An Improved Linear Complementarity Solver for the Dynamic Analysis of Blast Loaded Structures
Source abstract
Abstract
Abstract The linear complementarity problem (LCP) approach, expedited by using the simple rigid–plastic theory, has been utilized successfully in predicting the numerical response of the ductile steel or concrete structures subjected to short-duration, high-intensity dynamic loads. The current study attempts to improve the computational stability of this powerful technique while determining the response of skeletal structures under blast loading. The performance of the Lemke LCP solver is amplified by introducing an automatic time-stepping scheme to efficiently trace the complex dynamic response using either lumped mass or continuous mass discretization. The computational efficiency of this solver is tested against carefully chosen three numerical examples, and the acquired results are in good agreement with the derived closed-form solution and results from other sources.
Source: crossref · Quality: baseline
Research context
OpenAlex topics: Structural Response to Dynamic Loads · Structural Behavior of Reinforced Concrete · Seismic Performance and Analysis
SciVX discovery tags are terminology-based. OpenAlex topics are source-provided classifications.
References (56)
Show source-provided references
1. Andersen, M., Niebe, S., & Erleben, K. (2017). A fast linear complementarity problem solver for fluid animation using high level algebra interfaces for GPU libraries. Computational Graphics, 69, 36–48. https://doi.org/10.1016/j.cag.2017.09.00610.1016/j.cag.2017.09.006 ↗
2. Biju, A. M., Athulya Sreesa, E. K., Remesh, D., Rinsa, K., & Anusree, A. (2017). Numerical Study of Reinforced Concrete beam subjected to blast loading using Finite element package ABAQUS. IOSR Journal of Mechanical and Civil Engineering, 14, 58–61. https://doi.org/10.9790/1684-140302586110.9790/1684-1403025861 ↗
3. Bleich, H. H., & Shaw, R. (1960). Dominance of shear stresses in early stages of impulsive motion of beams. Journal Applied Mechanics Transactions of ASME, 27, 132–138. https://doi.org/10.1115/1.364388710.1115/1.3643887 ↗
4. Capurso, M. (1972). A quadratic programming approach to the impulsive loading analysis of rigid plastic structures. Meccanica, 7, 45–57.10.1007/BF02133604 ↗
5. Cennamo, C., Gesualdo, A., & Monaco, M. (2017). Shear plastic constitutive behavior for near-fault ground motion. Journal of Engineering Mechanics, 143, 04017086. https://doi.org/10.1061/(asce)em.1943-7889.000130010.1061/(asce)em.1943-7889.0001300 ↗
6. Chen, S., Li, Q., Liu, Y., Xia, J., & Xue, Z. (2011). Dynamic elastoplastic analysis using the meshless local natural neighbor interpolation method. International Journal of Computational Methods, 8, 463–481. https://doi.org/10.1142/S021987621100262910.1142/S0219876211002629 ↗
7. Dantzig, G. B. (1998). Linear programming and extensions (Vol. 48). Princeton University Press.
8. Dantzig, G. B., Orden, A., & Wolfe, P. (1955). The generalized simplex method for minimizing a linear form under linear inequality restraints. Pacific J Math, 5, 183–195. https://doi.org/10.2140/pjm.1955.5.18310.2140/pjm.1955.5.183 ↗
9. Garrido, A., Antonelli, L., Martin, J., Alemany, M. M. E., & Mula, J. (2020). Using LEL and scenarios to derive mathematical programming models. Application in a fresh tomato packing problem. Computers and Electronics in Agriculture. https://doi.org/10.1016/j.compag.2020.10524210.1016/j.compag.2020.105242 ↗
10. Guzas, E. L., & Earls, C. J. (2011). Simulating blast effects on steel beam-column members: applications. Computers & Structures, 89, 2133–2148. https://doi.org/10.1016/j.compstruc.2011.08.01410.1016/j.compstruc.2011.08.014 ↗
11. Jahami, A., Temsah, Y., & Khatib, J. (2019). The efficiency of using CFRP as a strengthening technique for reinforced concrete beams subjected to blast loading. International Journal of Advanced Structural Engineering, 11, 411–420. https://doi.org/10.1007/s40091-019-00242-w10.1007/s40091-019-00242-w ↗
12. Jones N (1986). Some comments on the dynamic plastic behaviour of structures.(retroactive coverage). In: International Symposium on intense dynamic loading and its effects (pp. 49–71).
