Analytical and numerical modelling of repeated impacts on elastic-strain hardening beams
Source abstract
Abstract
The repeated impact problem of a clamped elastic, strain-hardening plastic beam repeatedly impinged by a rigid heavy wedge with a low velocity at the mid-span is studied analytically and numerically. The beam motion is described using a Single-Degree-of-Freedom mass-spring model, governed by two structural parameters, i.e., structural resistance and the equivalent mass of beam. The explicit expressions of resistance functions of the beam during loading/unloading/reloading process are obtained from a series of simplified nonlinear quasi-static analysis with material strain hardening being taken into account. The equivalent mass of beam is related to the assumed transverse displacement profile of the beam which varies with its elastic-plastic state. Thereafter, the analytical solutions of the repeated impact response of beams made from the elastic-linear hardening (bi-linear) material are well validated by the detailed numerical simulations obtained by using ABAQUS/Explicit. Additional theoretical and numerical investigations with various tangent modulus values reveal that strain hardening can increase the elastic strain energy absorbed by the beam, but it has little influence on the duration of each impact.
Source: openaire · Quality: candidate unverified · Source record ↗
Research context
OpenAlex topics: High-Velocity Impact and Material Behavior · Structural Response to Dynamic Loads · Mechanical Behavior of Composites
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (34)
Show source-provided references
1. Alves, M., Yu, J.L.: Material influence on the response of impacted beams. Latin Am. J. Solids Struct. 2, 167–193 (2005)
2. Brake, M.R.: An analytical elastic-perfectly plastic contact model. Int. J. Solids Struct. 49(22), 3129–3141 (2012). https://doi.org/10.1016/j.ijsolstr.2012.06.01310.1016/j.ijsolstr.2012.06.013 ↗
3. Brake, M.R.: An analytical elastic plastic contact model with strain hardening and frictional effects for normal and oblique impacts. Int. J. Solids Struct. 62, 104–123 (2015). https://doi.org/10.1016/j.ijsolstr.2015.02.01810.1016/j.ijsolstr.2015.02.018 ↗
4. Campbell, T., Charlton, T.: Finite deformation of a fully fixed beam comprised of a nonlinear material. Int. J. Mech. Sci. 15(5), 415–422 (1973). https://doi.org/10.1016/0020-7403(73)90040-410.1016/0020-7403(73)90040-4 ↗
5. Cho, S.R., Truong, D.D., Shin, H.K.: Repeated lateral impacts on steel beams at room and sub-zero temperatures. Int. J. Impact Eng 72, 75–84 (2014). https://doi.org/10.1016/j.ijimpeng.2014.05.01010.1016/j.ijimpeng.2014.05.010 ↗
6. Dai, X., Yuan, T., Zu, Z., et al.: Experimental investigation on the response and residual compressive property of honeycomb sandwich structures under single and repeated low velocity impacts. Mater. Today Commun. 25, 101309 (2020). https://doi.org/10.1016/j.mtcomm.2020.10130910.1016/j.mtcomm.2020.101309 ↗
7. Den Hartog, J.P.: Advanced Strength of Materials. McGraw-Hill, New York (1952)
8. Guo, K., Zhu, L., Li, Y., et al.: Experimental study on the dynamic behavior of aluminium foam sandwich plate under repeated impacts. Int. J. Impact Eng. 114, 123–132 (2018). https://doi.org/10.1016/j.ijimpeng.2017.12.00110.1016/j.ijimpeng.2017.12.001 ↗
9. Guo, K., Zhu, L., Li, Y., Yu, T.X.: Numerical study on mechanical behavior of foam core sandwich plates under repeated impact loadings. Compos. Struct. 224, 111030 (2019). https://doi.org/10.1016/j.compstruct.2019.11103010.1016/j.compstruct.2019.111030 ↗
10. Guo, Y., Yin, X., Yu, B., et al.: Experimental analysis of dynamic behavior of elastic visco-plastic beam under repeated mass impacts. Int. J. Impact Eng. 171, 104371 (2023). https://doi.org/10.1016/j.ijimpeng.2022.10437110.1016/j.ijimpeng.2022.104371 ↗
11. He, X., Guedes Soares, C.: Experimental study on the dynamic behavior of beams under repeated impacts. Int. J. Impact Eng. 147, 103724 (2021a). https://doi.org/10.1016/j.ijimpeng.2020.10372410.1016/j.ijimpeng.2020.103724 ↗
12. He, X., Guedes Soares, C.: Numerical study on the pseudo-shakedown of beams under repeated impacts. Ocean Eng. 242, 110137 (2021b). https://doi.org/10.1016/j.oceaneng.2021.11013710.1016/j.oceaneng.2021.110137 ↗
13. Huang, Z.Q., Chen, Q.S., Zhang, W.T.: Pseudo-shakedown in the collision mechanics of ships. Int. J. Impact Eng. 24(1), 19–31 (2000). https://doi.org/10.1016/S0734-743X(99)00041-X10.1016/S0734-743X(99)00041-X ↗
