Justus Benad

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In this work, different numerical methods for simulating deformations and stresses in turbine blade fir-tree connections are examined. The main focus is on the Method of Dimensionality Reduction (MDR) and the Boundary Element Method (BEM). Generally, the fir-tree connections require a computationally expensive finite element setup. Their complex geometry exceeds the limitations of the faster numerical techniques which are used with great success within the framework of the half-space approximation. Ways of extending the application range of the MDR and the BEM to the particular problem of highly undulating surfaces of the fir-tree connection are shown and discussed.


Fir-tree Connections, Navier Equation, Boundary Element Method, FFT

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Bräunling, W., 2015, Flugzeugtriebwerke, 3 ed, Springer, Berlin.

Torenbeek, E., 1982, Synthesis of Subsonic Airplane Design, Kluwer Academic Publishers, Dordrecht.

Raymer, D., 1999, Aircraft Design: A Conceptual Approach, 3 ed, American Institute of Aeronautics and Astronautics, Inc., Reston.

Popov, V.L., Heß, M., 2015, Method of dimensionality reduction in contact mechanics and friction, Springer, Berlin.

Putignano, C., Afferrante, L., Carbone, G., Demelio, G., 2012, A new efficient numerical method for contact mechanics of rough surfaces, International Journal of Solids and Structures, 49(2), pp. 338-343.

Popov, V.L., 2017, Contact Mechanics and Friction, 2 ed, Springer, Berlin.

Dimaki, A., Dmitriev, A., Menga, N., Papangelo, A., Ciavarella, M., Popov, V.L., 2016, Fast high-resolution simulation of the gross slip wear of axially symmetric contacts, Tribology Transactions, 59(1), pp. 189-194.

Li, Q., Forsbach, F., Schuster, M., Pielsticker, D., Popov, V.L., 2018, Wear Analysis of a Heterogeneous Annular Cylinder, Lubricants, 6(1), 28.

Popov, V.L., Pohrt, R., 2018, Adhesive wear and particle emission: Numerical approach based on asperity-free formulation of Rabinowicz criterion, Friction, 6(3), pp. 260-273.

Cleynen, O., 2012, Turbine of a sectioned Rolls-Royce Turboméca Adour turbofan, accessed 2019 at

Benad, J., 2018, Acceleration of the Boundary Element Method for arbitrary shapes with the Fast Fourier Transformation, arXiv preprint, arXiv:1809.00845.

Benad, J., 2018, Efficient calculation of the BEM integrals on arbitrary shapes with the FFT, Facta Universitatis-Series Mechanical Engineering, 16(3), pp. 405-417.

ATSB Transport Safety Report, 2013, In-flight uncontained engine failure Airbus A380-842, accessed 2019 at

Popov, V.L., Psakhie, S., 2007, Numerical simulation methods in tribology, Tribology International, 40(6), pp. 916-923.

Popov, V.L., 2018, Is tribology approaching its Golden Age? Grand Challenges in Engineering Education and Tribological Research, Frontiers in Mechanical Engineering, 4, pp. 16.

Dimaki, A., Dmitriev, A., Chai, Y., Popov, V.L., 2014, Rapid simulation procedure for fretting wear on the basis of the method of dimensionality reduction, International Journal of Solids and Structures, 51(25-26), pp. 4215-4220.

Archard, J., Hirst, W., 1956, The wear of metals under unlubricated conditions, Proc. R. Soc. Lond. A, 236(1206), pp. 397-410.

Nakano, K., Kawaguchi, K., Takeshima, K., Shiraishi, Y., Forsbach, F., Benad, J., Popov, M., Popov, V.L., 2019, Investigation on dynamic response of rubber in frictional contact, Frontiers in Mechanical Engineering, 5, pp. 9.

Barber, J., 2018, Contact Mechanics, Solid Mechanics and Its Applications, Springer, New York.

Hahn, H., 1985, Elastizitätstheorie, Vieweg Teubner Verlag, Wiesbaden.

Pohrt, R., Li, Q., 2014, Complete Boundary Element Formulation for Normal and Tangential Contact Problems, Physical Mesomechanics, 17(4), pp. 334-340.

Johnson, K., 2003, Contact mechanics, Cambridge University Press.

Coulomb, C., 1821, Theorie des machines simple, Bachelier, Paris.

Gao, H., 1991, Stress concentration at slightly undulating surfaces, Journal of the Mechanics and Physics of Solids, 39(4), pp. 443-458.

Phillips, J., White, K., 1997, A precorrected FFT-method for electrostatic analysis of complicated 3-D structues, IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems, 16(10), pp. 1059-1072.

Masters, N., Ye, W., 2004, Fast BEM solution for coupled electrostatic and linear elastic problems, NSTI-Nanotech, 2, pp. 426-429.

Lim, K., He, X., Lim, S., 2008, Fast Fourier transform on multipoles (FFTM) algorithm for Laplace equation with direct and indirect boundary element method, Computational Mechanics, 41, pp. 313-323.

Benedetti, I., Aliabadi, M., Davi, G., 2008, A fast 3D dual boundary element method based on hierarchical matrices, International journal of solids and structures, 45(7-8), pp. 2355-2376.

Irgens, F., 2008, Theory of Elasticity, Continuum Mechanics, Springer, Berlin.

Galin, L., 2008, Plane Elasticity Theory, Contact Problems, G. Gladwell, Editor, Springer, Dordrecht.

Kelly, P., 2013, Linear Elasticity, An introduction to Solid Mechanics (Lecture Notes), University of Auckland.

Betti, E., 1872, Teoria della elasticità, Il Nuovo Cimento, 7(1), pp. 69-97.

Gaul, L., Fiedler, C., 2013, Methode der Randelemente in Statik und Dynamik, 2 ed, Springer, Berlin.

Gross, D., Hauger, W., Wriggers, P., 2014, Technische Mechanik 4, 9 ed, Springer, Berlin.



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ISSN: 2335-0164 (Online)

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