A structure-dependent integration method may experience an unusual overshooting behavior in the steady-state response of a high frequency mode. In order to explore this unusual overshooting behavior, a local truncation error is established from a forced vibration response rather than a free vibration response. As a result, this local truncation error can reveal the root cause of the inaccurate integration of the steady-state response of a high frequency mode. In addition, it generates a loading correction scheme to overcome this unusual overshooting behavior by means of the adjustment the difference equation for displacement. Apparently, these analytical results are applicable to a general structure-dependent integration method.
Issue Section:
Research Papers
References
1.
Chang
, S. Y.
, 2002
, “Explicit Pseudodynamic Algorithm With Unconditional Stability
,” ASCE J. Eng. Mech.
, 128
(9
), pp. 935
–947
.2.
Chang
, S. Y.
, 2007
, “Improved Explicit Method for Structural Dynamics
,” ASCE J. Eng. Mech.
, 133
(7
), pp. 748
–760
.3.
Chang
, S. Y.
, 2009
, “An Explicit Method With Improved Stability Property
,” Int. J. Numer. Methods Eng.
, 77
(8
), pp. 1100
–1120
.4.
Belytschko
, T.
, and Hughes
, T. J. R.
, 1983
, Computational Methods for Transient Analysis
, Elsevier Science Publishers B.V.
, Amsterdam, The Netherlands
.5.
Newmark
, N. M.
, 1959
, “A Method of Computation for Structural Dynamics
,” ASCE J. Eng. Mech. Div.
, 85
(3
), pp. 67
–94
.6.
Hilber
, H. M.
, Hughes
, T. J. R.
, and Taylor
, R. L.
, 1977
, “Improved Numerical Dissipation for Time Integration Algorithms in Structural Dynamics
,” Earthquake Eng. Struct. Dyn.
, 5
(3
), pp. 283
–292
.7.
Wood
, W. L.
, Bossak
, M.
, and Zienkiewicz
, O. C.
, 1981
, “An Alpha Modification of Newmark's Method
,” Int. J. Numer. Methods Eng.
, 15
(10
), pp. 1562
–1566
.8.
Chung
, J.
, and Hulbert
, G. M.
, 1993
, “A Time Integration Algorithm for Structural Dynamics With Improved Numerical Dissipation: The Generalized-α Method
,” ASME J. Appl. Mech.
, 60
(6
), pp. 371
–375
.9.
Chang
, S. Y.
, 2006
, “Accurate Representation of External Force in Time History Analysis
,” ASCE J. Eng. Mech.
, 132
(1
), pp. 34
–45
.10.
Hughes
, T. J. R.
, 1987
, The Finite Element Method
, Prentice-Hall
, Englewood Cliffs, NJ
.11.
Goudreau
, G. L.
, and Taylor
, R. L.
, 1972
, “Evaluation of Numerical Integration Methods in Elasto-Dynamics
,” Comput. Methods Appl. Mech. Eng.
, 2
(1
), pp. 69
–97
.Copyright © 2017 by ASME
You do not currently have access to this content.
