A high-precision numerical time step integration method is proposed for a linear time-invariant structural dynamic system. Its numerical results are almost identical to the precise solution and are almost independent of the time step size for a wide range of step sizes. Numerical examples illustrate this high precision.
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References
1.
ZienkiewiczO. C.The finite element method. 1977 (McGraw-Hill, London).
2.
BatheK. J.WilsonE. L.Numerical methods in finite element analysis, 1976 (Prentice-Hall, Engelwood Cliffs, N. J.).
3.
SubbarajK.DokainishM. A.A survey of direct time integration methods in computational structural dynamics: I. Explicit methods; II. Implicit methods. Computers and Structs, 1989, 32, 1371–1386, 1387–1401.
4.
ZhongW. X.ZhongX. X.Computational structural mechanics, optimal control and semi-analytical method for PDE. Computers and Structs, 1990, 37, 993–1004.
5.
ZhongW. X.LinJ. H.QiuC. H.Computational structural mechanics and optimal control. Int. J. Numer. Meth. Engng, 1992, 33, 197–211.
6.
ZhongW. X.ZhongX. X.Elliptic partial differential equation and optimal control. Numer. Meth. for PDE, 1992, 8, 149–169.
7.
ZhongW. X.LinJ. H.ZhuJ. P.State vector method and symplectic eigensolutions of gyroscopic systems Asia-Pacific Conference on Computational Mechanics, Sydney, 3–6 August1993 In Computational mechanics (Ed. Valliappan), 1993, pp. 19–28 (Balkema, Rotterdam, The Netherlands).
8.
ZhongW. X.YangZ. S.On the computation of main eigenpairs of continuous-time linear quadratic control problem. Appl. Math. Mech., 1991, 12, 45–50.
9.
PeaseM. C.Methods of matrix algebra, 1965 (Academic Press, New York).
10.
PressW. H.TeukolskyS. A.VetterlingW. T.FlanneryB. P.Numerical recipes, 1992 (Cambridge University Press).
11.
LaubA. J.Numerical linear algebra aspect of control design computations. IEEE Trans. Automat. Control, 1985, AC-30, 97–108.