13. Jones N, Shen WQ. Criteria for the inelastic rupture of ductile metal beams subjected to large dynamic loads. Struct Crashworthiness Fail 1993:95–130.
14. Jones, N. (1976). Plastic failure of ductile beams loaded dynamically. Journal of Manufacturing Science and Engineering Transaction of ASME, 98, 131–136. https://doi.org/10.1115/1.343880510.1115/1.3438805 ↗
15. Jones, N. (1990). Structural impact. Cambridge University Press. https://doi.org/10.1017/cbo978051162428510.1017/cbo9780511624285 ↗
16. Karlos, V., & Solomon, G. (2013). Calculation of blast loads for application to structural components (pp. 1–58). Publications Office of the European Union.
17. Khan, A., Smith, D. L., & Izzuddin, B. A. (2013). Investigation of rigid-plastic beams subjected to impact using linear complementarity. Engineering Structures, 50, 137–148. https://doi.org/10.1016/j.engstruct.2012.12.00510.1016/j.engstruct.2012.12.005 ↗
18. Khan, A., Ahmad, I., Khan, W., Khan, N. B., & Aslam, M. (2021). A modified Lemke Algorithm for dynamic rigid plastic response of skeletal structures. Computers and Structures. https://doi.org/10.1016/j.compstruc.2021.10663810.1016/j.compstruc.2021.106638 ↗
19. Kirsch, U., & Bogomolni, M. (2007). Nonlinear and dynamic structural analysis using combined approximations. Computers & Structures, 85, 566–578. https://doi.org/10.1016/j.compstruc.2006.08.07310.1016/j.compstruc.2006.08.073 ↗
20. Lee, M. J., & Kwak, H. G. (2018). Blast and impact analyses of RC beams considering bond-slip effect and loading history of constituent materials. International Journal of Concrete Structures and Materials. https://doi.org/10.1186/s40069-018-0244-910.1186/s40069-018-0244-9 ↗
21. Lee, E. H., & Symonds, P. S. (1952a). Large Plastic deformations of beams under transverse impact. Journal of Applied Mechanics, 19, 308–314. https://doi.org/10.1115/1.401050310.1115/1.4010503 ↗
22. Lee, E. H., & Symonds, P. S. (1952b). Large plastic deformations of beams under transverse impact. Journal of Applied Mechanics ASME, 19, 308–314.10.1115/1.4010503 ↗
23. Lemke, C. E. (1978). Some pivot schemes for the linear complementarity problem (pp. 15–35). Springer.
24. Li, Y., Algassem, O., & Aoude, H. (2018). Response of high-strength reinforced concrete beams under shock-tube induced blast loading. Construction and Building Materials, 189, 420–437. https://doi.org/10.1016/j.conbuildmat.2018.09.00510.1016/j.conbuildmat.2018.09.005 ↗
25. Ling, Q., He, Y., He, Y., & Pang, C. (2017). Dynamic response of multibody structure subjected to blast loading. European Journal of Mechanics A/Solids, 64, 46–57. https://doi.org/10.1016/j.euromechsol.2017.01.01010.1016/j.euromechsol.2017.01.010 ↗
26. Liu, Y., Yan, J., & Huang, F. (2018). Behavior of reinforced concrete beams and columns subjected to blast loading. Defence Technology, 14, 550–559. https://doi.org/10.1016/j.dt.2018.07.02610.1016/j.dt.2018.07.026 ↗
27. Lloyd Smith, D., & Sahlit, C. L. (1991). Dynamic response of pulse loaded structures as a linear complementarity problem. Engineering Optimization, 18, 23–41.10.1080/03052159108941010 ↗
28. Lowe, W. T., Al-Hassani, S. T. S., & Johnson, W. (1972). Impact behaviour of small scale model motor coaches. Proceedings of the Institution of Mechanical Engineers. https://doi.org/10.1243/pime_proc_1972_186_042_0210.1243/pime_proc_1972_186_042_02 ↗
29. Magnusson, J., Hallgren, M., & Ansell, A. (2010). Air-blast-loaded, high-strength concrete beams. Part I: Experimental investigation. Magazine of Concrete Research, 62, 127–136.10.1680/macr.2008.62.2.127 ↗
30. Magnusson, J., & Hallgren, M. (2004). Reinforced high strength concrete beams subjected to air blast loading. Structures and Materials, 15, 53–62.
