Browse > Article
http://dx.doi.org/10.12989/eas.2018.14.1.045

A remedy for a family of dissipative, non-iterative structure-dependent integration methods  

Chang, Shuenn-Yih (Department of Civil Engineering, National Taipei University of Technology)
Wu, Tsui-Huang (Department of Civil Engineering, National Taipei University of Technology)
Publication Information
Earthquakes and Structures / v.14, no.1, 2018 , pp. 45-53 More about this Journal
Abstract
A family of the structure-dependent methods seems very promising for time integration since it can simultaneously have desired numerical properties, such as unconditional stability, second-order accuracy, explicit formulation and numerical dissipation. However, an unusual overshoot, which is essentially different from that found by Goudreau and Taylor in the transient response, has been experienced in the steady-state response of a high frequency mode. The root cause of this unusual overshoot is analytically explored and then a remedy is successfully developed to eliminate it. As a result, an improved formulation of this family method can be achieved.
Keywords
overshooting; steady-state response; local truncation error; structure-dependent integration method;
Citations & Related Records
Times Cited By KSCI : 9  (Citation Analysis)
연도 인용수 순위
1 Wood, W.L., Bossak, M. and Zienkiewicz, O.C. (1981), "An alpha modification of Newmark's method", Int. J. Numer. Meth. Eng., 15, 1562-1566.
2 Bathe, K.J. and Wilson, E.L. (1973), "Stability and accuracy analysis of direct integration methods", Earthq. Eng. Struct. Dyn., 1, 283-291.
3 Bayat, M., Bayat, M. and Pakar, I. (2015), "Analytical study of nonlinear vibration of oscillators with damping", Earthq. Struct., 9(1), 221-232.   DOI
4 Belytschko, T. and Hughes, T.J.R. (1983), Computational Methods for Transient Analysis, Elsevier Science Publishers B.V., North-Holland.
5 Chang, S.Y. (2002), "Explicit pseudodynamic algorithm with unconditional stability", J. Eng. Mech., ASCE, 128(9), 935-947.   DOI
6 Chang, S.Y. (2006), "Accurate representation of external force in time history analysis", J. Eng. Mech., ASCE, 132(1), 34-45.   DOI
7 Chang, S.Y. (2009), "An explicit method with improved stability property", Int. J. Numer. Meth. Eng., 77(8), 1100-1120.   DOI
8 Chang, S.Y. (2010), "A new family of explicit method for linear structural dynamics", Comput. Struct., 88(11-12), 755-772.   DOI
9 Chang, S.Y. (2014b), "Numerical dissipation for explicit, unconditionally stable time integration methods", Earthq. Struct., 7(2), 157-176.
10 Chang, S.Y. (2014a), "A family of non-iterative integration methods with desired numerical dissipation", Int. J. Numer. Meth. Eng., 100(1), 62-86.   DOI
11 Chang, S.Y. (2015), "Dissipative, non-iterative integration algorithms with unconditional stability for mildly nonlinear structural dynamics", Nonlin. Dyn., 79(2), 1625-1649.   DOI
12 Chang, S.Y. (2016), "A virtual parameter to improve stability properties for an integration method", Earthq. Struct., 11(2), 297-313.   DOI
13 Chang, S.Y., Wu, T.H. and Tran, N.C. (2015), "A family of dissipative structure-dependent integration methods", Struct. Eng. Mech., 55(4), 815-837.   DOI
14 Chung, J. and Hulbert, G.M. (1993), "A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-${\alpha}$ method", J. Appl. Mech., 60(6), 371-375.   DOI
15 Fattah, M.Y., Hamoo, M.J. and Dawood, S.H. (2015), "Dynamic response of a lined tunnel with transmitting boundaries", Earthq. Struct., 8(1), 275-304.   DOI
16 Gao, Q., Wu, F., Zhang, H.W., Zhong, W.X., Howson, W.P. and Williams, F.W. (2012), "A fast precise integration method for structural dynamics problems", Struct. Eng. Mech., 43(1), 1-13.   DOI
17 Goudreau, G.L. and Taylor, R.L. (1972), "Evaluation of numerical integration methods in elasto- dynamics", Comput. Meth. Appl. Mech. Eng., 2, 69-97.
18 Hilber, H.M. and Hughes, T.J.R. (1978), "Collocation, dissipation, and 'overshoot' for time integration schemes in structural dynamics", Earthq. Eng. Struct. Dyn., 6, 99-118.   DOI
19 Kaveh, A., Aghakouchak, A.A. and Zakian, P. (2015), "Reduced record method for efficient time history dynamic analysis and optimal design", Earthq. Struct., 8(3), 639-663.   DOI
20 Hilber, H.M., Hughes, T.J.R. and Taylor, R.L. (1977), "Improved numerical dissipation for time integration algorithms in structural dynamics", Earthq. Eng. Struct. Dyn., 5, 283-292.   DOI
21 Rezaiee-Pajand, M. and Alamatian, J. (2008), "Implicit higherorder accuracy method for numerical integration in dynamic analysis", J. Struct. Eng., 134 (6), 973-985.   DOI
22 Rezaiee-Pajand, M. and Karimi-Rad, M. (2017), "A family of second-order fully explicit time integration schemes", Comput. Appl. Math., 1-24.
23 Rezaiee-Pajand, M., Sarafrazi, S.R. and Hashemian, M. (2011), "Improving stability domains of the implicit higher order accuracy method", Int. J. Numer. Meth. Eng., 88 (9), 880-896.   DOI
24 Rezaiee-Pajanda, M. and Hashemian, M. (2016), "Time integration method based on discrete transfer function", Int. J. Struct. Stab. Dyn., 16(5), 1550009.   DOI
25 Rezaiee-Pajanda, M., Hashemian, M. and Bohlulyb, A. (2017), "A novel time integration formulation for nonlinear dynamic analysis", Aerosp. Sci. Technol., 69, 625-635.   DOI
26 Romero, A., Galvin, P. and Dominguez, J. (2012) "A time domain analysis of train induced vibrations", Earthq. Struct., 3(3), 297-313.   DOI
27 Su, C., Huang, H., Ma, H. and Xu, R. (2014), "Efficient MCS for random vibration of hysteretic systems by an explicit iteration approach", Earthq. Struct., 7(2), 119-139.   DOI
28 Verma, M., Rajasankar, J. and Iyer, N.R. (2015), "Numerical assessment of step-by-step integration methods in the paradigm of real-time hybrid testing", Earthq. Struct., 8(6), 1325-1348.   DOI