Prediction of Random Vibration Fatigue Damage Using Isogeometric Modelling

Shubiao Wang; Leila Khalij; Renata Troian; Lujie Shi

doi:10.24423/cames.363

Shubiao Wang Normandie Université
Leila Khalij Normandy Université
Renata Troian Normandy Université
Lujie Shi Normandy Université

DOI: http://dx.doi.org/10.24423/cames.363

Abstract

The finite element analysis (FEA) method is indispensable in simulation technology, as it can help engineers predict results to avoid the cost of experimental testing. However, the finite element mesh generation process can be time-consuming, and the approximate mesh model can lead to inaccurate stress results. Improving the accuracy of stress estimation leads to a better assessment of damage or life of mechanical components. In this study, we applied the isogeometric analysis (IGA) implemented in LS-DYNA software to study two specimens subjreted to the stationary Gaussian random loads. These geometric models were represented by non-uniform rational B-spline (NURBS) to assess the damage and fatigue life in the frequency domain by using Dirlik’s distribution and cumulative damage. A comparison with FEA was conducted to highlight the main differences. Experimental fatigue tests with an electrodynamic shaker were also carried out to check if the fatigue lives predicted by numerical models are consistent. The study showed that IGA predicts similar results to FEA with an acceptable relative error and reduced the time for mesh generation, requiring fewer integration points and mesh elements.

Keywords

isogeometric analysis, finite element method, random acceleration, vibration-based bending fatigue,