14. Jones, N.: Influence of strain-hardening and strain-rate sensitivity on the permanent deformation of impulsively loaded rigid-plastic beams. Int. J. Mech. Sci. 9(12), 777–796 (1967). https://doi.org/10.1016/0020-7403(67)90007-010.1016/0020-7403(67)90007-0 ↗
15. Jones, N.: Structural Impact, 2nd edn. Cambridge University Press, Cambridge (2012)
16. Jones, N.: Pseudo-shakedown phenomenon for the mass impact loading of plating. Int. J. Impact Eng. 65, 33–39 (2014). https://doi.org/10.1016/j.ijimpeng.2013.10.00910.1016/j.ijimpeng.2013.10.009 ↗
17. Karagiozova, D., Yu, T.X., Shi, S.Y., Zhu, L.: On the influence of elasticity on the large deflections response of circular plates to uniform quasi-static pressure. Int. J. Mech. Sci. 131, 894–907 (2017). https://doi.org/10.1016/j.ijmecsci.2017.07.03210.1016/j.ijmecsci.2017.07.032 ↗
18. Liao, B., Zhou, J., Li, Y., et al.: Damage accumulation mechanism of composite laminates subjected to repeated low velocity impacts. Int. J. Mech. Sci. 182, 105783 (2020). https://doi.org/10.1016/j.ijmecsci.2020.10578310.1016/j.ijmecsci.2020.105783 ↗
19. Pashah, S., Massenzio, M., Jacquelin, E.: Prediction of structural response for low velocity impact. Int. J. Impact Eng. 35, 119–132 (2008). https://doi.org/10.1016/j.ijimpeng.2006.12.00610.1016/j.ijimpeng.2006.12.006 ↗
20. Ren, J., Zhao, Z., Zhou, Y., Qiang, L., Lu, T.J.: Springback of a fully-clamped metallic beam loaded impulsively. Int. J. Mech. Mater. Des. 18(2), 435–459 (2022). https://doi.org/10.1007/s10999-022-09590-010.1007/s10999-022-09590-0 ↗
21. Sha, Y., Hao, H.: A simplified approach for predicting bridge pier responses subjected to barge impact loading. Adv. Struct. Eng. 17(1), 11–23 (2014). https://doi.org/10.1260/1369-4332.17.1.1110.1260/1369-4332.17.1.11 ↗
22. Sherbourne, A.N., Lu, F.: Effect of axial restraints on the deflection of strain hardening beams. Int. J. Mech. Sci. 35(5), 397–413 (1993). https://doi.org/10.1016/0020-7403(93)90011-I10.1016/0020-7403(93)90011-I ↗
23. Shi, S.Y., Zhu, L., Yu, T.X.: Elastic-plastic response of clamped square plates subjected to repeated quasi-static uniform pressure. Int. J. Appl. Mech. (2018). https://doi.org/10.1142/S175882511850067910.1142/S1758825118500679 ↗
24. Shi, S.Y., Zhu, L., Yu, T.X.: Dynamic modelling of elastic-plastic beams under impact. Int. J. Impact Eng 126, 1–10 (2019). https://doi.org/10.1016/j.ijimpeng.2018.11.01710.1016/j.ijimpeng.2018.11.017 ↗
25. Truong, D.D., Jung, H.J., Shin, H.K., et al.: Response of low-temperature steel beams subjected to single and repeated lateral impacts. Int. J. Nav. Arch. Ocean Eng. 10(6), 670–682 (2018a). https://doi.org/10.1016/j.ijnaoe.2017.10.00210.1016/j.ijnaoe.2017.10.002 ↗
26. Truong, D.D., Shin, H.K., Cho, S.R.: Repeated lateral impacts on steel grillage structures at room and sub-zero temperatures. Int. J. Impact Eng. 113, 40–53 (2018b). https://doi.org/10.1016/j.ijimpeng.2017.11.00710.1016/j.ijimpeng.2017.11.007 ↗
27. Wu, K.Q., Yu, T.X.: Simple dynamic models of elastic-plastic structures under impact. Int. J. Impact Eng. 25, 733–754 (2001). https://doi.org/10.1016/S0734-743X(01)00017-310.1016/S0734-743X(01)00017-3 ↗
28. Yu, T.X., Johnson, W.: Influence of axial force on the elastic-plastic bending and spring-back of a beam. J. Mech. Work. Technol. 6(1), 5–21 (1982). https://doi.org/10.1016/0378-3804(82)90016-X10.1016/0378-3804(82)90016-X ↗
29. Zeng, Y., Chen, H., Yu, R., et al.: Experimental research on dynamic behavior of circular mild steel plates with surface cracks subjected to repeated impacts in low temperature. Shock Vib. (2020). https://doi.org/10.1155/2020/371370910.1155/2020/3713709 ↗
30. Zhang, Y., Li, Y., Guo, K.: Dynamic mechanical behavior and energy absorption of aluminium honeycomb sandwich panels under repeated impact loads. Ocean Eng. 219, 108344 (2021). https://doi.org/10.1016/j.oceaneng.2020.10834410.1016/j.oceaneng.2020.108344 ↗
31. Zhu, L.: Dynamic inelastic behavior of ship plates in collision. Ph.D. thesis, Department of Naval Architecture and Ocean Engineering, University of Glasgow (1990)
32. Zhu, L., Faulkner, D.: Damage estimate for plating of ships and platforms under repeated impacts. Mar. Struct. 9(7), 697–720 (1996). https://doi.org/10.1016/0951-8339(95)00018-610.1016/0951-8339(95)00018-6 ↗
33. Zhu, L.: Modeling of repeated impacts on ships and offshore platforms. In: Proceedings of the 1st International Conference on Safety & Reliability of Ship, Offshore & Subsea Structures, Glasgow (2014)
34. Zhu, L., Shi, S.Y., Jones, N.: Dynamic response of stiffened plates under repeated impacts. Int. J. Impact Eng. 117, 113–122 (2018). https://doi.org/10.1016/j.oceaneng.2020.10834410.1016/j.oceaneng.2020.108344 ↗