Progressive collapse analysis on multicore computers using nonlinear dynamic approach
Abstract
A method for solving the problem of structural progressive destruction is proposed, based on nonlinear finite element dynamic analysis, taking into account both physical and geometrical nonlinearity. Unlike most existing approaches, a specialized method has been implemented to simulate the sudden removal of groups of finite elements at given times, which makes it possible to simulate not only the removal of columns but also fragments of load-bearing walls and staircase-elevator blocks. The proposed approach involves the numerical integration of the Cauchy problem using an implicit method of the predictor-corrector type, with multithreaded parallelization of all key algorithms to accelerate the solution. The reliability of the numerical results is substantiated by comparison with the experimental results presented in other studies. The behavior of realistic structural models with bearing walls as well as without them, consisting of exclusively nonlinear finite elements, under the sudden removal of a fragment of a staircase-elevator block, is studied.
Keywords
progressive collapse analysis, nonlinear dynamic analysis, finite element method, Cauchy problem, multithreaded parallelization,References
1. Z.P. Bazant, J.L. Le, F. Greening, D.B. Benson, Collapse of World Trade Center towers: What did and did not cause it?, Structural engineering Report No, 07-05/C605c, Department of Civil and Environmental Engineering Northwestern University Evanston, Illinois, USA, 2007, https://www.researchgate.net/publication/_Collapse_of_world_trade_center_towers_what_did_and_did_not_cause_it.2. F. Kiakojouri, M.R. Sheidaii, V. De Biagi, B. Chiaia, Progressive collapse of structures: A discussion on annotated nomenclature, Structures, 29: 1417–1423, 2021, doi: 10.1016/j.istruc.2020.12.006.
3. J.M. Adam, F. Parisi, J. Sagaseta, X. Lu, Research and practice on progressive collapse and robustness of building structures in the 21st century, Engineering Structures, 173: 122–149, 2018, doi: 10.1016/j.engstruct.2018.06.082.
4. H. Wang, A. Zhang, Y. Li, W. Yan, A review on progressive collapse of building structures, Open Civil Engineering Journal, 8: 183–192, 2014, https://opencivilengineeringjournal.com/contents/volumes/V8/TOCIEJ-8-183/TOCIEJ-8-183.pdf.
5. L. Kwasniewski, Nonlinear dynamic simulations of progressive collapse for a multistory building, Engineering Structures, 32: 1223–1235, 2010, doi: 10.1016/j.engstruct.2009.12.048.
6. F. Fu, 3-D nonlinear dynamic progressive collapse analysis of multi-storey steel composite frame buildings – Parametric study, Engineering Structures, 32: 3974–3980, 2010, doi: 10.1016/j.engstruct.2010.09.008.
7. J. Li, H. Hao, Numerical study of structural progressive collapse using substructure technique, Engineering Structures, 52: 101–113, 2013, doi: 10.1016/j.engstruct.2013.02.016.
8. S. Kokot, A. Anthoine, P. Negro, G. Solomos, Static and dynamic analysis of a reinforced concrete flat slab frame building for progressive collapse, Engineering Structures, 40: 205–217, 2012, doi: 10.1016/j.engstruct.2012.02.026.
9. S. Kokot, Response spectrum of a reinforced concrete frame structure under various column removal scenarios, Journal of Building Engineering, 49: 103992: 1–17, 2022, doi: 10.1016/j.jobe.2022.103992.
10. F. Sadek, J.A. Main, H.S. Lew, Y. Bao, Testing and analysis of steel and concrete beamcolumn assemblies under a column removal scenario, Journal of Structural Engineering, 137(9): 881–892, 2011, doi: 10.1061/(ASCE)ST.1943-541X.0000422.
11. B.A. Izzuddin, A.G. Vlassis, A.Y. Elghazouli, D.A. Nethercot, Progressive collapse of multi-storey buildings due to sudden column loss — Part I: Simplified assessment framework, Engineering Structures, 30: 1308–1318, 2008, doi: 10.1016/j.engstruct.2007.07.011.
12. E. Stoddart, M. Byfield, B. Davison, A. Tyas, Strain rate dependent component based connection modelling for use in non-linear dynamic progressive collapse analysis, Engineering Structures, 55: 35–43, 2013, doi: 10.1016/j.engstruct.2012.05.042.
13. A. McKay, K. Marchand, M. Diaz, Alternate path method in progressive collapse analysis: variation of dynamic and nonlinear load increase factors, Practice Periodical on Structural Design and Construction, 17(4): 152–160, 2012, doi: 10.1061/(ASCE)SC.1943-5576.0000126.
14. M. Liu, A new dynamic increase factor for nonlinear static alternate path analysis of building frames against progressive collapse, Engineering Structures, 48: 666–673, 2013, doi: 10.1016/j.engstruct.2012.12.011.
15. J. Mashhadi, H. Saffari, Dynamic increase factor based on residual strength to assess progressive collapse, Steel and Composite Structures, 25(5): 617–624, 2017, doi: 10.12989/scs.2017.25.5.617.
16. O.A. Mohamed, Calculation of load increase factors for assessment of progressive collapse potential in framed steel structures, Case Studies in Structural Engineering, 3: 11–18, 2015, doi: 10.1016/j.csse.2015.01.001.
17. M. Ferraioli, Dynamic increase factor for nonlinear static analysis of RC frame buildings against progressive collapse, International Journal of Civil Engineering, 17(3): 281–303, 2019, doi: 10.1007/s40999-017-0253-0.
18. S.Yu. Fialko, Application of finite element method to analysis of strength and bearing capacity of thin-walled concrete structures, taking into account the physical nonlinearity [in Russian], ASV, SCAD Soft, Moscow, 2018.