References

1. A. Ringeval, Y. Huang, Random vibration fatigue analysis with LS-DYNA, [in:] Proceedings of the 12th International LS-DYNA Users Conference, Dearborn, Michigan, USA, 2012.
2. T. Dirlik, Application of computers in fatigue analysis, PhD thesis, University of Warwick, Coventry, England, 1985.
3. S.J. Owen et al., An immersive topology environment for meshing, [in:] M.L. Brewer, D. Marcum [Eds], Proceedings of the 16th International Meshing Roundtable, pp. 553–577, Springer, Berlin, Heidelberg, 2008.
4. T.J.R. Hughes, J.A. Cottrell, Y. Bazilevs, Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement, Computer Methods in Applied Mechanics and Engineering, 194(39): 4135–4195, 2005, doi: 10.1016/j.cma.2004.10.008.
5. J. Lu, Isogeometric contact analysis: Geometric basis and formulation for frictionless contact, Computer Methods in Applied Mechanics and Engineering, 200(5–8): 726–741, 2011, doi: 10.1016/j.cma.2010.10.001.
6. İ. Temizer, P. Wriggers, T.J.R. Hughes, Contact treatment in isogeometric analysis with NURBS, Computer Methods in Applied Mechanics and Engineering, 200(9–12): 1100– 1112, 2011, doi: 10.1016/j.cma.2010.11.020.
7. İ. Temizer, P. Wriggers, T.J.R. Hughes, Three-dimensional mortar-based frictional contact treatment in isogeometric analysis with NURBS, Computer Methods in Applied Mechanics and Engineering, 209–212: 115–128, 2012, doi: 10.1016/j.cma.2011.10.014.
8. Y. Bazilevs, T.J.R. Hughes, NURBS-based isogeometric analysis for the computation of flows about rotating components, Computational Mechanics, 43: 143–150, 2008, doi: 10.1007/s00466-008-0277-z.
9. Y. Bazilevs, V.M. Calo, Y. Zhang, T.J.R. Hughes, Isogeometric fluid–structure interaction analysis with applications to arterial blood flow, Computational Mechanics, 38: 310–322, 2006, doi: 10.1007/s00466-006-0084-3.
10. Y. Bazilevs, V.M. Calo, T.J.R. Hughes, Y.J. Zhang, Isogeometric fluid-structure interaction: theory, algorithms, and computations, Computational Mechanics, 43: 3–37, 2008, doi: 10.1007/s00466-008-0315-x.
11. X. Qian, Full analytical sensitivities in NURBS based isogeometric shape optimization, Computer Methods in Applied Mechanics and Engineering, 199(29–32): 2059–2071, 2010, doi: 10.1016/j.cma.2010.03.005.
12. W.A. Wall, M.A. Frenzel, C. Cyron, Isogeometric structural shape optimization, Computer Methods in Applied Mechanics and Engineering, 197(33–40): 2976–2988, 2008, doi: 10.1016/j.cma.2008.01.025.
13. B. Hassani, S.M. Tavakkoli, N.Z. Moghadam, Application of isogeometric analysis in structural shape optimization, Scientia Iranica, 18(4): 846–852, 2011, doi: 10.1016/j.scient. 2011.07.014.
14. S. Shojaee, N. Valizadeh, M. Arjomand, Isogeometric structural shape optimization using particle swarm algorithm, International Journal of Optimization in Civil Engineering, 1(4): 633–645, 2011.
15. J. Kiendl, K.-U. Bletzinger, J. Linhard, R. Wüchner, Isogeometric shell analysis with Kirchhoff–Love elements, Computer Methods in Applied Mechanics and Engineering, 198(49–52): 3902–3914, 2009, doi: 10.1016/j.cma.2009.08.013.
16. D.J. Benson, Y. Bazilevs, M.-C. Hsu, T.J.R. Hughes, Isogeometric shell analysis: The Reissner-Mindlin shell, Computer Methods in Applied Mechanics and Engineering, 199(5–8): 276–289, 2010, doi: 10.1016/j.cma.2009.05.011.
17. D.J. Benson, Y. Bazilevs, M.-C. Hsu, T.J.R. Hughes, A large deformation, rotation-free, isogeometric shell, Computer Methods in Applied Mechanics and Engineering, 200(13–16): 1367–1378, 2011, doi: 10.1016/j.cma.2010.12.003.
18. T.-K. Uhm, S.-K. Youn, T-spline finite element method for the analysis of shell structures, International Journal for Numerical Methods in Engineering, 80: 507–536, 2009, doi: 10.1002/nme.2648.
19. J. Kiendl, Y. Bazilevs, M.-C. Hsu, R. Wüchner, K.-U. Bletzinger, The bending strip method for isogeometric analysis of Kirchhoff–Love shell structures comprised of multiple patches, Computer Methods in Applied Mechanics and Engineering, 199(37–40): 2403– 2416, 2010, doi: 10.1016/j.cma.2010.03.029.
20. S.-I. Moon, I.-J. Cho, D. Yoon, Fatigue life evaluation of mechanical components using vibration fatigue analysis technique, Journal of Mechanical Science and Technology, 25: 631–637, 2011, doi: 10.1007/s12206-011-0124-6.
21. Y. Eldoğan, E. Ciğeroğlu, Vibration fatigue analysis of a cantilever beam using different fatigue theories, [in:] R. Allemang, J. De Clerck, C. Niezrecki, A. Wicks [Eds], Topics in Modal Analysis, Vol. 7, Conference Proceedings of the Society for Experimental Mechanics Series, pp. 471–478, Springer, New York, NY, 2014, doi: 10.1007/978-1-4614-6585-0_45.
