COMPARISON of ANALYTICAL and FINITE ELEMENT SOLUTIONS of LOW VELOCITY IMPACT PROBLEM for SIMPLY SUPPORTED BEAM

Year 2022, Issue: 051, 263 - 282, 31.12.2022

Yaşar Erbaş , Bahadır Alyavuz

Abstract

The aim of this study is to compare the results obtained from analytical and finite element solutions of low velocity transverse impact problem of a sphere onto simply supported beam. Twelve models with various mass ratios were created by keeping the beam dimensions constant and changing the sphere radius. The effect of the element size in the finite element solution was analyzed with five separate meshes whose element size gradually decreases at the impact point. In the solutions, the deflections of the beam and the displacement of the sphere at the impact point were taken into account. To check the validity of the model, a comparison with an experimental study in the literature was also made. Comparisons show that the deflections obtained from the analytical solution are compatible with the finite element solution within the period of repetitive or continuous contact between the sphere and beam. Particularly, as the mass ratio defined for beam and sphere gets smaller, maximum deflection values obtained from analytical and finite elements become closer. For the cases including sub-impact, after the sphere leaves the beam there exist differences in the results mainly because of the sub-impacts.

Keywords

Low velocity transverse impact, Analytical solution, Finite Element Analysis

Thanks

The authors received no specific grant for the research, authorship, and/or publication of this article.

References

• [1] Cox, H., (1849), On impacts on elastic beams, Cambridge Philosophical Transactions, 9, 73-78.
• [2] Timoshenko, S.P., (1913), Zur frage nach der wirkung eines stosses auf einen balken, Zeitschrift für Mathematik und Physik, 62(2), 198-209.
• [3] Hertz, H., (1881), Über die berührung fester elastischer körper, Journal für die Reine und Angewandte Mathematik, 92, 156-171.
• [4] Goldsmith, W., (2001), Impact the theory and physical behaviour of colliding solids, Dover Publications, New York.
• [5] Gültop, T., Yılmaz, M.C., Alyavuz, B., (2015), An analytical investigation of rigid plastic beams under impact loading, Journal of the Faculty of Engineering and Architecture of Gazi University, 30(1), 87-94.
• [6] Eringen, A.C., (1952), Transverse impact on beams and plates with arbitrary edge conditions, Naval Research Department Technical Report No 2.
• [7] Schwieger, H., (1965), A simple calculation of the transverse impact on beams and its experimental verification, Experimental Mechanics, 5(11), 378-384.
• [8] Yılmaz, M.C., Anıl, Ö., Alyavuz, B., Kantar, E., (2014), Load displacement behavior of concrete beam under monotonic static and low velocity impact load, International Journal of Civil Engineering Transaction A: Civil Engineering, 12(4), 88-503.
• [9] Anıl, Ö., Kantar, E., Yılmaz, M.C., (2015), Low velocity impact behavior of rc slabs with different support types, Construction and Building Materials, 93, 1078-1088.
• [10] Jin, L., Xu, J., Zhang, R., Du, X., (2017), Numerical study on the impact performances of reinforced concrete beams: a mesoscopic simulation method, Engineering Failure Analysis, 80, 141-163.
• [11] Othman, H., Marzouk, H., (2017), Finite-element analysis of reinforced concrete plates subjected to repeated impact loads, Journal of Structural Engineering, 143(9), 04017120.
• [12] Saatci, S., Vecchio, F.J., (2009), Nonlinear finite element modeling of reinforced concrete structures under impact loads, ACI Structural Journal, 106(5), 717-725.
• [13] [Qiao, P., Yang, M., (2007), Impact analysis of fiber reinforced polymer honeycomb composite sandwich beams, Composites Part B: Engineering, 38(5-6), 739-750.
• [14] Foo, C.C., Seah, L.K., Chai, G.B., (2008), Low-velocity impact failure of aluminum honeycomb sandwich panels, Composite Structures, 85(1), 20-28.
• [15] Hughes, T.J., Taylor, R.L., Sackman, J.L., (1975), Finite element formulation and solution of contact‐impact problems in continuum mechanics‐IV Report No. UC SESM 76‐4, Department of Civil Engineering University of California, Berkeley.
• [16] Hughes, T.J.R., Taylor, R.L., Sackman, J.L., Curnier, A., Kanoknukulchai, W., (1976), A finite element method for a class of contact-impact problems, Computer Methods in Applied Mechanics and Engineering, 8(3), 249-276.
• [17] [Belytschko, T., Liu, W.K., Moran, B., (2000), Nonlinear finite elements for continua and structures, Wiley, Chichester.
• [18] ABAQUS Analysis User’s Manual, (2011), Simulia.
• [19] Yu, J., Jones, N., (1989), Numerical simulation of a clamped beam under impact loading, Computers and Structures, 32(2), 281-293.
• [20] Yu, J., Jones, N., (1997), Numerical simulation of impact loaded steel beams and the failure criteria, International Journal of Solids and Structures, 34(30), 3977-4004.
• [21] Li, Q.M., Jones, N., (2002), Response and failure of a double-shear beam subjected to mass impact, International Journal of Solids and Structures, 39(7), 1919-1947.
• [22] Al-Thairy, H., Wang, Y.C., (2011), A numerical study of the behaviour and failure modes of axially compressed steel columns subjected to transverse impact, International Journal of Impact Engineering, 38(8-9), 732-744.
• [23] Wang, R., Pei, C., (2013), Parametric analysis of dynamic response of hot-rolled h-shaped steel beam under lateral impact load, Gongcheng Lixue/Engineering Mechanics, 30(SUPPL.1), 258-262.
• [24] Shi, S., Zhu, L., Yu, T.X., (2019), Dynamic modelling of elastic-plastic beams under impact, International Journal of Impact Engineering, 126, 1-10.
• [25] Pashah, S., Massenzio, M., Jacquelin, E., (2008), Prediction of structural response for low velocity impact, International Journal of Impact Engineering, 35(2), 119-132.
• [26] Zhang, L., Yin, X., Yang, J., Wang, H., Deng, Q., Yu, B. et al, (2018), Transient impact response analysis of an elastic-plastic beam, Applied Mathematical Modelling, 55, 616-636.
• [27] Seifried, R., (2006), Multiple impacts of transversely struck aluminum beams, Proceedings in Applied Mathematics & Mechanics, 6, 333-334.
• [28] Arnold, R.N., (1937), Impact stresses in a freely supported beam, Proceedings of the Institution of Mechanical Engineers, 137(1), 217-281.
• [29] Qi, X., Yin, X., (2016), Experimental studying multi-impact phenomena exhibited during the collision of a sphere onto a steel beam, Advances in Mechanical Engineering, 8(9), 1-16.
• [30] LS-DYNA Theory Manual, (2006), Livermore Software Technology Corporation, Livermore.
• [31] Qi, X., Yin, X., (2017), Sub-impacts of simply supported beam struck by steel sphere - Part II: Numerical simulations, Advances in Mechanical Engineering, 9(1), 1-11.
• [32] Weaver, W., Timoshenko, S.P., Yong, D.H., (1990), Vibration problems in engineering, John Wiley & Sons, New York.
• [33] Stronge, W. J., (2000), Impact mechanics, Cambridge University Press, Cambridge.
• [34] Olsson, R., (2015), Analytical prediction of damage due to large mass impact on thin ply composites, Composites: Part A, 72, 184-191.