Examination of Two Distinct Integration Techniques Used in Pseudo-Dynamic Test Method by Means of Experimental and Numerical Studies

Öz

Experimental techniques are of great importance in determination of earthquake behavior of structures and structural members. Structural behavior could be determined by means of quasi-static tests in which prescribed displacement protocols are applied, by real time shake table tests realized with real acceleration records or by pseudo-dynamic tests in which experimental and numerical simulation efforts work together. In pseudo-dynamic test, the reactional forces measured from test specimen (stiffness matrix) are utilized for the numerical solution of dynamic equilibrium equation and for the determination of target displacement vector to be applied to test specimen in the next step. In pseudo-dynamic test method, the through interaction of the analytical and experimental parts is very effective on the success. For the success of the test; in addition to the sensitivity of the measuring devices used, the stability of the numerical integration technique to be used in the solution of the dynamic equilibrium equation is also of great importance. In order to ensure the stability of the numerical integration, the selected time interval should be small enough. In this study, the central difference method (CDM) and linear acceleration-based force separation method (Li-OSM) used as a numerical integration tool in pseudo-dynamic test method are compared with numerical and experimental studies. The performed numerical studies; regardless of the constitutive model used, showed that Li-OSM method produces more stable results than CDM method in the case of the integration step interval selected up to half of the earthquake record interval. From the experimental studies; instead of using “quarter” integration step interval in CDM method, it was concluded that in case of using “half” integration step interval in Li-OSM method, the total testing time will decrease by half and the stability of the test will increase.

Anahtar Kelimeler

• Pseudo-dynamic test method
• Central difference method
• Linear acceleration-based operator splitting method
• Dynamic equilibrium equation
• Numerical integration

Benzeşik Dinamik Deney Tekniğinde Kullanılan iki Farklı İntegrasyon Tekniğinin Deneysel ve Sayısal Çalışmalar ile İrdelenmesi

Öz

Yapı sistemlerinin ve yapı elemanlarının deprem etkisindeki davranışlarının belirlenmesinde, deneysel yöntemler çok önemlidir. Yapısal davranış; öngörülen bir yerdeğiştirme protokolü etkisinde gerçekleştirilen statik karakterli deneyler ile ivme kayıtlarının kullanılabildiği gerçek zamandaki sarsma masası deneyleri ile ya da analitik çözümlerin etkileşimli olarak gerçekleştirildiği statik karakterli benzeşik dinamik deneyler ile belirlenebilmektedir. Benzeşik dinamik deneyde, numuneden ölçülen reaksiyon kuvvetleri (rijitlik matrisi) dinamik denge denkleminin çözümünde ve bir sonraki deney adımında numuneye etkitilecek hedef yerdeğiştirme vektörünün hesabında kullanılmaktadır. Benzeşik dinamik deney tekniğinde, analitik ve deneysel bölümlerin doğru etkileşimi deneyin başarısı üzerinde çok etkilidir. Deneyin başarısı için; kullanılan ölçüm cihazlarının hassasiyeti yanında dinamik denge denkleminin çözümünde kullanılacak sayısal integrasyon yönteminin kararlılığı da büyük önem taşımaktadır. Sayısal hesapta kararlılık sağlanabilmesi için, integrasyon için seçilen hesap adım aralığının yeterli düzeyde küçük olması gerekmektedir. Bu çalışmada, benzeşik dinamik deney metodunda sayısal integrasyon aracı olarak kullanılan merkezi farklar yöntemi (CDM) ile lineer ivme tabanlı kuvvet ayırımı yöntemi (Li-OSM) sayısal ve deneysel çalışmalar ile karşılaştırılmıştır. Gerçekleştirilen sayısal çalışmalar; davranış modelinden bağımsız olarak, deprem kaydı adım aralığının yarısı kadar seçilen hesap adım aralığı durumunda, Li-OSM yönteminin CDM yöntemine göre daha kararlı sonuçlar ürettiğini göstermiştir. Deneysel çalışmalardan; CDM yönteminde “dörtte birlik” hesap adım aralığı ile çalışmak yerine, Li-OSM yönteminde “yarım” hesap adım aralığının kullanımı durumunda, toplam deney süresinin yarıya düşeceği ve deneyin kararlılığının artacağı sonucuna ulaşılmıştır.