22. J.A. Cottrell, A. Reali, Y. Bazilevs, T.J.R. Hughes, Isogeometric analysis of structural vibrations, Computer Methods in Applied Mechanics and Engineering, 195(41–43): 5257–5296, 2006, doi: 10.1016/j.cma.2005.09.027.
23. D. Wang, W. Liu, H. Zhang, Novel higher order mass matrices for isogeometric structural vibration analysis, Computer Methods in Applied Mechanics and Engineering, 260: 92–108, 2013, doi: 10.1016/j.cma.2013.03.011.
24. S. Shojaee, E. Izadpanah, N. Valizadeh, J. Kiendl, Free vibration analysis of thin plates by using a NURBS-based isogeometric approach, Finite Elements in Analysis and Design, 61: 23–34, 2012, doi: 10.1016/j.finel.2012.06.005.
25. S. Gondegaon, H.K. Voruganti, Static structural and modal analysis using isogeometric analysis, Journal of Theoretical and Applied Mechanics, 46(4): 36–75, 2016, doi: 10.1515/jtam-2016-0020.
26. T.D. Hien, H.-C. Noh, Stochastic isogeometric analysis of free vibration of functionally graded plates considering material randomness, Computer Methods in Applied Mechanics and Engineering, 318: 845–863, 2017, doi: 10.1016/j.cma.2017.02.007.
27. S. Hartmann, D.J. Benson, D. Lorenz, About isogeometric analysis and the new NURBS-based finite elements in LS-DYNA, [in:] 8th European LS-DYNA Users Conference, Strasbourg, France, 2011.
28. Y. Huang, S. Hartmann, D.J. Benson, Random vibration fatigue analysis based on IGA model in LS-DYNA, Ansys TechCon 2020, October 2020, https://ftp.lstc.com/anony mous/outgoing/huang/nvh/papers.htm.
29. V. Agrawal, S.S. Gautam, IGA: A simplified introduction and implementation details for finite element users, Journal of The Institution of Engineers (India): Series C, 100: 561–585, 2019, doi: 10.1007/s40032-018-0462-6.
30. O.C. Zienkiewicz, R.L. Taylor, J.Z. Zhu, The Finite Element Method: Its Basis and Fundamentals, 6th Ed., Elsevier, Butterworth-Heinemann, 2005.
31. P. Milić, D. Marinković, Isogeometric structural analysis based on NURBS shape functions, Facta Universitatis, Series: Mechanical Engineering, 11(2): 193–202, 2013.
32. G. Kirsch, Die Theorie der Elastizität und die Bedurfnisse der Festigkeitslehre [in German], Zantralblatt Verlin Deutscher Ingenieure, 42: 797–807, 1898.
33. J. Schijve, Four lectures on fatigue crack growth: I. Fatigue crack growth and fracture mechanics, Engineering Fracture Mechanics, 11: 169–181, 1979.
34. M.A. Miner, Cumulative damage in fatigue, Journal of Applied Mechanics, 12(3): 159–164, 1945, doi: 10.1115/1.4009458.
35. A. Palmgren, Die Lebensdauer von Kugellagern [in German; in English: Durability of ball bearings], Zeitschrift des Vereines Deutscher Ingenieure (ZVDI), 14: 339–341, 1924.
36. B.R. Krasnowski, Application of damage tolerance to increase safety of helicopters in service, Defense Technical Information Center, 1999.
37. A. Strauss, D.M. Frangopol, K. Bergmeister, Life-cycle and Sustainability of Civil Infrastructure Systems, [in:] A. Strauss, D. M. Frangopol, K. Bergmeister [Eds], Proceedings of the Third International Symposium on Life-Cycle Civil Engineering, Vienna, Austria, October 3–6, 2012, CRC Press, 2013.
38. G. Risitano, D. Corallo, A. Risitano, Cumulative damage by Miner’s rule and by energetic analysis, Structural Durability Health Monitoring, 8(2): 91–109, 2012, doi: 10.3970/ sdhm.2012.008.091.
39. Y.-L. Lee, D. Taylor, Cycle counting techniques, [in:] Y.-L. Lee, J. Pan, R.B. Hathaway, M.E. Barkey [Eds], Fatigue Testing and Analysis, vol. 3, pp. 77–102, Burlington, Butterworth-Heinemann, 2005.
40. I. Milne, R.O. Ritchie, B.L. Karihaloo, Cyclic loading and fatigue, [in:] R.O. Ritchie, Y. Murakami [Eds], Comprehensive Structural Integrity. Volume 4: Cyclic Loading and Fatigue, Elsevier, 2003.
41. A. Appert, C. Gautrelet, L. Khalij, R. Troian, Development of a test bench for vibratory fatigue experiments of a cantilever beam with an electrodynamic shaker, [in:] Proceedings of the 12th International Fatigue Congress (FATIGUE 2018). MATEC Web Conferece, vol. 165, 8 pages, 2018, doi: 10.1051/matecconf/201816510007.
42. L. Khalij, C. Gautrelet, A. Guillet, Fatigue curves of a low carbon steel obtained from vibration experiments with an electrodynamic shaker, Materials and Design, 86: 640–648, 2015, doi: 10.1016/j.matdes.2015.07.153.
43. W. Xu, X. Yang, B. Zhong, Y. He, C. Tao, Failure criterion of titanium alloy irregular sheet specimens for vibration-based bending fatigue testing, Engineering Fracture Mechanics, 195: 44–56, 2018, doi: 10.1016/j.engfracmech.2018.03.031.
44. H.-T. Hu,Y.-L. Li, T. Suo, F. Zhao, Y.-G. Miao, P. Xue, Q. Deng, Fatigue behavior of aluminum stiffened plate subjected to random vibration loading, Transactions of Nonferrous Metals Society of China, 24(5): 1331–1336, 2014, doi: 10.1016/S1003-6326(14)63196-4.