31. Maier, G. (1984). Mathematical programming applications to structural mechanics: Some introductory thoughts. Engineering Structures, 6, 2–6. https://doi.org/10.1016/0141-0296(84)90055-510.1016/0141-0296(84)90055-5 ↗
32. Maier, G., & Munro, J. (1982). Mathematical programming applications to engineering plastic analysis. Applied Mechanics Reviews, 35, 1631–1643.
33. Martin, J. B. (1964). A note on the uniqueness of solutions for dynamically loaded rigid-plastic and rigid-viscoplastic continua. J Appl Mech Trans ASME, 33, 207–209. https://doi.org/10.1115/1.362498810.1115/1.3624988 ↗
34. Mehreganian, N., Fallah, A. S., & Louca, L. A. (2019). Plastic dynamic response of simply supported thick square plates subject to localised blast loading. International Journal of Impact Engineering, 126, 85–100. https://doi.org/10.1016/j.ijimpeng.2018.12.01010.1016/j.ijimpeng.2018.12.010 ↗
35. Menkes, S. B., & Opat, H. J. (1973). Broken beams. Experimental Mechanics, 13, 480–486. https://doi.org/10.1007/bf0232273410.1007/bf02322734 ↗
36. Milani, G., Lourenço, P. B., & Tralli, A. (2009). Homogenized rigid-plastic model for masonry walls subjected to impact. International Journal of Solids and Structures, 46, 4133–4149. https://doi.org/10.1016/j.ijsolstr.2009.08.00710.1016/j.ijsolstr.2009.08.007 ↗
37. Murty, K. G. (1983). Linear programming. Springer.
38. Nawar, M. T., Arafa, I. T., & Elhosseiny, O. M. (2021). Numerical damage evaluation of perforated steel columns subjected to blast loading. Defence Technology. https://doi.org/10.1016/j.dt.2021.03.01910.1016/j.dt.2021.03.019 ↗
39. Nuseirat, A.M.A.-F., & Stavroulakis, G. E. (2000). A complementarity problem formulation of the frictional grasping problem. Computer Methods in Applied Mechanics and Engineering, 190, 941–952.10.1016/S0045-7825(99)00454-5 ↗
40. Parkes, E. (1955). The permanent deformation of a cantilever struck transversely at its tip. Proceedings of the Royal Society London Series A Mathematical and Physical Sciences, 228, 462–476. https://doi.org/10.1098/rspa.1955.006210.1098/rspa.1955.0062 ↗
41. Parkes, E. (1958). The permanent deformation of an encastré beam struck transversely at any point in its span. Proceedings of the Institution of Civil Engineers, 10, 277–304. https://doi.org/10.1680/iicep.1958.203710.1680/iicep.1958.2037 ↗
42. Patsios, T. N., & Spiliopoulos, K. V. (2018). A force-based mathematical programming method for the incremental analysis of 3D frames with non-holonomic hardening plastic hinges. Computers & Structures, 208, 51–74. https://doi.org/10.1016/j.compstruc.2018.05.01110.1016/j.compstruc.2018.05.011 ↗
43. Portioli, F. P. A. (2020). Rigid block modelling of historic masonry structures using mathematical programming: A unified formulation for non-linear time history, static pushover and limit equilibrium analysis. Bulletin of Earthquake Engineering, 18, 211–239. https://doi.org/10.1007/s10518-019-00722-010.1007/s10518-019-00722-0 ↗
44. Rodigari, D., Franchi, A., Genna, F., Crespi, P., & De Col, R. (2019). A linear complementarity approach to the time integration of dynamic elastic–plastic structural problems. Meccanica, 54, 1597–1609. https://doi.org/10.1007/s11012-019-01028-w10.1007/s11012-019-01028-w ↗