Anahtar Kelimeler

• Benzeşik dinamik deney tekniği
• Merkezi farklar yöntemi
• Lineer ivme yöntemi tabanlı kuvvet ayırımı metodu
• Dinamik denge denklemi
• Sayısal integrasyon

Kaynakça

1. [1] Hakuno M, Shidawara M, Hara T. 1969. Dynamic destructive test of a cantilever beam controlled by an analog-computer, Transactions of Japan Society of Civil Engineers, Cilt. 171, s. 1-9.
2. [2] Takanashi K. 1975. Non-linear earthquake response analysis of structures by a computer actuator on-line system, Transactions of the Architectural Institute of Japan, Cilt. 229, s. 77-83.
3. [3] Okada T, Takanashi K, Seki M, Taniguchi H. 1980. Nonlinear earthquake response of system anchored on RC building floor, Bulletin of Earthquake Resistant Structure Research Center, Cilt. 13, s. 63-85.
4. [4] Okada T, Matsutaro Seki M, Park Y.J. 1980. A simulation of Earthquake Response of Reinforced Concrete Building Frames to bi-directional Ground Motion by IIS Computer Actuator On-line System, Seventh World Conference on Earthquake Engineering, 9-13 September, Istanbul, Turkey.
5. [5] Balendra T, Lam K, Liaw C, Lee S. 1987. Behavior of eccentrically braced frame by pseudo-dynamic tests, Journal of Structural Engineering, ASCE, Cilt. 113(4), s. 673-688.
6. [6] Peek R, Yi W. 1990. Error analysis for pseudo dynamic test method: 1.Analysis, Journal of Engineering Mechanics ASCE, Cilt. 116(7), s. 1618-1637.
7. [7] Peek R, Yi W. 1990. Error analysis for pseudo dynamic test Method: 2.Application, Journal of Engineering Mechanics, ASCE, Cilt. 116(7), s. 1638-1658.
8. [8] Shing P.B, Mahin S.A. 1987. Cumulative experimental errors in pseudo dynamic tests, Earthquake Engineering and Structural Dynamics, Cilt. 15(4), s. 409-424.

