Insight Into Feasibility of Structure-Dependent Methods for Dynamic Analysis
DOI:
https://doi.org/10.13052/ejcm2642-2085.31561Keywords:
An eigen-based theory, low frequency modes, high frequency modes, eigen-dependent method, structure-dependent methodAbstract
The first family of structure-dependent integration methods have been successfully developed for nonlinear dynamic analysis. Although its numerical properties were evaluated and its performance was numerically corroborated for both linear and nonlinear systems, its feasibility is still under debate due to the lack of a theoretical background. It seems that an eigen-based theory can provide a fundamental basis for the proof of the feasibility of structure-dependent integration methods. This can be manifested from each major stage of the development of structure-dependent integration methods. Therefore, the development of the first family of structure-dependent integration methods will be presented and the correlation between each major stage and an eigen-based theory will be explored and explained. Besides, this developing sequence can lay a typical procedure for developing a general structure-dependent integration method.
Downloads
References
Chang, S.Y. (2002), “Explicit pseudodynamic algorithm with unconditional stability”, Journal of Engineering Mechanics, ASCE, 128 (9), 935–947. https://doi.org/10.1061/(ASCE)0733-9399(2002)128:9(935).
Chang, S.Y. (2009), “An explicit method with improved stability property”, International Journal for Numerical Method in Engineering, 77 (8), 1100–1120. https://doi.org/10.1002/nme.2452.
Chang, S.Y. (2010), “A new family of explicit method for linear structural dynamics”, Computers & Structures, 88 (11–12), 755–772. https://doi.org/10.1016/j.compstruc.2010.03.002.
Chang, S.Y. (2015), “Dissipative, non-iterative integration algorithms with unconditional stability for mildly nonlinear structural dynamics”, Nonlinear Dynamics, 79 (2), 1625–1649. https://doi.org/10.1007/s11071-014-1765-7.
Chang, S.Y. (2019) “A dual family of dissipative structure-dependent integration methods”, Nonlinear Dynamics, 98(1), 703–734. https://doi.org/10.1007/s11071-019-05223-y.
Chang, S.Y. (2020) “Non-iterative methods for dynamic analysis of nonlinear velocity-dependent problems.” Nonlinear Dynamics, 101, 1473–1500. https://doi.org/10.1007/s11071-020-05836-8.
Newmark, N.M. (1959), “A method of computation for structural dynamics”, Journal of Engineering Mechanics Division, 85 (3), 67–94.
Hilber, H.M., Hughes, T.J.R., Taylor, R.L. (1977), “Improved numerical dissipation for time integration algorithms in structural dynamics”, Earthquake Engineering and Structural Dynamics, 5, 283–292. https://doi.org/10.1002/eqe.4290050306.
Wood, W.L., Bossak, M., Zienkiewicz, O.C. An alpha modification of Newmark’s method. International Journal for Numerical Methods in Engineering 15 (1981) 1562–1566. https://doi.org/10.1002/nme.1620151011.
Chung, J., Hulbert, G.M. A time integration algorithm for structural dynamics with improved numerical dissipation: the generalized-α
method. Journal of Applied Mechanics 60(6) (1993) 371–375. https://doi.org/10.1115/1.2900803.
Noels, L., Stainier, L., Ponthot, J.P., Bonini, J. Combined implicit-explicit algorithms for non-linear structural dynamics, European Journal of Computational Mechanics 11(5) (2002) 565–591. https://journals.riverpublishers.com/index.php/EJCM/article/view/2551.
Papathanasiou, T.K. A Linearised θ
Numerical Scheme for the Vibrations of Inextensible Beams. European Journal of Computational Mechanics 30(1) (2021) 121–144. https://doi.org/10.13052/ejcm1779-7179.3015.
Zhou, X, Tamma, K.K. (2004), “Design, analysis, and synthesis of generalized single step single solve and optimal algorithms for structural dynamics.” International Journal for Numerical Methods in Engineering, 59, 597–668. https://doi.org/10.1002/nme.873.
Krenk, S. (2006), “Energy conservation in Newmark based time integration algorithms”, Computer Methods in Applied Mechanics and Engineering, 195, 6110–6124. https://doi.org/10.1016/j.cma.2005.12.001.
Tang, Y., Ren, D., Qin, H., Luo, C. (2021), “New family of explicit structure-dependent integration algorithms with controllable numerical dispersion”, Journal of Engineering Mechanics, 147(3), 04021001. http://10.1061/(ASCE)EM.1943-7889.0001901.
Li, J., Yu, K., Li, X. (2018), “A generalized structure-dependent semi-explicit method for Structural dynamics”, ASME. Journal of Computational and Nonlinear Dynamics, 13(11), 111008. https://doi.org/10.1115/1.4041239.
Chang, S.Y. An explicit structure-dependent algorithm for pseudo-dynamic testing, Engineering Structures, 46 (2013) 511–525. http://dx.doi.org/10.1016%2Fj.engstruct.2012.08.009.
Namadchi, A.H., Jandaghi, E., Alamatian, J. (2020) “A new model-dependent time integration scheme with effective numerical damping for dynamic analysis”, Engineering with Computers, 37(4) 2543–2558. https://doi.org/10.1007/s00366-020-00960-w.
Qing, L.C., Zhong, J.L. (2018) “Unconditionally stable explicit displacement method for analyzing nonlinear structural dynamics problems”, Journal of Engineering Mechanics, 144(9), 04018079. https://doi.org/10.1061/(ASCE)EM.1943-7889.0001454.
Dahlquist, G. Convergence and stability in the numerical integration of ordinary differential equations, Mathematica Scandinavica 4 (1956) 33–53. https://doi.org/10.7146/math.scand.a-10454.
Clough, R.W., Penzien, J., Dynamics of Structures, 2nd Edition, McGraw-Hill, 1993. https://doi.org/10.12989/sem.2012.43.1.001.
Belytschko, T. and Hughes, T.J.R. (1983), Computational Methods for Transient Analysis, Elsevier Science Publishers B.V., North-Holland, Amsterdam.
Chang, S.Y. An unusual amplitude growth property and its remedy for structure-dependent integration methods, Computer Methods in Applied Mechanics and Engineering, 330 (2018) 498–521. https://doi.org/10.1016/j.cma.2017.11.012.
Lax, P.D., Richtmyer, R.D. (1956), “Survey of the stability of linear finite difference equations”, Communications on Pure and Applied Mathematics, 9, 267–293. https://doi.org/10.1002/cpa.3160090206.
Dahlquist, G. (1963), “A special stability problem for linear multistep methods”, BIT, 3, 27–43. https://doi.org/10.1007/BF01963532.
Chang, S.Y. (2018) “Weak instability of CR explicit method for structural dynamics,” Journal of Computational and Nonlinear Dynamics, 13(5), 054501 https://doi.org/10.1115/1.4039379.
Strang, G. (2020), Linear Algebra and Its Applications, 4th Editions, Cengage Learning, Inc.
Oua, J.P., Long, X., Li, Q.S. (2007), “Seismic response analysis of structures with velocity-dependent dampers. Journal of Constructional Steel Research, 63, 628–638. https://doi.org/10.1016/j.jcsr.2006.06.034.
Sadek, F., Mohraz, B., Riley, M.A. (2000), “Linear procedures for structures with velocity-dependent dampers”, Journal of Structural Engineering, 126(8), 887–895. https://doi.Org/10.1061/(ASCE)0733-9445(2000)126:8(887).
Building Seismic Safety Council (BSSC). NEHRP guidelines for the seismic rehabilitation of buildings. FEMA 273, 1997, Washington, D.C.