19. CSI Analysis Reference Manual (last access 11.07.2024), Computers & Structures, Inc., Berkeley, CA, USA, https://docs.csiamerica.com/manuals/sap2000/CSiRefer.pdf.
20. E.L. Wilson, Three-Dimensional Static and Dynamic Analysis of Structures, 3rd ed., Computers and Structures, Inc., Berkeley, CA, USA, 2002.
21. G.A. Geniev, V.N. Kissyuk, G.A. Tyupin, The Theory of Plasticity of Concrete and Reinforced Concrete [in Russian], Stroyizdat, Moscow, 1974.
22. M.A. Criesfield, Non-linear Finite Element Analysis for Solids and Structures, Vol. 1, Essentials, John Wiley & Sons, Chichester, New York, 2000.
23. S. Fialko, Quadrilateral finite element for analysis of reinforced concrete floor slabs and foundation plates, Applied Mechanics and Materials, 725–726: 820–835, 2015, doi: 10.4028/www.scientific.net/AMM.725-726.820.
24. S.Yu. Fialko, Dynamic analysis of the elasto-plastic behaviour of buildings and structures in the SCAD++ software package, Journal of Physics: Conference Series, 1425: 012041, 2019, doi: 10.1088/1742-6596/1425/1/012041.
25. K.J. Bathe, Finite Element Procedures, Prentice Hall, New Jersey, 1996.
26. K.U. Bletzinger, M. Bischoff, E. Ramm, A unified approach for shear-locking-free triangular and rectangular shell finite elements, Computers & Structures, 75: 321–334, 2000, doi: 10.1016/S0045-7949(99)00140-6.
27. IntelMKL Resource & Documentation Center (last access 22.01.2023), https://www.intel.com/content/www/us/en/develop/documentation/onemkldeveloper-reference-c/top.html.
28. T.J.R. Hughes, T. Belytschko, Nonlinear finite element analysis, Course Notes, September 4–8, Munich, Germany, 1995.
29. I. Miranda, R.M. Ferencz, T.J.R. Hughes, An improved implicit-explicit time integration method for structural dynamics, Earthquake Engineering and Structural Dynamics, 18: 643–653, 1089, doi: 10.1002/eqe.4290180505.
30. S. Fialko, Parallel finite element solver for multi-core computers with shared memory, Computers and Mathematics with Applications, 94: 1–14, 2021, doi: 10.1016/j.camwa.2021.04.013.
31. S. Fialko, Parallel algorithms for forward and back substitution in linear algebraic equations of finite element method, Journal of Telecommunications and Information Technology, 4: 20–29, 2019, doi: 10.26636/jtit.2019.134919.
32. S.Yu. Fialko, V.S. Karpilowskyi, Triangular and quadrilateral flat shell finite elements for nonlinear analysis of thin-walled reinforced concrete structures in SCAD software, [in:] W. Pietraszkiewicz, W. Witkowski [Eds.], Shell Structures: Theory and Applications, Vol. 4, pp. 367–370, CRC Press Taylor & Francis Group, London, New York, 2017, doi: 10.1201/9781315166605-83.
33. S. Fialko, V. Karpilovskyi, Spatial thin-walled reinforced concrete structures taking into account physical nonlinearity in SCAD software. Rod finite element, [in:] 13th International Conference Modern Building Materials, Structures and Techniques, May 16–17, pp. 728–735, Vilnius Gediminas Technical University, 2019, doi: 10.3846/mbmst.2019.086.
34. A.V. Savchenko, A.V. Ioskevich, L.F. Khazieva, A.A. Nesterov, V.V. Ioskevich, Solution of the longitudinal and transverse bending beam in different software package, Construction of Unique Buildings and Structures, 38(11): 89–105, 2015, doi: 10.18720/CUBS.38.7.
35. A.S. Vol’mir, Stability in Deformable Systems [in Russian], Fizmatgiz, Moscow, 1967.
36. J. Nemecek, P. Padevet, B. Patzák, Z. Bittnar, Effect of transversal reinforcement in normal and high strength concrete columns, Materials and Structures, 38(7): 665–671, 2005, doi: 10.1007/BF02484311.
37. J.M. Adam, M. Buitrago, E. Bertolesi, J. Sagaseta, J.J. Moragues, Dynamic performance of a real-scale reinforced concrete building test under a corner-column failure scenario, Engineering Structures, 210: 104414, 2020, doi: 10.1016/j.engstruct.2020.110414.
38. A.V. Perelmuter, V.I. Slivker, Numerical Structural Analysis, Springer, Berlin, Heidelberg, 2003, doi: 10.1007/978-3-540-36500-6.
39. S.Yu. Fialko, Application of rigid links in structural design models, International Journal for Computational Civil and Structural Engineering, 13(3): 119–137, 2017, doi: 10.22337/1524-5845-2017-13-3-119-137.
40. S.Yu. Fialko, O.V. Kabantsev, A.V. Perelmuter, Elasto-plastic progressive collapse analysis based on the integration of the equations of motion, Magazine of Civil Engineering, 102(2): 10214, 2021, doi: 10.34910/MCE.102.14.
41. O.A. Mohamed, O. Najm, Outrigger systems to mitigate disproportionate collapse in building structures, Procedia Engineering, 161: 839–844, 2016, doi: 10.1016/j.proeng.2016.08.725.
42. M. Ferraioli, A. Lavino, A. Mandara, Progressive collapse assessment and retrofit of a multistory steel braced office building, International Journal of Steel Structures, 22(4): 1086–1107, 2022, doi: 10.1007/s13296-022-00626-x.
43. F. Freddi, L. Ciman, N. Tondini, Retrofit of existing steel structures against progressive collapse through roof-truss, Journal of Constructional Steel Research, 188: 107037, 2022, doi: 10.1016/j.jcsr.2021.107037.
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