Conference article

Thermal Deformation Analysis Using Modelica

Eunkyeong Kim
Hitachi, Ltd., Research & Development Group, Japan

Tatsurou Yashiki
Hitachi, Ltd., Research & Development Group, Japan

Fumiyuki Suzuki
Mitsubishi Hitachi Power Systems, Ltd., Japan

Yukinori Katagiri
Hitachi, Ltd., Research & Development Group, Japan

Takuya Yoshida
Hitachi, Ltd., Research & Development Group, Japan

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Published in: The First Japanese Modelica Conferences, May 23-24, Tokyo, Japan

Linköping Electronic Conference Proceedings 124:16, p. 121-128

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Published: 2016-05-18

ISBN: 978-91-7685-749-6

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


This paper presents a thermal deformation analysis method fully utilizing the non-causality of the Modelica language as a means of solving large scale simultaneous equations including equilibrium equations related to stresses, stress-strain relations and strain-displacement relations. As an illustrative example, a model for thermal deformation analysis of a cylindrical object in the two-dimensional circular polar coordinate system is described. Simulations are performed for a cylindrically shaped object under a uniform temperature distribution and a radial temperature distribution. The results of the simulations show that the differences in displacements between the proposed model and a model based on finite element (FE) methods are less than 9% while the number of elements that compose the proposed model is about 1/8 compared to that of the FE model.


thermal deformation, stress-strain relation, strain-displacement relation, equilibrium equations, displacement gradient, physical modeling, finite volume method, non-causality, Modelica, Dymola


Elmqvist H., Mattsson S.E. (1997a): Modelica - The next generation modeling language an international design effort, Proceedings of the 1st World Congress on System Simulation.

Elmqvist H., Mattsson S.E. (1997b): An introduction to the physical modeling language Modelica, Proceedings of the 9th European Simulation Symposium.

Elmqvist H, Mattsson S.E., Otter M. (1998a): Modelica - The new object-oriented modeling language, 12th European Simulation Multiconference.

Elmqvist H., Mattsson S.E., Otter M. (1998b): Modelica - An international effort to design an object-oriented modeling language, Summer Computer Simulation Conference.

Ferziger J.H., Peric M. (2002): Computational Methods for Fluid Dynamics, Springer-Verlag, pp.21-37.

Fritzson P. (2003): Principles of object-oriented Modeling and Simulation with Modelica 2.1, John Wiley & Sons, Inc., pp.19-25.

Fritzson P. (2011): Introduction to Modeling and Simulation of Technical and Physical Systems with Modelica, John Wiley & Sons, Inc., pp.29-39.

Fritzson P., Engelson V. (1998): Modelica—A unified object-oriented language for system modeling and simulation, ECOOP’98, LNCS 1445, pp. 67-90.

Gere J.M. (2006), Mechanics of meterials, Thomson learning, pp.93-104.

Voller V.R. (2009): Basic control volume finite element methods for fluids and solids, World Scientific Publishing Co. Pte. Ltd., pp.10-20.

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