9. [9] Nakashima M. 1983. Stability and accuracy of integration techniques in pseudo dynamic testing”. Building Research Institute, Ministry of Construction, Japan, Technical Report, 105.
10. [10] Shing P.B, Mahin, S.A. 1985. Computational aspect of a seismic performance test method using on-line computer control, Earthquake Engineering and Structural Dynamics, Cilt. 13(4), s. 507-526.
11. [11] Shing P.S.B, Manivannan T. 1990. On the accuracy of an Implicit algorithm for pseudo dynamic tests, Earthquake Engineering and Structural Dynamics, Cilt. 19(5), s. 631-651
12. [12] Kabayama K, Toyoshima M, Kumazawa F, Nakano Y, Okada T. 1993. On-line tests of frame structures, Bulletin of Earthquake Resistant Structure Research Center, Cilt. 26, s. 75-82.
13. [13] Paguette J, Bruneau M. 2000. Pseudo-dynamic testing of unreinforced masonry buildings with flexible diaphragm, 12WCEE 2000 12th World Conference on Earthquake Engineering, 30 January-4 February, Auckland, New Zeland.
14. [14] Nakajima K, Iemura H, Takahashi Y, Ogawa K. 2000. Pseudo dynamic tests and implementation of sliding bridge isolators with vertical motion, 12WCEE 2000 12th World Conference on Earthquake Engineering, 30 January-4 February, Auckland, New Zeland.
15. [15] Pinto A, Pegon P, Magonette G, Molina J, Buchet P, Tsionis G. 2002. Pseudodynamic tests on a large-scale model of an existing RC bridge using non-linear substructuring and asynchronous motion”. Institute for the Protection and Security of the Citizen Eurpean Laboratory for Structural Assesment (ELSA), Report, EUR 20525 EN.
16. [16] Yuksel E, Ozkaynak H, Surmeli M. 2011. Benzeşik dinamik deney tekniği ve bir uygulama, İnşaat Mühendisleri Odası Teknik Dergi, Cilt. 352, s. 5463-5469.
17. [17] Yuksel E, Ozkaynak H, Surmeli M. 2009. Benzeşik dinamik deney tekniği ve bir uygulaması, Sigma Mühendislik ve Fen Bilimleri Dergisi, Cilt. 27(4), s. 286-302.
18. [18] Ozkaynak H, Yuksel E, Güney A.K. 2014. Evaluation of integration techniques used in pseudo dynamic testing methodology. EURODYN 2014 9th European Conference on Structural Dynamics, 30 June–2 July Porto, Portugal.
19. [19] Mercan O. 2003. Evaluation of real-time pseudodynamic testing algorithms for seismic testing of structural assemblages. MSc Thesis, Lehigh University, Pennsylvania, USA.
20. [20] Dermitzakis SN, Mahin SA. 1985. Development of substructuring techniques for on-line computer controlled seismic performance testing, Earthquake Engineering Research Center, University of California, Berkeley, USA, Report UCB/EERC-85/04.
21. [21] Nakashima M, Kaminoso T, Ishida M, Ando K. 1990. Integration techniques for substructuring pseudodynamic test, 4th US National Conference on Earthquake Engineering, 20-24 May, California, USA.
22. [22] Vannan MT. 1991. The pseudodynamic test method with substructuring application. PhD Thesis, College of Engineering and Applied Sciences, University of Calorado Boulder, Colorado, USA,
23. [23] Buchet P, Pegon P. 1994. PSD testing with substructuring: implementation and use, JRC Special Publication, Cilt. I.94 (25), s. 1-21.
24. [24] Chung-Chan Hung, Wei-Ming Yen, Wei-Ting Lu 2012. An unconditionally stable algorithm with the capability of restraining the influence of actuator control errors in hybrid simulation, Engineering Structures, Cilt. 42, s. 168–178.
25. [25] Öztürk S, Doran B, Aksoylar C. 2017. An Analytical and Experimental Study of Time Integration Methods in Pseudo Dynamic Analysis. Digital Proceeding of ICOCEE–CAPPADOCIA 2017, 8-10 May Nevşehir, Turkey.
26. [26] Jiang C. X., Zhu T.S. 2014. Stability Analysis Research of Modified CD-Newmark Numerical Integral Method in Seismic Pseudo-dynamic Test, Applied Mechanics and Materials, Cilt. 638-640, s. 1869-1872.
27. [27] Ammanagi S., Manohar C. S. 2016. Adaptive time stepping in pseudo-dynamic testing of earthquake driven structures, Bulletin of Earthquake Engineering, Cilt. 14, s. 3047–3074.
28. [28] Baiping Dong, Richard Sause and James M. Ricles. 2015. Accurate real-time hybrid earthquake simulations on large-scale MDOF steel structure with nonlinear viscous dampers, Earthquake Engineering and Structural Dynamics, Cilt. 44, s. 2035–2055,.
29. [29] Mohit Verma, J. Rajasankar and Nagesh R. Iyer 2015. Numerical assessment of step-by-step integration methods in the paradigm of real-time hybrid testing, Earthquakes and Structures, Cilt. 8(6), s. 1325-1348.
30. [30] D.P. McCrum, M.S. Williams 2016. An overview of seismic hybrid testing of engineering structures, Engineering Structures, Cilt. 118, s. 240–261.
31. [31] E. E. Bas & M. A. Moustafa 2020. Performance and Limitations of Real-Time Hybrid Simulation with Nonlinear Computational Substructures, Experimental Techniques, Cilt. 44, s. 715–734.
32. [32] Clough R.W, Penzien J. 1975. Dynamics of Structures. New York, USA, McGraw-Hill, 752s.
33. [33] Paz. M. 1991. Structural Dynamics Theory and Computation. 3rd ed. New York, USA, Van Nostrand Reinhold, 621s.
34. [34] Dokainish M.A, Subbaraj K. 1989. A survey of direct time-integration methods in computational structural dynamics-I. Explicit methods, Computers & Structures, Cilt. 32(6), s. 1371-1386.
35. [35] Dokainish M.A, Subbaraj K. 1989. A survey of direct time-integration methods in computational structural dynamics-II. implicit methods, Computers & Structures, Cilt. 32(6), s. 1387-1401
36. [36] McCrum D.P, Williams M.S. 2016. An overview of seismic hybrid testing of engineering structures, Engineering Structures, Cilt. 118, s. 240-261.
37. [37] Zhang Y, Sause R, Ricles JM, Naito CJ. 2005. Modified predictor–corrector numerical scheme for real-time pseudo dynamic tests using state-space formulation, Earthquake Engineering & Structural Dynamics, Cilt. 34(3), s. 271-288.
38. [38] Hughes TJR, Pister KS, Taylor RL. 1979. Implicit-explicit finite elements in nonlinear transient analysis, Computer Methods in Applied Mechanics and Engineering, Cilt. 17/18(1), s. 159-182.
39. [39] Combescure D, Pegon P. 1997. α-Operator splitting time integration technique for pseudo dynamic testing error propagation analysis, Soil Dynamics and Earthquake Engineering, Cilt. 16(7-8), s. 427-443.
40. [40] Bonelli A, Bursi OS. 2005. Predictor-corrector procedures for pseudo-dynamic tests, International Journal for Computer-aided Engineering and Software, Cilt. 22(7), s. 783-834.
41. [41] Chung J, Hulbert GM. 1993. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-alpha method, Journal of Applied Mechanics, Cilt. 60, s. 371-375.
42. [42] Wu B, Xu G, Wang Q, Williams MS. 2006. Operator-splitting method for real-time substructure testing, Earthquake Engineering & Structural Dynamics, Cilt. 35(3), s. 293-314.
43. [43] Hung C-C, Yen W-M, Lu W-T. 2010. An unconditionally stable algorithm with the capability of restraining the influence of actuator control errors in hybrid simulation, Engineering Structures, Cilt. 42, s. 168-178.
44. [44] MATLAB and Statistics Toolbox Release 2012b, The MathWorks, Inc., Natick, Massachusetts, United States. https://www.mathworks.com/products/matlab.html (Erişim Tarihi: 04.05.2012).
45. [45] Güney A.K. 2011. Benzeşik dinamik deney yönteminde integrasyon metodunun etkisi. İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü Yüksek Lisans Tezi, 105s, İstanbul.