45. Smith, D.L. (1974). Plastic Limit analysis and synthesis of structures by linear programming.
46. Smith, D. L. (1990). Mathematical programming methods in structural plasticity. Springer. https://doi.org/10.1007/978-3-7091-2618-910.1007/978-3-7091-2618-9 ↗
47. Symonds, P.S. (1967). Survey of methods of analysis for plastic deformation of structures under dynamic loading. Division of Engineering Report BU/NSRDC/ (pp. 1–148). Brown University.10.21236/AD0659972 ↗
48. Symonds, P. S., & Frye, C. W. G. (1988). On the relation between rigid-plastic and elastic-plastic predictions of response to pulse loading. International Journal of Impact Engineering, 7, 139–149. https://doi.org/10.1016/0734-743X(88)90022-X10.1016/0734-743X(88)90022-X ↗
49. Tamuzh, V. P. (1962). On a minimum principle in dynamics of rigid-plastic bodies. Journal of Applied Mathematics and Mechanics, 26, 1067–1077.10.1016/0021-8928(62)90165-X ↗
50. Taylor, G. I. (1948). The use of flat-ended projectiles for determining dynamic yield stress I. Theoretical considerations. Proceedings of the Royal Society of London Series A Mathematical and Physical Sciences, 194, 289–299.
51. Temsah, Y., Jahami, A., Khatib, J., & Sonebi, M. (2018). Numerical analysis of a reinforced concrete beam under blast loading. MATEC Web of Conferences, 149, 02063. https://doi.org/10.1051/matecconf/20181490206310.1051/matecconf/201814902063 ↗
52. Tian, L. R., Chen, F. L., Zhu, L., & Yu, T. X. (2020). Large deformation of square plates under pulse loading by combined saturation analysis and membrane factor methods. International Journal of Impact Engineering. https://doi.org/10.1016/j.ijimpeng.2020.10354610.1016/j.ijimpeng.2020.103546 ↗
53. Wu, J., Zhou, Y., Zhang, R., Liu, C., & Zhang, Z. (2020). Numerical simulation of reinforced concrete slab subjected to blast loading and the structural damage assessment. Engineering Failure Analysis. https://doi.org/10.1016/j.engfailanal.2020.10492610.1016/j.engfailanal.2020.104926 ↗
54. Lee, J. Y., Shin, H. O., Yoo, D. Y., & Yoon, Y. S. (2018). Structural response of steel-fiber-reinforced concrete beams under various loading rates. Engineering Structures, 156, 271–283.10.1016/j.engstruct.2017.11.052 ↗
55. Yu, R., Chen, L., Fang, Q., Yan, H., & Chen, G. (2019). Generation of pressure–impulse diagrams for failure modes of RC columns subjected to blast loads. Engineering Failure Analysis, 100, 520–535. https://doi.org/10.1016/j.engfailanal.2019.02.00110.1016/j.engfailanal.2019.02.001 ↗
56. Zhang, D., Yao, S. J., Lu, F., Chen, X. G., Lin, G., Wang, W., et al. (2013). Experimental study on scaling of RC beams under close-in blast loading. Engineering Failure Analysis, 33, 497–504. https://doi.org/10.1016/j.engfailanal.2013.06.02010.1016/j.engfailanal.2013.06.020 ↗