Conference article

Import of Distributed Parameter Models into Lumped Parameter Model Libraries for the Example of Linearly Deformable Solid Bodies

Tobias Zaiczek
Fraunhofer Institute for Integrated Circuits, Design Automation Division, Dresden, Germany

Olaf Enge-Rosenblatt
Fraunhofer Institute for Integrated Circuits, Design Automation Division, Dresden, Germany

Download article

Published in: 3rd International Workshop on Equation-Based Object-Oriented Modeling Languages and Tools; Oslo; Norway; October 3

Linköping Electronic Conference Proceedings 47:6, p. 53-62

Show more +

Published: 2010-09-21

ISBN: 978-91-7519-824-8

ISSN: 1650-3686 (print), 1650-3740 (online)


Modelling of heterogeneous systems is always a trade-off between model complexity and accuracy. Most libraries of object-oriented; equation-based; multi-physical simulation tools are based on lumped parameter description models. However; there are different ways of including spatial dependency of certain variables in the model. One way that might be quite difficult is to manually discretize the model into an interconnection of lumped parameter models. This approach can get very time-consuming and is always sensitive to modelling or identification errors.

To avoid these issues; we try to take advantage of the well-established methods for automatically discretizing a distributed parameter model for example by means of Finite Element methods. However; to achieve a suffiently good approximation; these methods very often result in large-scale dynamic systems that can not be handled within equation-based simulators. To overcome this drawback there exist different approaches within the literature.

On the basis of deformable mechanical structures; one way of including distributed parameter models into libraries of lumped parameter models for the purpose of common simulation is pointed out in the present paper. For the implementation of the resulting models the authors take advantage of equation-based modelling libraries as new models can here easily be integrated.


distribuded parameter systems; FEM import; mechanical systems; deformable bodies


[1] A. C. Antoulas. Approximation of large-scale dynamical systems. Society for Industrial & Applied Mathematics; 2005.

[2] K.-J. Bathe. Finite Element Procedures. Prentice Hall; 1996.

[3] H. Bremer and F. Pfeiffer. Elastische Mehrkörpersysteme. Teubner; 1992

[4] V. Duindam; A. Macchelli; S. Stramigioli; and H. Bruyninckx (Eds.). Modeling and Control of Complex Physical Systems. Springer; 2009.

[5] O. Enge-Rosenblatt; P. Schneider; C. Clauss; and A. Schneider. Functional Digital Mock-up – Coupling of Advanced Visualization and Functional Simulation for Mechatronic System Design. ASIM Workshop; Ulm; 2010.

[6] R.W. Freund. Model reduction methods based on Krylov subspaces. Acta Numerica; 12:267–319; 2003.

[7] E. J. Haug. Computer aided kinematics and dynamics of mechanical systems - 1. Prentice Hall; 1989.

[8] A. Köhler. Modellreduktion von linearen Deskriptorsystemen erster und zweiter Ordnung mit Hilfe von Block- Krylov-Unterraumverfahren. Diplomarbeit. TU Dresden; Germany; 2006.

[9] A. Köhler; C. Clauss; S. Reitz; J. Haase; and P. Schneider. Snapshot - Based Parametric Model Order Reduction. MATHMOD Wien; February; 2009.

[10] A. Macchelli; A. J. van der Schaft; and C. Melchiorri. Distributed port-Hamiltonian formulation of infinite dimensional systems. In: Proc. 16th International Symposium on Mathematical Theory of Networks and Systems; MTNS 2004 (2004).

[11] K.W. Morton and D.F. Mayers. Numerical Solution of Partial Differential Equations. An Introduction. Cambridge University Press; 2005.

[12] L. Saldamli. PDEModelica – A High-Level Language for Modeling with Partial Differential Equations. Linköping Studies in Science and Technology; Dissertation No. 1022; Linköping; 2006.

[13] P. Schneider et. al. Functional Digital Mock-up - More Insight to Complex Multi-physical Systems. Multiphysics Simulation - Advanced Methods for Industrial Engineering 1st International Conference; Bonn; Germany; June 22-23; 2010; Proceedings.

[14] P. Schneider; P. Schwarz; and S. Wünsche. Beschreibungsmittel für komplexe Systeme. 40. Intern. Wiss. Kolloquiumder TH Ilmenau; September 7-9; 1995; Band 3; p. 102–108.

[15] A. A. Shabana. Dynamics of Multibody Systems. Cambridge University Press; 2nd Edition; 1998.

[16] A. L. Schwab and J. P. Meijaard. Beam Benchmark Problems for Validation of Flexible Multibody Dynamics Codes. MULTIBODY DYNAMICS 2009; ECCOMAS Thematic Conference; June 29 - July 2; 2009.

[17] P. Schwarz. Physically oriented modeling of heterogeneous systems. 3. IMACS Symp. MATHMOD pp. 309-318; Wien; 2000.

[18] R. Schwertassek and O. Wallrapp. Dynamik flexibler Mehrkörpersysteme. Vieweg Verlag; 1999.

[19] A. Stork. FunctionalDMU – Eine Initiative der Fraunhofer Gesellschaft. 2006; URL:; seen at 17 May; 2010.

[20] R. E. Valembois; P. Fisette; and J. C. Samin. Comparison of Various Techniques for Modelling Flexible Beams in Multibody Dynamics. In: Nonlinear Dynamics; p. 367- 397; Kluwer Acadamic Publishers; 1997.

Citations in Crossref