wear are considered in this paper.
Full paper (pdf, 836 Kb)

23. Gennady Mikheev. Simulation of Railway Vehicles and Bridge Interaction in Materials of Multibody Dynamics 2009, 29th June - 2nd July 2009, Warsaw, Poland.

The present paper describes the CAE-based approach for analysis of dynamics and stress state of parts of mechanical systems. The approach is being implemented in Universal Mechanism (UM) software. Object of researches is considered as rigid-flexible multibody system. Dynamics of flexible bodies is simulated using data imported from finite element analysis (FEA) software. An application of the approach to the investigation of dynamics of a railway vehicle and a bridge is considered taking into account flexibility of the bridge.
Presentation (zip archive, 45 Mb)
Abstracts (pdf, 252 Kb)

1. Mechanical Engineering with Universal Mechanism

Using UM for modeling of mechanical systems, main features of the program package and its modules are discussed in the presentation.
Download PowerPoint presentation (zip archive, 71 Mb)

2. Pogorelov D. Numeric Algorithms for Computer-Aided Simulation of Multibody Systems. Formulations and Implementations. Lecture at the Pusan National University, South Korea, 2002.

A number of general questions concerning simulation of dynamics of mechanical systems are considered. Analysis of kinematical structure of mechanical systems and some features of simulation of systems with closed kinematical loops, subsystem technique, some approaches for generation of motion equations (direct method, composite body method, articulated body method), methods of numerical integration of motion equations are discussed. Some features of simulation of railway vehicle, hybrid systems ("rigid bodies" + "elastic bodies") and systems with long kinematical chains are considered. Use program package "Universal Mechanism" for educational, scientific and applied purposes is shown.
Download PowerPoint presentation (zip archive, 43.3 Mb)

3. Simulation of railway vehicle dynamics in UM

UM-models of railway vehicles such as diesel and electric locomotives, freight and metro cars and other are shown. Models of rail-wheel interaction forces, tools for description of rail and wheel profiles and railway track irregularities, tools for linear analysis and parametrical optimization are presented.
Download PowerPoint presentation with animations (zip archive, 29 Mb)
Download PDF presentation with animations (pdf file, 26.7 Mb)

4. Dmitrochenko O.N., Pogorelov D.Yu. Modeling of Coupled Rigid-Elastic Multibody Systems using DAE and ODE Formalisms. EUROMECH 452 "Advances in Simulation Techniques for Applied Dynamics March 1-4, 2004, Halle (Saale), Germany

We consider hybrid systems of both rigid and elastic bodies coupled into united structures using joints of various kinds. Typical way to simulate them is using differential-algebraic equations (DAE) that consist of differential equations of motion of separated rigid and elastic bodies as well as of algebraic equations of constraints between the bodies. DAE introduce additional diffculties into numerical investigations, e. g. problems of constraint violations. They can be successfully solved using different methods. However it is possible in many cases to avoid DAE.
Abstracts (PDF, 54 KB)
Presentation (PDF, 353 KB)
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