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[1] Logg, A., Mardal, K.A. & Wells, G.N. (eds), Automated Solution of DifferentialEquationsby the Finite Element Method: The FEniCS Book, Vol. 84, Springer, 2012.
[2] Chung, J. & Hubert, G.M., A time integration algorithm for structural dynamics withimproved numerical dissipation: The generalized-α method. ASME Journal of AppliedMechanics, 60(2), pp. 371–375, 1993. [Crossref]
[3] Johnson, K.L., Contact Mechanics, Cambridge University Press, 1985.
[4] Covaciu, D. & Dima, D.S., Crash tests data acquisition and processing. In CONAT 2016International Congress of Automotive and Transport Engineering, pp. 782–789, 2017.
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Open Access
Research article

Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact

Tomáš Janda,
Alena Zemanová,
Petr Hála,
Petr Konrád,
Jaroslav Schmidt
Czech Technical University in Prague, Czech Republic
International Journal of Computational Methods and Experimental Measurements
|
Volume 8, Issue 1, 2020
|
Pages 36-46
Received: N/A,
Revised: N/A,
Accepted: N/A,
Available online: N/A
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Abstract:

This article concerns a reduced order model of unconstrained glass plate exposed to low-velocity impact. First, three-parametric model consisting of two masses connected with elastic spring is introduced, its calibration procedure is described, and the simulation of its response to force impulses with different duration is shown. Then a five-parametric variant of the reduced order model is presented, calibrated and tested. Combined with the Hertzian theory of non-adhesive contact, the model allows us to determine the time evolution of contact force for arbitrary mass, stiffness and initial velocity of the impactor. The simulated results are compared to experimentally obtained data and observations about the model properties and accuracy are made.

Keywords: Dynamic analysis, Force impulse, Glass plate, Hertzian contact, Impact loading, Reduced order model

1. Introduction

2. Reduced Order Model

3. Loading by Impact

4. Conclusions

Data Availability

The data used to support the findings of this study are available from the corresponding author upon request.

Acknowledgments

This research was supported by the Czech Science Foundation under project No. 19-15326S.

Conflicts of Interest

The authors declare that they have no conflicts of interest.

References
[1] Logg, A., Mardal, K.A. & Wells, G.N. (eds), Automated Solution of DifferentialEquationsby the Finite Element Method: The FEniCS Book, Vol. 84, Springer, 2012.
[2] Chung, J. & Hubert, G.M., A time integration algorithm for structural dynamics withimproved numerical dissipation: The generalized-α method. ASME Journal of AppliedMechanics, 60(2), pp. 371–375, 1993. [Crossref]
[3] Johnson, K.L., Contact Mechanics, Cambridge University Press, 1985.
[4] Covaciu, D. & Dima, D.S., Crash tests data acquisition and processing. In CONAT 2016International Congress of Automotive and Transport Engineering, pp. 782–789, 2017.
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Janda, T., Zemanová, A., Hála, P., Konrád, P., & Schmidt, J. (2020). Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact. Int. J. Comput. Methods Exp. Meas., 8(1), 36-46. https://doi.org/10.2495/CMEM-V8-N1-36-46
T. Janda, A. Zemanová, P. Hála, P. Konrád, and J. Schmidt, "Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact," Int. J. Comput. Methods Exp. Meas., vol. 8, no. 1, pp. 36-46, 2020. https://doi.org/10.2495/CMEM-V8-N1-36-46
@research-article{Janda2020ReducedOM,
title={Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact},
author={Tomáš Janda and Alena Zemanová and Petr HáLa and Petr KonráD and Jaroslav Schmidt},
journal={International Journal of Computational Methods and Experimental Measurements},
year={2020},
page={36-46},
doi={https://doi.org/10.2495/CMEM-V8-N1-36-46}
}
Tomáš Janda, et al. "Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact." International Journal of Computational Methods and Experimental Measurements, v 8, pp 36-46. doi: https://doi.org/10.2495/CMEM-V8-N1-36-46
Tomáš Janda, Alena Zemanová, Petr HáLa, Petr KonráD and Jaroslav Schmidt. "Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact." International Journal of Computational Methods and Experimental Measurements, 8, (2020): 36-46. doi: https://doi.org/10.2495/CMEM-V8-N1-36-46
JANDA T， ZEMANOVÁ A， HÁLA P， et al. Reduced Order Model of Glass Plate Loaded by Low-Velocity Impact[J]. International Journal of Computational Methods and Experimental Measurements， 2020， 8(1)： 36-46. https://doi.org/10.2495/CMEM-V8-N1-36-46